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Flemington-Raritan Regional School District Flemington, New Jersey
Mathematics Curriculum Grades 7-8
Gregory Nolan, Superintendent Daniel Bland, Assistant Superintendent Sandra Pollock, Mathematics Supervisor
Kristen Campbell Susan Hubert
Donna Jablonski Sherry Kodidek Melissa Neuman
Elizabeth Roll Jackie Schorr Jennifer Tobin
Council of Instruction Review Date: November 9, 2009 BOE Curriculum Committee Review Date: November 4, 2009 Board of Education Approval Date: December 7, 2009
Flemington-Raritan Regional Schools Mathematics Curriculum
Grades 7-8
Table of Contents
Mission Statement 1
Philosophy 2
2004 New Jersey Core Curriculum Content Standards 4
Program Description 5
Calculator Philosophy 7
Grade 7 Curriculum 9
7th Grade Interdisciplinary Connections 10
7th Grade Math Curriculum 18
7th Grade Algebra IA Curriculum 63
7th Grade Algebra IB Curriculum 107
Grade 8 Curriculum 147
8th Grade Interdisciplinary Connections 148
8th Grade Pre-Algebra Curriculum 156
8th Grade Algebra IB Curriculum 205
8th Grade Advanced Algebra Curriculum 247
8th Grade Algebra II Curriculum 292
Flemington-Raritan Regional Schools
Mathematics Curriculum
Grades 7-8
District Mission Statement
The Flemington-Raritan Regional School District, a caring and proactive district, in partnership with the community, will provide each student with:
• A sound educational foundation, • The guidance to strive for his/her full potential, and • The inspiration to become a lifelong learner and a responsible,
productive citizen in an ever-changing global society.
1
Flemington-Raritan Regional Schools
Mathematics Curriculum Grades 7-8
Philosophy
The Grades 7-8 Mathematics Curriculum is based on the belief that all students can learn mathematics. The mathematics program develops each child’s mathematical reasoning in understanding the big ideas (concepts) of mathematics. The program sets high benchmarks and expectations for students to effectively express mathematical content, process, and skills through verbal and written communication. The use of technological tools is a vital component of the program, not only to enhance the understanding of concepts, but an important tool used in the adult world to access and analyze real world data. In accordance with the above beliefs, the program includes a comprehensive range of content in a variety of contexts. The program integrates skills, concepts, and applications based on the 2004 New Jersey Core Curriculum Content Standards for Mathematics, providing each student the opportunity to become an active participant in his/her mathematical education. Students explore the beauty of mathematics with confidence, with the aim to become a generation of mathematically literate adults. The grades 7-8 mathematics program is built on developmentally appropriate practice for middle school students:
• All students can learn and understand mathematics; • Students construct their own meaning based on prior experience; • Learning occurs in social situations; • Learning is tied to contextual, real-world situations; • Learning involves numerous strategies involving higher order thinking
skills. Students continually reflect on the following question: “Does this make sense?”
2
Flemington-Raritan Regional Schools
Mathematics Curriculum Grades 7-8
The 21st Century Learning and Thinking Skills are an integral part of the 7-8 mathematics program including:
• Critical Thinking and Problem Solving Skills • Communication Skills • Creativity and Innovation Skills • Collaboration Skills • Information and Media Literacy Skills • Contextual Learning Skills
3
Flemington-Raritan Regional Schools
Mathematics Curriculum Grades 7-8
2004 New Jersey Core Curriculum Content Standards – Mathematics
The 2004 New Jersey Core Curriculum Content Standards contain Specific Cumulative Progress Indicators for each grade and the Mathematics Curriculum for grades 7 and 8 reflects the relevant cumulative progress indicators for grades 7, 8 and, where appropriate, grade 12. There are five standards altogether, each of which has a number of lettered strands. These standards and their associated strands, are enumerated below:
4.1 Number and Numerical Operations A. Number Sense B. Numerical Operations C. Estimation 4.2 Geometry and Measurement A. Geometric Properties B. Transforming Shapes C. Coordinate Geometry D. Units of Measure E. Measuring Geometric Objects 4.3 Patterns and Algebra A. Patterns B. Functions and Relationships C. Modeling D. Procedures 4.4 Data Analysis, Probability, and Discrete Mathematics A. Data Analysis (Statistics) B. Probability C. Discrete Mathematics -- Systematic Listing and Counting D. Discrete Mathematics -- Vertex-Edge Graphs and Algorithms 4.5 Mathematical Processes A. Problem Solving B. Communication C. Connections D. Reasoning E. Representation F. Technology
4
Flemington-Raritan Regional Schools
Mathematics Curriculum Grades 7-8
Program Description
The curriculum emphasizes a balance between hands-on, inquiry-based problem solving, and traditional mathematical computation and arithmetic. Teachers focus on making connections between facts and fostering new understanding in students, and tailor their teaching strategies to student responses, encouraging students to analyze, interpret, and predict information. Teachers also rely heavily on open-ended questions and promote extensive dialogue among students through cooperative learning strategies.
Assessments consist of teacher-created quizzes, tests, teacher observations, student responses, student projects, student daily work, district wide and state wide testing as well as the Hunterdon Central High School placement exams. In practice, assessment is ongoing and serves to provide feedback to students and to inform instruction. Teachers use a variety of assessment techniques, both quantitative and qualitative, to assess student development in the areas of mathematical conceptual understanding, mathematical procedures, and mathematical process. Multiple choice, short answer, and open-ended responses requiring written explanations are all components of the ongoing assessments in the classroom.
In grades 7 and 8, all students are grouped homogeneously by ability and achievement in mathematics. Various district wide tests, teacher recommendation, and student performance are considered when placing students for mathematics. Mathematics textbooks, support materials, and teacher instruction are modified according to the different needs of students in order for students to meet the New Jersey Core Curriculum Standards for each grade level. Continual assessment and reflection upon student work and achievement drives instruction. All student data, performance and achievement are constantly monitored in order to move students forward to their fullest mathematical potential. Placements procedures include not only student ability and achievement in concepts and computation, but also the ability to work independently at an accelerated pace.
5
Flemington-Raritan Regional Schools
Mathematics Curriculum
Grades 7-8
The following textbooks are used in grades 7 and 8 mathematics classes at J.P. Case Middle School:
Level Textbook Grade 7 7th Grade Math McDougal Littell Course 2 Holt Course 2 (Special Education) Algebra IA Discovering Algebra (first half) Algebra IB Discovering Algebra (second half) Grade 8 Pre-Algebra McDougal Littell Course 3 Holt Course 3 (Special Education) Algebra IB Discovering Algebra (second half) Advanced Algebra Discovering Advanced Algebra Algebra II McDougal Littell Algebra 2
6
Flemington-Raritan Regional Schools
Mathematics Curriculum Grades 7-8
Calculator Philosophy
The J.P. Case Middle School mathematics program believes that calculators are a vital component of the mathematics program. The following rationale from Texas Instruments covers many of the advantages of using calculators, as outlined by the NCTM and the 2004 New Jersey Core Curriculum Standards. Calculators are valuable educational tools that allow students to reach a higher level of mathematical power and understanding. By reducing the time that, in the past, was spent on performing tedious paper-and-pencil arithmetic and algebraic algorithms, calculator use today allows students and teachers to spend more time developing mathematical understanding, reasoning, number sense, and applications. They afford students learning tools that complement, but do not replace, mental and paper-and-pencil skills, and they expand students’ ability to solve problems by providing multiple solution techniques. Calculator technology allows students who would ordinarily be frustrated or bored by tedious manipulations to have access to the real mathematics itself, thus gaining a higher level of mathematical understanding, rather than giving up. The fact is, calculators are better tools to do some of the computations and manipulations that were once done with paper and pencil. In the past, paper and pencil were the only tools available. Appropriate use of technology and associated pedagogy will get more students thinking and reasoning mathematically. Thus more students will develop useful mathematical understanding and mathematical power. Despite all of their benefits and capabilities, calculators will never be able to replace the human mind when it comes to knowing how to read and understand a problem situation, writing an appropriate equation for the problem, choosing which operations to use to solve the problem, correctly interpreting the solution displayed on the calculator, and determining the appropriateness of the answer. Calculators are only as effective as the information students enter into them. Calculators, in conjunction with mental, paper-and-pencil, and estimation skills when appropriate, comprise the tools to help students work through the computations and manipulations necessary for solving problems. Calculators are like computer word processors to English students. Computer word processors do not “create” essays but they
7
do facilitate the creation of an essay. Calculators do not “understand” mathematics but they do facilitate the understanding of mathematics. Despite all of their capabilities, however, they will never replace the important, complex thought processes of which only humans are capable.
8
7th Grade Curriculum
9
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.1.A.2. Demonstrate a sense of the relative magnitudes
of numbers.
Science
Social Studies
Parts per Billion Lab
Population of the Middle Ages
4.1.A.3. Understand and use ratios, rates, proportions,
and percents (including percents greater than 100 and
less than 1) in a variety of situations.
Social Studies Junior Scholatic Magazines
4.1.B. 1. Use and explain procedures for performing
calculations with integers and all number types named
above with: Pencil-and-paper; Mental math; Calculator.
Science Labs throughout the year
4.1.C.1. Use equivalent representations of numbers such
as fractions, decimals, and percents to facilitate
estimation.
All Disciplines Discussions, labs all year long
4.2.A.2. Understand and apply the concept of similarity:
Using proportions to find missing measures; Scale
drawings; Models of 3D objects.
Art
Social Studies
Scale Drawings, Polygon Project
Reading a map, identifying landmarks on a
map
7th Grade Interdisciplinary Connections 10
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.2.B.1. Understand and apply transformations: Finding
the image, given the pre-image, and vice-versa; Finding
the image, given the pre-image, and vice-versa;
Sequence of transformations needed to map one figure
onto another; Reflections, rotations, and translations
result in images congruent to the pre-image; Dilations
(stretching/shrinking) result in images similar to the pre-
image.
Art Tessellations, Transformations
4.2.C.1. Use coordinates in four quadrants to represent
geometric concepts.
Social Studies Map Reading
4.2.D.1. Solve problems requiring calculations that
involve different units of measurement within a
measurement system (e.g., 4’3” plus 7’10” equals 12’1”).
Science
Social Studies
Art
Labs, Metric system use
Reading a scale on a map
Making a scale drawing
4.2.E.1. Develop and apply strategies for finding
perimeter and area: Geometric figures made by
combining triangles, rectangles and circles or parts of
circles; Estimation of area using grids of various sizes.
Social Studies iSearch, population density
7th Grade Interdisciplinary Connections 11
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.3.A.1. Recognize, describe, extend, and create patterns
involving whole numbers, rational numbers, and
integers: Descriptions using tables, verbal and symbolic
rules, graphs, simple equations or expressions; Finite
and infinite sequences; Arithmetic sequences (i.e.,
sequences generated by repeated addition of a fixed
number, positive or negative); Geometric sequences (i.e.,
sequences generated by repeated multiplication by a
fixed positive ratio, greater than 1 or less than 1).
Social Studies iSearch data gathering
4.3.C.1. Analyze functional relationships to explain how
a change in one quantity can result in a change in
another, using pictures, graphs, charts, and equations.
Science Volume and Density labs
Motion and Sound labs
4.3.C.2. Use patterns, relations, symbolic algebra, and
linear functions to model situations: Using
manipulatives, tables, graphs, verbal rules, algebraic
expressions/equations/inequalities; Growth situations,
such as population growth and compound interest, using
recursive (e.g., NOW- NEXT) formulas (cf. science
standards and social studies standards).
Science Volume and Density labs
Motion and Sound labs
7th Grade Interdisciplinary Connections 12
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.3.D.2. Solve simple linear equations informally and
graphically: Multi-step, integer coefficients only
(although answers may not be integers); Using paper-
and-pencil, calculators, graphing calculators,
spreadsheets, and other technology.
Science Motion and Sound unit
Volume and Density unit
4.4.A.1. Select and use appropriate representations for
sets of data, and measures of central tendency (mean,
median, and mode): Type of display most appropriate
for given data; Box-and-whisker plot, upper quartile,
lower quartile; Scatter plot; Calculators and computer
used to record and process information.
Social Studies
Discovering Algebra
iSearch Paper
Use of Statistics to compare gender equality,
life expectancy, zoology, election results,
deomgraphics, penny data
4.4.A.2. Make inferences and formulate and evaluate
arguments based on displays and analysis of data.
Science Lab write-ups
Daily Discussions in Social Studies and
Science
4.4.B.1. Interpret probabilities as ratios, percents, and
decimals.
Science Probability of weather occurring
4.4.B.3. Estimate probabilities and make predictions
based on experimental and theoretical probabilities.
Economics Insurance Industry
7th Grade Interdisciplinary Connections 13
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.4.C.1. Apply the multiplication principle of counting:
Permutations: ordered situations with replacement (e.g.,
number of possible license plates) vs. ordered situations
without replacement (e.g., number of possible slates of 3
class officers from a 23 student class).
Social Studies Population increases and license plate
number, area codes, phone numbers
(availability)
4.4.C.2. Explore counting problems involving Venn
diagrams with three attributes.
Language Arts Venn Diagrams - compare and contrast
4.5.A.2. Solve problems that arise in mathematics and in
other contexts: Open-ended problems; Non-routine
problems; Problems with multiple solutions; Problems
that can be solved in several ways.
Language Arts Reading Skills
4.5.A.6. Distinguish relevant from irrelevant
information, and identify missing information.
Language Arts Reading Skills
4.5.B.1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Language Arts Grammar Usage, Paragraph Construction
Skills
7th Grade Interdisciplinary Connections 14
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.5.B.2. Communicate mathematical thinking coherently
and clearly to peers, teachers, and others, both orally
and in writing.
Language Arts Grammar Usage, Paragraph Construction
Skills
4.5.B.3. Analyze and evaluate the mathematical thinking
and strategies of others.
Language Arts Peer editing
4.5.C.3. Recognize that mathematics is used in a variety
of contexts outside of mathematics.
Science
Social Studies
Art
Computer Applications
Cooking and Sewing
Physics Formulas, graphs, tables
Statistics
Transformations, perspectives, scale
drawing, computer aided design
Marble maze
Measuring Ingredients, Measuring material
4.5.C.4. Apply mathematics in practical situations and
in other disciplines.
Science
Social Studies
Art
Computer Applications
Cooking and Sewing
Physics Formulas, graphs, tables
Statistics
Transformations, perspectives, scale
drawing, computer aided design
Marble maze
Measuring Ingredients, Measuring material
7th Grade Interdisciplinary Connections 15
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.5.D.2. Use reasoning to support their mathematical
conclusions and problem solutions.
Language Arts Persuasive writing, supporting their ideas
4.5.D.5. Make and investigate mathematical conjectures:
Counterexamples as a means of disproving conjectures;
Verifying conjectures using informal reasoning or
proofs.
Science Scientific Method
4.5.D.6. Evaluate examples of mathematical reasoning
and determine whether they are valid.
Science Scientific Method
4.5.E.1. Create and use representations to organize,
record, and communicate mathematical ideas: Concrete
representations (e.g., base-ten blocks or algebra tiles);
Pictorial representations (e.g., diagrams, charts, or
tables); Symbolic representations (e.g., a formula);
Graphical representations (e.g., a line graph).
Science
Social Studies
Gathering Data from Labs
Graph Population over time
4.5.E.3. Use representations to model and interpret
physical, social, and mathematical phenomena.
See 4.4 Standards
7th Grade Interdisciplinary Connections 16
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Interdisciplinary Connections
Standard Subject Learning Experience
4.5.F.1. Use technology to gather, analyze, and
communicate mathematical information.
Science
Social Studies
Labs, temperature probes, sound waves,
light refraction
iSearch
4.5.F.2. Use computer spreadsheets, software, and
graphing utilities to organize and display quantitative
information.
Computers
4.5.F.6. Use computer-based laboratory technology for
mathematical applications in the sciences.
Science Long run value
7th Grade Interdisciplinary Connections 17
7th Grade Math Curriculum
18
A. Number Sense
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring, or labeling help to make sense of the world around us?
Resources
Essential Questions :
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 7 pertain to these sets of numbers as
well): Rational numbers; Percents; Whole
numbers with exponents.
Interactive Student Line-Up
Games
Geometer’s Sketchpad- Lesson
Links
Newspaper Coupons
McDougal Littell Chapter 2,4,6,9
Pre-Algebra With Pizzazz!!
Math With Pizzazz! Books C-E
Developing Skills in Algebra One,
Book A
Holt Chapter 1,2,3*
Flemington Raritan School District
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations.
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7-8
McDougal Littell Chapter 8,9
Pre-Algebra With Pizzazz!
Math With Pizzazz! Books C-E
Holt Chapter 5,6*
McDougal Littell Chapter 1,2,4,6
Pre-Algebra With Pizzazz!
Math With Pizzazz! Books C-E
Holt Chapter 1,2,3*
2. Demonstrate a sense of the relative
magnitudes of numbers.
Number Line Graphing
Comparing Bar Graphs
Spend $1000/sec, How long to
spend a trillion dollars?
Calculator Use
Standard 4.1 Number and Numerical Operations
Teacher Observation
Test/Quiz
Do Now
Teacher Observation
Test/Quiz
Do Now
Teacher Observation
Test/Quiz
Do Now
Dilations, Reductions
Similarity Lab
Sales Tax
Newspaper Coupons
Grades
Real World Problems
Assessments
4.1.A 7th Grade Math 19
A. Number Sense
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring, or labeling help to make sense of the world around us?
Resources
Essential Questions :
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Assessments
McDougal Littell Chapter 2,4,6
Pre-Algebra With Pizzazz
Math With Pizzazz Books C-E
Holt Chapter 2*
McDougal Littell Chapter 2,4,5,9
Pre-Algebra With Pizzazz!
Math With Pizzazz! Books C-E
Developing Skills in Algebra One,
Book A
Holt Chapter 2*
4. Compare and order numbers of all named
types.
Teacher Observation
Test/Quiz
Do Now
Interactive Student Line-Up
Graphing Ordered Pairs
Measures of Center
I Have-Who Has Game
White Board Activities
Teacher-Generated Questions
Daily Use of Common Fractions,
Decimal and Percents
Coupons
5. Use whole numbers, fractions, decimals, and
percents to represent equivalent forms of the
same number.
Teacher Observation
Test/Quiz
Do Now
4.1.A 7th Grade Math 20
A. Number Sense
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring, or labeling help to make sense of the world around us?
Resources
Essential Questions :
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Assessments
Teacher Observation
Test/Quiz
Do Now
Teacher will emphasize the
difference through class
discussion and practice
problems
6. Understand that all fractions can be
represented as repeating or terminating
decimals.
McDougal Littell Chapter 4,7
Pre-Algebra With Pizzazz!
Math With Pizzazz! Books C-E
White Board Activities
Teacher-Generated Questions
Daily Use of Common Fractions,
Decimal and Percents
Coupons
4.1.A 7th Grade Math 21
· What makes a computational strategy both effective and efficient?
· How do operations affect numbers?
· How do mathematical representations reflect the needs of society across cultures?
Resources
Teacher Observation
Do Now
Test/Quiz
Use of Graphing Calculator
Minute Math*
McDougal Littell Chapter 2,5,6
Geometer’s Sketchpad Lesson
Links
Mad Minute
Holt Chapter 2,3*
Teacher Observation
Do Now
Test/Quiz
Minute Math*
Geometer’s Sketchpad-Lesson
Links
Use of Graphing Calculator
Teacher-Created Worksheets
3. Understand and apply the standard
algebraic order of operations, including
appropriate use of parentheses.
McDougal Littell Chapter 1
Discovering Algebra Chapter 4
Holt Chapter 1*
Teacher Observation
Do Now
Test/Quiz
Minute Math*
Geometer’s Sketchpad
Discovering Algebra 4.1
Use of Graphing Calculator
2. Use exponentiation to find whole number
powers of numbers.
1. Use and explain procedures for performing
calculations with integers and all number
types named above with: Pencil-and-paper;
Mental math; Calculator.
McDougal Littell Chapter 1
Holt Chapter 1*
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Assessments
B. Numerical Operations
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences
4.1.B 7th Grade Math 22
C. Estimation
· How can we decide when to use an exact answer and when to use an estimate?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
1. Use equivalent representations of numbers
such as fractions, decimals, and percents to
facilitate estimation.
McDougal Littell Chapter
1,2,4,5,6,9
Pgs 736-737 in Student Text
Teacher Edition A2
Holt Chapter 2,3*
Daily Warm-Ups
Everyday Use of Numbers
Teacher-Generated Questions
Teacher Observation
Test/Quiz
Do Now
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
4.1.C 7th Grade Math 23
Standard 4.2 Geometry and Geometrical Properties
· How can spatial relationships be described by careful use of geometric language?
· How do geometric relationships help to solve problems and/or make sense of phenomena?
Resources
2. Understand and apply the concept of
similarity: Using proportions to find missing
measures; Scale drawings; Models of 3D
objects.
McDougal Littell Chapter 8,12
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 5,6,10*
Similarity Lab
Graphing Calculators
Flagpole Measurement by using
shadow of pole and student
Math Cartoons
Teacher Observation
Test/Quiz
Do Now
Warm-up Exercises
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply properties of
polygons: Quadrilaterals, including squares,
rectangles, parallelograms, trapezoids,
rhombi; Regular polygons.
McDougal Littell Chapter 10
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 8*
Geoboards
White Boards
Communicators*
Polygon Name Projects
Teacher Observation
Test/Quiz
Do Now
Warm-up Exercises
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
A. Geometric Properties
4.2.A 7th Grade Math 24
Standard 4.2 Geometry and Geometrical Properties
· How can spatial relationships be described by careful use of geometric language?
· How do geometric relationships help to solve problems and/or make sense of phenomena?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
A. Geometric Properties
3. Use logic and reasoning to make and
support conjectures about geometric objects.
McDougal Littell Chapter 10
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 8,9*
Teacher-Generated Questions
Question of Same Perimeter,
What is the Maximum Area?
Give closed properties, have
class draw shape. If class has
different shapes, ask for more
properties. Discuss necessary
properties and subsets.
Teacher Observation
Test/Quiz
Do Now
Warm-up Exercises
4.2.A 7th Grade Math 25
Standard 4.2 Geometry and Geometrical Properties
· What situations can be analyzed using transformations and symmetries?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
McDougal Littell Chapter 10
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 8*
White Boards – Class Graphing
Activities
Can You Transform? Game
Communicators*
Hands-on rotations*
See 4.2 C
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
B. Transforming Shapes
4.2.B 7th Grade Math 26
Standard 4.2 Geometry and Geometrical Properties
· How can geometric/algebraic relationships best be represented and verified?
Resources
Teacher Observation
Test/Quiz
Do Now
Daily Warm-ups
2. Use a coordinate grid to model and quantify
transformations (e.g., translate right 4 units).
McDougal Littell Chapter 10
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 8*
Knowledge/Skills/Understanding Learning Experiences
Can You Transform? Game
Communicators*
Coordinate plane white boards
Give coordinates for a figure,
then give new coordinates and
have students express in
algebraic terms. Ex (x,y)= (x+3,y-
2) or (x,y) = (3x,2y) which
preserve the shape
Teacher Observation
Test/Quiz
Do Now
Daily Warm-ups
Assessments
1. Use coordinates in four quadrants to
represent geometric concepts.
McDougal Littell Chapter 6
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 4, 8*
White Boards – Graphing Points
Geometer’s Sketchpad
Communicators*
Coordinate plane white boards
Geoboards
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
C. Coordinate Geometry
4.2.C 7th Grade Math 27
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
1. Solve problems requiring calculations that
involve different units of measurement within
a measurement system (e.g., 4’3” plus 7’10”
equals 12’1”).
McDougal Littell Chapter 2
NJ ASK Coach
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 1,5*
2. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
Knowledge/Skills/Understanding
Teacher Observation
Test/Quiz
Do Now
Daily Warm-ups
Measuring Length in the
Classroom
Measuring Student Heights
3. Recognize that all measurements of
continuous quantities are approximations.
McDougal Littell Chapter 10-12
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 5,9*
Essential Questions :
Measuring Lines
Constructing Graphs
Real-World Examples
Teacher Observation
Test/Quiz
Do Now
Daily Warm-ups
Assessments
Teacher Observation
Test/Quiz
Do Now
Daily Warm-ups
McDougal Littell Chapter 2,5
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 9*
Various Investigations
On-Going Class Discussions
Geometer’s Sketchpad – Lesson
Link
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
D. Units of Measurement
Learning Experiences
4.2.D 7th Grade Math 28
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
2. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height (e.g.,
use rice to compare volumes of figures with
same base and height).
McDougal Littell Chapter 12
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Pages 750-751 in Student Text
Teacher Edition A16
Holt Chapter 10*
Use 3-D objects to
demonstrate with water
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Develop and apply strategies for finding
perimeter and area: Geometric figures made
by combining triangles, rectangles and circles
or parts of circles; Estimation of area using
grids of various sizes.
McDougal Littell Chapter 1,11
Math with Pizzazz! Books C-E
Pre-Algebra with Pizzazz!
Holt Chapter 8,9,10*
Pattern Blocks
Same Perimeter, Maximum Area
Problems
Use Geoboards*
Physically measuring objects
around room*
Find the value of pi by
measuring circumference and
diameter of circular objects*
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
E. Measuring Geometric Objects
4.2.E 7th Grade Math 29
· How can change be best represented mathematically?
Resources
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Standard 4.3 Patterns and Algebra
Assessments
Essential Questions :
A. Patterns
Knowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
1. Recognize, describe, extend, and create
patterns involving whole numbers, rational
numbers, and integers: Descriptions using
tables, verbal and symbolic rules, graphs,
simple equations or expressions; Finite and
infinite sequences; Generating sequences by
using calculators to repeatedly apply a
formula.
McDougal Littell Chapter 1,7
Holt Chapter 1,2*
Geometer’s Sketchpad-to graph
patterns
Use of Graphing Calculators
Teacher-Created Problems
Flashlight and Bridge
Locker Problem
Dot patterns that involve a
recursive routine. Students write
the recursive routine and then it's
explicit formula expressing the
number of dots as a function of
the term number.
Use a line-up to explore
patterns*
4.3.A 7th Grade Math 30
· How are patterns of change related to the behavior of functions?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
B. Functions and Relationships
1. Graph functions, and understand and
describe their general behavior: Equations
involving two variables.
McDougal Littell Chapter 7
Pre-Algebra with Pizzazz!
Holt Chapter 1,4*
Use of Graphing Calculator
Cartesian Cartoons
Input/Output tables
Geometer’s Sketchpad Lesson
Links
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
Essential Questions :
4.3.B 7th Grade Math
31
· How can mathematical models be used to describe physical relationships?
· How can physical models be used to clarify mathematical relationships?
Resources Assessments
Input/Output Tables
Geometer’s Sketchpad –Lesson
Links
Population Growth Activity
Lesson Investigation 1.6
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Graphing Lines-Describing the
Relationship
Use of Graphing Calculator
Measures of Center
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
McDougal Littell Chapter 7
NJ ASK Coach
TinkerPlots
Holt Chapter 4*
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations: Using
manipulatives, tables, graphs, verbal rules,
algebraic expressions/equations/inequalities;
Growth situations, such as population growth
and compound interest, using recursive (e.g.,
NOW- NEXT) formulas (cf. science standards
and social studies standards).
Standard 4.3 Patterns and Algebra
C. Modeling
McDougal Littell Chapter 7
Discovering Algebra - 1.6
Holt Chapter 4*
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Knowledge/Skills/Understanding Learning Experiences
Essential Questions :
4.3.C 7th Grade Math 32
· What makes an algebraic algorithm both effective and efficient?
Resources
McDougal Littell Chapter 1,7
Discovering Algebra Chapter 4.1
Pre-Algebra with Pizzazz!
Holt Chapter 1,2*
Lesson Investigation 4.1
Graphing/Scientific Calculator
Use
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
2. Solve simple linear equations informally
and graphically: Multi-step, integer
coefficients only (although answers may not be
integers); Using paper-and-pencil, calculators,
graphing calculators, spreadsheets, and other
technology.
McDougal Littell Chapter 1,2,5,7
Discovering Algebra Chapter 4
Pre-Algebra with Pizzazz!
Holt Chapter 12*
Working Backwards Tables
Hands on Equations Balance
Graphing Calculator Use
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
3. Create, evaluate, and simplify algebraic
expressions involving variables: Order of
operations, including appropriate use of
parentheses; Substitution of a number for a
variable.
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use graphing techniques on a number line:
Absolute value; Arithmetic operations
represented by vectors (arrows) (e.g., “-3 + 6”
is “left 3, right 6”)
McDougal Littell Chapter 1,6,7
Geometer’s Sketchpad
Holt Chapter 2*
Geometer's Sketchpad-Lesson
Links
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures
4.3.D 7th Grade Math 33
· What makes an algebraic algorithm both effective and efficient?
Resources
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures
4. Understand and apply the properties of
operations, numbers, equations, and
inequalities: Additive inverse; Multiplicative
inverse.
McDougal Littell Chapter 6
Discovering Algebra 4.2/4.3
Holt Chapter 1*
Lesson Investigation 4.2/4.3
Hands on Equations Balance
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
4.3.D 7th Grade Math 34
Resources
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data.
McDougal Littell Chapter 3
Student Pages 758-7579
TE A24
Discovering Algebra Chapter 1
Holt Chapter 7*
Penny Data Investigation
Layer Various graphs on the
same number line
TinkerPlots Prepared Data
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode): Type of
display most appropriate for given data; Box-
and-whisker plot, upper quartile, lower
quartile; Scatter plot; Calculators and
computer used to record and process
information.
McDougal Littell Chapter 3
Student Pages 756-757
TE A22
Discovering Algebra Chapter 1
Holt Chapter 7*
Tinkerplots Prepared Data
Geometer's Sketchpad - Lesson
Links
Penny Data Investigation
Class Line-up to find the five
number summary
Graphing Calculator Use
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
· How can the collection, organization, interpretation, and display of data be used to answer
questions?
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.A 7th Grade Math 35
Resources
2. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
McDougal Littell Chapter 13
Connected Mathematics “What Do
You Expect?”
Holt Chapter 11*
"What Do You Expect?"
Investigations
Graphing Calculator Use
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
3. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
McDougal Littell Chapter 13
Connected Mathematics “What Do
You Expect?”
Holt Chapter 11*
"What Do You Expect?"
Investigations
Graph Class results as well as
group results, have students
compare/contrast results.
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Interpret probabilities as ratios, percents,
and decimals.
McDougal Littell Chapter 13
Connected Mathematics “What Do
You Expect?”
Holt Chapter 11*
Graphing Calculator Use
Hands on Simulation -Rolling
Die, M & M's, Spinners
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.B 7th Grade Math 36
Resources
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4. Play and analyze probability-based games,
and discuss the concepts of fairness and
expected value.
McDougal Littell Chapter 13
Connected Mathematics “What Do
You Expect?”
Holt Chapter 11*
"What Do You Expect?"
Investigations
Game Discussions
Candy land vs. Chutes and
Ladders
Design own "Zark" Game
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
4.4.B 7th Grade Math 37
· What counting strategy works best here?
Resources
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
McDougal Littell Chapter 13
Connected Mathematics "What Do
You Expect?"
NJ ASK Coach
Holt Chapter 11*
"What Do You Expect?"
Investigations
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement (e.g., number of possible
license plates) vs. ordered situations without
replacement (e.g., number of possible slates of
3 class officers from a 23 student class).
McDougal Littell Chapter 13
NJ ASK Coach
Holt Chapter 11*
Winning the Lottery
License Plate Combinations
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
2. Explore counting problems involving Venn
diagrams with three attributes.
McDougal Littell Chapter 13
Student Edition Pg 790
NJ ASK Coach
Holt Chapter 11*
Card Probabilities
Mutually Exclusive Events
Discussion of Overlap of Events
Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
Essential Questions :
· How can attributes be used to classify data/objects?
· What is the best way to solve this?
Knowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.C 7th Grade Math 38
· How can algorithmic thinking be used to solve problems?
Resources
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use vertex-edge graphs to represent and
find solutions to practical problems: Finding
the shortest network connecting specified
sites; Finding the shortest route on a map
from one site to another; Finding the shortest
circuit on a map that makes a tour of specified
sites.
Student Edition pg 744-745
TE A10
Rutgers Prepared Activities Teacher Observation
Quiz/Test
Do Now
Daily Warm-up
· How can visual tools such as networks (vertex-edge graphs) be used to answer questions?
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.D 7th Grade Math 39
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Grade Math
40
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Pose problems of various types and levels of
difficulty.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Grade Math
41
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Monitor their progress and reflect on the
process of their problem solving activity.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Distinguish relevant from irrelevant
information, and identify missing information.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Grade Math
42
Resources
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. Communication
4.5.B 7th Grade Math 43
Resources
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. Communication
3. Analyze and evaluate the mathematical
thinking and strategies of others.
4. Use the language of mathematics to express
mathematical ideas precisely.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.B 7th Grade Math 44
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
4.5.C 7th Grade Math
45
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
4. Apply mathematics in practical situations
and in other disciplines.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
4.5.C 7th Grade Math
46
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Trace the development of mathematical
concepts over time and across cultures (cf.
world languages and social studies standards).
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Learnia
Open-Ended Questions
4.5.C 7th Grade Math
47
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Grade Math 48
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Select and use various types of reasoning
and methods of proof.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Grade Math 49
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Grade Math 50
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
E. Representations
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
2. Select, apply, and translate among
mathematical representations to solve
problems.
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
4.5.E 7th Grade Math
51
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
E. Representations Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.E 7th Grade Math
52
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
1. Use technology to gather, analyze, and
communicate mathematical information.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.F 7th Grade Math
53
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.F 7th Grade Math
54
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
5. Use computer software to make and verify
conjectures about geometric objects.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.F 7th Grade Math
55
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
6. Use computer-based laboratory technology
for mathematical applications in the sciences.
McDougal Littell Chapters 1-13
Menu Problems (Middle School
Math Teacher)
NCTM Navigations Series
Van De Walle
Connected Mathematics
TinkerPlots
Geometer’s Sketchpad
Holt Chapters 1-12*
Direct Instruction
Investigations
Collaborative/Cooperative
Learning
Written Explanations
Student Directed Discussions
Do Now
Quiz/Test
Teacher Observation
Open-Ended Questions
4.5.F 7th Grade Math
56
14 5 11
Mid-Year Benchmark
Assessment
1
12 10
Integers 6 12
1
122
Percents
Number of Blocks
9 11 6 11
9
Data Analysis and
Statistics
3 15 7 13
Number Sense, Patterns
and Algebraic Thinking
1 6 3
Pacing Guide
UnitMcDougall Littell Mathematics
Course 2 ChaptersNumber of Blocks
Holt Mathematics Course
2 Chapters
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
Equations, Inequalities and
Functions
7 8
Ratios and Proportions 8
7th Grade Math Pacing Guide
57
Number of Blocks
Pacing Guide
UnitMcDougall Littell Mathematics
Course 2 ChaptersNumber of Blocks
Holt Mathematics Course
2 Chapters
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
6
Geometric Figures 10 6 8
Discrete Math 1 1
Probability 13
"What Do You Expect?"
7 11
"What Do You Expect?"
Venn Diagrams with three
attributes
End-of-the-Year
Benchmark Assessment
1 1
6
Measurement and Area 11 5 9
2 2
Surface Area and Volume 12 1 10 2
5
7th Grade Math Pacing Guide
58
UCSMP Transitions Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
Algebra Out Loud Pat Mower, PhD Jossey Bass 2003
Impact Mathematics Course 1 Glencoe 2003
New Jersey ASK Coach Jerome Kaplan Ed.D Triumph Learning 2005
Question Quest Level C Paul Lawrence LL Teach, Inc. 2002
Pre-Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002
Developing Skills in Algebra One - Books A
and B
Harold and Loretta Taylor Dale Seymour Publications 1984
Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
Title of Resource Author(s) Publisher Copyright
McDougall Littell Course 2
and all related resources (differentiation
including ELL)
Larson, Boswell, Kanold & Stiff McDougal Littell 2008
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
Resources
Holt Mathematics Course 2 and all related
resources (differentiation including ELL)
Bennett, Burger, Chard, Jackson,
Kennedy, Renfro, Scheer & Waits
Holt, Rinehart and Winston 2007
7th Grade Resources
59
Title of Resource Author(s) Publisher Copyright
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
Resources
1998
2003
Algebra Puzzles & Problems
Algebra Teacher's Activities Kit
Greenes/Findell
Judith & Robert Muschla
Creative Publications
Jossey Bass
Tinker Plots Clifford Konold & Craig D. Miller Key Curriculum Press 2005
Geometer's Sketchpad 4 Nicholas Jackiw Key Curriculum Press 2006
UCSMP Algebra Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
Explain It Lepore, Fleetwood & Hall Creative Publications 2001
ASK Workout
Differentiated Middle School Math
Jerome Kaplan Ed.D Triumph Learning
Exemplars
2008
Teaching Student-Centered Mathematics
Grades 5-8
Hands -On Algebra !
Daily Word Problems Grade 6
Middle School Collection: Geometry: Basic
Concepts, Geometry: Solids, Geometry:
Polygons, Pre-Algebra
John A. Van de Walle & LouAnn
H. Lovin
Frances M. Thompson
Amy Beth Tuttle, Wes Tuttle
D.W. Skrabanek
Pearson Education
The Center for Applied Research
Education
Evan-Moor Publishers
Steck-Vaugh Company
2006
1998
2001
2000
7th Grade Resources
60
Title of Resource Author(s) Publisher Copyright
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
Resources
Middle Grade Math Minutes
Mathematical Reasoning Through Verbal
Analysis Book 2
Doug Stoffel
Warren Hill & Ronald Edwards
Creative Teaching Press
Critical Thinking Books &
Software
2000
1991
Measuring Up to the NJ Core Curriculum
Content Standards
Kenneth Owens Peoples Publishing Group 2003
NCTM Navigation Series: Probability, Data
Analysis, Geometry
8-Step Model Drawing
Bright, Frierson Jr., Tarr,
Thomas, Brewer, McClain,
Mooney, Pugalee, Frykholm,
Johnson, Slovin, Malloy, Preston
Bob Hogan & Char Forsten
The National Council of
Teachers of Mathematics
Crystal Spring Books
2003
2007
Geometry Activities for Middle School
Students
Shape Makers: Developing Geometric
Reasoning in Middle School
What Do You Expect?
Strategies for Success in Mathematics: Level
G
Key Curriculum Press
Key Curriculum Press
Dale Seymour Publications
Steck-Vaugh Company
Wyatt, Lawrence, Foletta
Michael T. Battista
Lappan, Fey, Fitzgerald, Friel
and Phillips
Weisenfeld, Coultas, Swalm
2003
2004
1998
1999
7th Grade Resources
61
Title of Resource Author(s) Publisher Copyright
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Math
Resources
Curriculum and Evaluation Standards for
School Mathematics Addenda Series Grades 5-
8
Geddes, Zawojewski, Reys,
Phillips, Curcio, Bezuk
The National Council of
Teachers of Mathematics
1992
7th Grade Resources
62
Algebra 1A Math Curriculum
63
A. Number Sense
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring or labeling help to make sense of the world around us?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 8 pertain to these sets of numbers as
well): Rational numbers; Percents;
Exponents; Roots; Absolute Values; Numbers
represented in scientific notation
Discovering Algebra Chapter 2, 4
UCSMP Transitions
Investigate decimal patterns
using a calculator
Lesson Investigations
Direct Instruction
Do Now
Quiz/Test
Teacher Observation
2. Demonstrate a sense of the relative
magnitudes of numbers.
Elementary and Middle School
Math Chapter 26
Number line graphing
Lesson Investigations throughout
the textbook
On-going
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations.
Discovering Algebra Chapter 2, 3 Lesson Investigations 2.2, 2.3,
3.1, 3.2, 3.3
Similarity Lab
Do Now
Quiz/Test
Class discussion
Teacher Observation
4.1.A 7th Algebra 1A 64
A. Number Sense
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring or labeling help to make sense of the world around us?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Teacher-created review
Calculator Activities
I have . . . who has
6. Recognize that repeating decimals
correspond to fractions and determine their
fractional equivalents .
Discovering Algebra Chapter 2 Lesson Investigation 2.1
Calculator Activities
Do Now
Quiz/Test
Class discussion
Teacher Observation
4. Compare and order numbers of all named
types.
Van De Walle Chapter 24 Student Line-Up Student Line Up
5. Use whole numbers, fractions, decimals, and
percents to represent equivalent forms of the
same number.
UCSMP Transitions Lesson
Masters
National Council of Teachers of
Mathematics, Developing Number
Sense
4.1.A 7th Algebra 1A 65
· What makes a computational strategy both effective and efficient?
· How do operations affect numbers?
· How do mathematical representations reflect the needs of society across cultures?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
B. Numerical Operations
Lesson Investigations 2.2, 2.3 Teacher Observation
Discussion of Lesson
Investigation results
Do Now
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Pencil-and-paper; Mental math;
Calculator.
Teacher-created problems
Math With Pizzazz! Book E
Pre-Algebra with Pizzazz!
Algebra with Pizzazz!
Mental Math Warm-Ups Do Now
Quiz/Test
Teacher Observation
2. Use exponentiation to find whole number
powers of numbers.
Teacher-created problems
Developing Skills in Algebra One –
Book A
Review as needed Quiz
3. Solve problems involving proportions and
percents.
Discovering Algebra Chapter 2
4.1.B 7th Algebra 1A 66
· What makes a computational strategy both effective and efficient?
· How do operations affect numbers?
· How do mathematical representations reflect the needs of society across cultures?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
B. Numerical OperationsEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Understand and apply the standard
algebraic order of operations, including
appropriate use of parentheses.
Teacher-created problems
Discovering Algebra Chapter 4
Pre-Algebra with Pizzazz!
Algebra with Pizzazz!
Lesson Investigation 4.1 Do Now
Teacher Observation
Quiz/Test
4.1.B 7th Algebra 1A 67
C. Estimation
· How can we decide when to use an exact answer and when to use an estimate?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use equivalent representations of numbers
such as fractions, decimals, and percents to
facilitate estimation.
Various Lesson Investigations
Daily discussions
Daily problems
Lesson Investigation 4.1
Do Now
Teacher Observation
2. Recognize the limitations of estimation and
assess the amount of error resulting from
estimation.
Various Lesson Investigations
Daily discussions
Daily problems On-going
4.1.C 7th Algebra 1A 68
Standard 4.2 Geometry and Geometrical Properties
· How can spatial relationships be described by careful use of geometric language?
· How do geometric relationships help to solve problems and/or make sense of phenomena?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
A. Geometric Properties
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply properties of
polygons: Quadrilaterals, including squares,
rectangles, parallelograms, trapezoids,
rhombi; Regular polygons
Navigations Series – Geometry
Geometer’s Sketchpad
Geoboard exploration
Manipulatives
Do Now
Teacher Observation
2. Understand and apply the concept of
similarity: Using proportions to find missing
measures; Scale drawings; Models of 3D
objects.
Discovering Algebra Chapter 3
Van De Walle pg 365-366
Lesson Investigation 3.3
Measure shadow of flagpole and
person to determine height
Quiz/Test
Do Now
Teacher Observation
3. Use logic and reasoning to make and
support conjectures about geometric objects.
Teacher-created problems
Geometer’s Sketchpad
Direct Instruction
Lesson Investigation 3.3
Teacher Observation
4.2.A 7th Algebra 1A 69
Standard 4.2 Geometry and Geometrical Properties
· What situations can be analyzed using transformations and symmetries?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
B. Transforming Shapes
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
UCSMP Transitions Lesson
Masters
Worksheets
Navigation Series – Geometry
Geometry in the Middle Grades
Discovering Algebra Chapter 3
Van De Walle pg 371
NJ ASK Coach
Manipulatives
Give coordinates for a figure,
then give new coordinates and
have students express in
algebraic terms. Ex (x,y)= (x+3,y-
2) or (x,y) = (3x,2y) which
preserve the shape
Do Now
Quiz/Test
Teacher Observation
4.2.B 7th Algebra 1A 70
Standard 4.2 Geometry and Geometrical Properties
· How can geometric/algebraic relationships best be represented and verified?
Resources
Do Now
Quiz/Test
Teacher Observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
C. Coordinate Geometry
2. Use a coordinate grid to model and quantify
transformations (e.g., translate right 4 units).
NJ ASK Coach
Teacher-made materials
Graphing Calculator
Give coordinates for a figure
then, give new coordinates and
have students express in
algebraic terms. Ex (x,y)= (x+3,y-
2) or (x,y) = (3x,2y) which
preserve the shape
Do Now
Quiz/Test
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use coordinates in four quadrants to
represent geometric concepts.
• Slope of a line
Discovering Algebra Chapter 4, 5
Algebra with Pizzazz!
Pre-Algebra with Pizzazz!
NJ ASK Coach
Developing Skills in Algebra One –
Book C
Lesson Investigations 4.4, 4.6,
4.7, 5.1, 5.2
Working Cooperatively
Graphing Calculator work
4.2.C 7th Algebra 1A 71
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
D. Units of Measurement
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Solve problems requiring calculations that
involve different units of measurement within
a measurement system (e.g., 4’3” plus 7’10”
equals 12’1”).
Discovering Algebra Chapter 2, 3 Lesson Investigations 2.3, 3.2 Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
2. Use approximate equivalents between
standard and metric systems to estimate
measurements (e.g., kilometers is about 3
miles).
Discovering Algebra Chapter 2
UCSMP Transitions Chapter 3
Lesson Investigations 2.3, 3.2 Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.2.D 7th Algebra 1A 72
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
D. Units of Measurement
Knowledge/Skills/Understanding Learning Experiences Assessments
Various Lesson Investigations Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
3. Recognize that the degree of precision
needed in calculations depends on how the
results will be used and the instruments used
to generate the measurements.
On-going class discussions Various Lesson Investigations Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
On-going class discussions Various Lesson Investigations Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
5. Recognize that all measurements of
continuous quantities are approximations.
On-going class discussions
4.2.D 7th Algebra 1A 73
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
D. Units of Measurement
Knowledge/Skills/Understanding Learning Experiences Assessments
6. Solve problems that involve compound
measurement units, such as speed (miles per
hour), air pressure (pounds per square inch),
and population density (persons per square
mile).
Discovering Algebra Chapter 2
Algebra with Pizzazz!
Lesson Investigation 2.3
Direct Instruction
Dimensional Analysis
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.2.D 7th Algebra 1A 74
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Teacher-created problems
Learnia
Do Now
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
E. Measuring Geometric Objects
2. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height (e.g.,
use rice to compare volumes of figures with
same base and height).
Van De Walle Chapter 19
Geometer’s Sketchpad
Navigations Series – Geometry
Math with Pizzazz! Book D
Pre-Algebra with Pizzazz!
NJ Ask Coach
Direct Instruction Teacher-created problems
Learnia
Do Now
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Develop and apply strategies for finding
perimeter and area: Geometric figures made
by combining triangles, rectangles and circles
or parts of circles; Estimation of area using
grids of various sizes.
Van De Walle Chapter 19
Geometer’s Sketchpad
Navigations Series – Geometry
Math with Pizzazz! Book D
Pre-Algebra with Pizzazz!
Investigations
4.2.E 7th Algebra 1A 75
· How can change be best represented mathematically?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
A. Patterns Essential Questions :
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize, describe, extend, and create
patterns involving whole numbers, rational
numbers, and integers: Descriptions using
tables, verbal and symbolic rules, graphs,
simple equations or expressions; Finite and
infinite sequences; Arithmetic sequences;
Geometric sequences; Generating sequences
by using calculators to repeatedly apply a
formula.
Discovering Algebra Chapter 4 Direct Instruction
Lesson Investigations 4.3, 4.4,
4.6
Modeling
Graphing Calculators
Do Now
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigations
4.3.A 7th Algebra 1A 76
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
B. Functions and RelationshipsEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Graph functions, and understand and
describe their general behavior: Equations
involving two variables; Equations involving
two variables; Rates of change (informal
notion of slope).
Discovering Algebra Chapter 4, 5 Direct Instruction
Lesson Investigations 4.4, 4.6,
4.7, 5.1, 5.2, 5.3
Do Now
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigations
4.3.B 7th Algebra 1A 77
· How can mathematical models be used to describe physical relationships?
· How can physical models be used to clarify mathematical relationships?
Resources
Direct Instruction
Modeling throughout lessons
Lesson Investigations 3.2, 4.3,
4.4, 4.6, 4.7, 5.1, 5.2, 5.3
Teacher observation
Discussion of Lesson
Investigations
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
C. Modeling
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations: Using
concrete materials (manipulatives), tables,
graphs, verbal rules, algebraic expressions/
equations/ inequalities; Growth situations,
such as population growth and compound
interest, using recursive (e.g., NOW-NEXT)
formulas (cf. science standards and social
studies standards).
Discovering Algebra Chapter 3, 4, 5 Direct Instruction
Modeling throughout lessons
Lesson Investigations 3.2, 4.3,
4.4, 4.6, 4.7, 5.1, 5.2, 5.3
Do Now
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
Discovering Algebra Chapter 3, 4, 5
4.3.C 7th Algebra 1A 78
· What makes an algebraic algorithm both effective and efficient?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use graphing techniques on a number line:
Absolute value; Arithmetic operations
represented by vectors (arrows) (e.g., “-3 + 6”
is “left 3, right 6”)
Teacher-created problems
Transitions Chapter 5
Pre-Algebra with Pizzazz!
Geometer’s Sketchpad
Direct Instruction
Geometer’s Sketchpad Lesson
Link
Do Now
Quiz/Test
Teacher Observation
2. Solve simple linear equations informally,
graphically, and using formal algebraic
methods:
Multi-step, integer coefficients only (although
answers may not be integers) Simple literal
equations (e.g., A = lw) Using paper-and-
pencil, calculators, graphing calculators,
spreadsheets, and other technology.
Discovering Algebra Chapter 2, 3, 4 Direct Instruction
Graphing Calculator
Do Now
Quiz/Test
Teacher Observation
4.3.D 7th Algebra 1A
79
· What makes an algebraic algorithm both effective and efficient?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Direct Instruction
Lesson Investigation 4.1
Graphing Calculator
Do Now
Quiz/Test
Teacher Observation
4. Understand and apply the properties of
operations, numbers, equations, and
inequalities: Additive inverse; Multiplicative
inverse; Addition and multiplication
properties of equality.
Discovering Algebra Chapter 2, 3, 4
Pre-Algebra with Pizzazz!
Developing Skills in Algebra One –
Book A
Direct Instruction
Graphing Calculator
Do Now
Quiz/Test
Teacher Observation
3. Create, evaluate, and simplify algebraic
expressions involving variables: Order of
operations, including appropriate use of
parentheses; Distributive property;
Substitution of a number for a variable;
Translation of a verbal phrase or sentence into
an algebraic expression, equation, or
inequality, and vice versa.
Discovering Algebra Chapter 2, 3, 4
Pre-Algebra with Pizzazz!
4.3.D 7th Algebra 1A
80
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can the collection, organization, interpretation, and display of data be used to answer
questions?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode): Type of
display most appropriate for given data; Box-
and-whisker plot, upper quartile, lower
quartile; Scatter plot; Calculators and
computer used to record and process
information; Finding the median and mean
(weighted average) using frequency data;
Effect of additional data on measures of
central tendency.
Discovering Algebra Chapter 1
More Practice with Your Skills
TinkerPlots
Direct Instruction
Graphing Calculator
Lesson Investigations 1.1-1.7
Class Discussion
Do Now
Graphing Calculator
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data sets.
Discovering Algebra Chapter 1
More Practice with Your Skills
TinkerPlots
Direct Instruction
Graphing Calculator
Lesson Investigations 1.1-1.7
Class Discussion
Do Now
Graphing Calculator
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.4.A 7th Algebra 1A 81
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can the collection, organization, interpretation, and display of data be used to answer
questions?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Estimate lines of best fit and use them to
interpolate within the range of the data.
Discovering Algebra Chapter 5 Lesson Investigation 5.3
Class Discussion
Do Now
Graphing Calculator
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.4.A 7th Algebra 1A 82
Resources
Do Now
Quiz/Test
Teacher Observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Lesson Investigations 2.6, 2.7
Experiments from Connected
Mathematics “What Do You
Expect?"
Do Now
Quiz/Test
Teacher Observation
Essential Questions :
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Interpret probabilities as ratios, percents,
and decimals.
Discovering Algebra Chapter 2
Connected Mathematics “What Do
You Expect?"
Math with Pizzazz! Book E
Pre-Algebra with Pizzazz!
Lesson Investigations 2.6, 2.7
Experiments from Connected
Mathematics “What Do You
Expect?"
2. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
Discovering Algebra Chapter 2
Connected Mathematics “What Do
You Expect?"
Math with Pizzazz! Book E
Pre-Algebra with Pizzazz!
Lesson Investigations 2.6, 2.7
Experiments from Connected
Mathematics “What Do You
Expect?"
Do Now
Quiz/Test
Teacher Observation
3. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
Discovering Algebra Chapter 2
Connected Mathematics “What Do
You Expect?"
Math with Pizzazz! Book E
Pre-Algebra with Pizzazz!
4.4.B 7th Algebra 1A
83
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Play and analyze probability-based games,
and discuss the concepts of fairness and
expected value.
Connected Mathematics “What Do
You Expect?"
Math with Pizzazz! Book E
Pre-Algebra with Pizzazz!
Experiments from Connected
Mathematics “What Do You
Expect?"
Do Now
Quiz/Test
Teacher Observation
4.4.B 7th Algebra 1A
84
· What counting strategy works best here?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Problems from UCSMP
Transitions Textbook and
UCSMP Algebra
Venn Diagrams
Teacher Observation
Quiz/Test
Essential Questions :
· How can attributes be used to classify data/objects?
· What is the best way to solve this?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
UCSMP Transitions Textbook
Math Counts
National Council of Teachers of
Mathematics Dealing with Data and
Chance Standards
Find number of ways to arrange
batters
Teacher Observation
Quiz/Test
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement vs. ordered situations
without replacement.
UCSMP Algebra Textbook
Math Counts
Pre-Algebra with Pizzazz!
Connected Mathematics “What Do
You Expect?”
NJ ASK Coach
Experiments from Connected
Mathematics “What Do You
Expect?”
Counting Trees
Teacher Observation
Quiz/Test
2. Explore counting problems involving Venn
diagrams with three attributes.
UCSMP Transitions Textbook
National Council of Teachers of
Mathematics Dealing with Data and
Chance Standards
NJ ASK Coach
4.4.C 7th Algebra 1A 85
· How can visual tools such as networks (vertex-edge graphs) be used to answer questions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can algorithmic thinking be used to solve problems?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use vertex-edge graphs to represent and
find solutions to practical problems: Finding
the shortest network connecting specified
sites; Finding the shortest route on a map
from one site to another; Finding the shortest
circuit on a map that makes a tour of specified
sites.
Teacher-created materials
Pgs 744-745 McDougal Littell
Rutgers prepared worksheets
Write a tour guide with map
Teacher-Created
worksheets
Tour Guide Project
4.4.D 7th Algebra 1A 86
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Algebra 1A
87
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Pose problems of various types and levels of
difficulty.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Algebra 1A
88
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Monitor their progress and reflect on the
process of their problem solving activity.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Test Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Distinguish relevant from irrelevant
information, and identify missing information.
Discovering Algebra Chapters 1-5
Math Counts
Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Question
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.A 7th Algebra 1A
89
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.B 7th Algebra 1A
90
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Analyze and evaluate the mathematical
thinking and strategies of others.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Use the language of mathematics to express
mathematical ideas precisely.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.B 7th Algebra 1A
91
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.C 7th Algebra 1A 92
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Apply mathematics in practical situations
and in other disciplines.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.C 7th Algebra 1A 93
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Trace the development of mathematical
concepts over time and across cultures (cf.
world languages and social studies standards).
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.C 7th Algebra 1A 94
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Algebra 1A 95
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Select and use various types of reasoning
and methods of proof.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Algebra 1A 96
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.D 7th Algebra 1A 97
Resources
E. Representations
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Journaling
Teacher Observation
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Journaling
Teacher Observation
2. Select, apply, and translate among
mathematical representations to solve
problems.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
4.5.E 7th Algebra 1A
98
Resources
E. Representations
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Journaling
Teacher Observation
4.5.E 7th Algebra 1A
99
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.F 7th Algebra 1A
100
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.F 7th Algebra 1A
101
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Use computer software to make and verify
conjectures about geometric objects.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
6. Use computer-based laboratory technology
for mathematical applications in the sciences.
Discovering Algebra Chapters 1-5
Math Counts
NCTM Navigation Series
Connected Mathematics
Elementary and Middle School
Mathematics
Question Quest Level C
Direct Instruction
Lesson Investigations
Collaborative/Cooperative
Learning
Written Explanations
Open-Ended Questions
Written Test/Quiz
Written Explanation
Open-ended Questions
Teacher Observation
4.5.F 7th Algebra 1A
102
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1A
Pacing Guide
UnitDiscovering Algebra
ChapterNumber of Blocks
Data Exploration
1 15
Proportional Reasoning
2 14
Variations and Graphs
3 14
Linear Equations
4 15
Slope and Fitting a Line to Data
5 14
Probability
2
"What Do You Expect ?"
12
Geometry
Math with Pizzazz
Pre-Algebra with Pizzazz
5
7th Grade Algebra 1A Pacing Guide 103
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1A
Resources
Title of Resource Author(s) Publisher Copyright
Discovering Algebra An Investigative
Approach
Jerald Murdock, Ellen Kamischke,
Eric Kamischke
Key Curriculum Press 2002
Developing Skills in Algebra One - Books A
and B
Harold and Loretta Taylor Dale Seymour Pulbications 1984
Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
LL Teach, Inc. 2002
Pre-Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
Middle School Math with Pizzazz- Books A-E Steve & Janis Marcy McGraw Hill 2002
Algebra Out Loud Pat Mower, Phd Jossey Bass 2003
New Jersey ASK Coach Jerome Kaplan Ed.D Triumph Learning 2005
Question Quest Level C Paul Lawrence
UCSMP Transitions Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
UCSMP Algebra Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
Tinker Plots Clifford Konold & Craig D. Miller Key Curriculum Press 2005
7th Grade Algebra 1A Resources
104
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1A
Resources
Title of Resource Author(s) Publisher Copyright
Geometer's Sketchpad 4 Nicholas Jackiw Key Curriculum Press 2006
Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998
Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003
Explain It Lepore, Fleetwood & Hall Creative Publications 2001
ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008
Differentiated Middle School Math Exemplars
Teaching Student-Centered Mathematics
Grades 5-8
John A. Van de Walle & LouAnn
H. Lovin
Pearson Education 2006
NCTM Navigation Series: Probability, Data
Analysis, Geometry
Bright, Frierson Jr., Tarr,
Thomas, Brewer, McClain,
Mooney, Pugalee, Frykholm,
Johnson, Sloving, Malloy,
The National Council of
Teachers of Mathematics
2003
Hands -On Algebra ! Frances M. Thompson The Center for Applied Research
Education
1998
Geometry Activities for Middle School
Students
Wyatt, Lawrence, Foletta Key Curriculum Press 2004
Shape Makers: Developing Geometric
Reasoning in Middle School
Michael T. Battista Key Curriculum Press 2003
7th Grade Algebra 1A Resources
105
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1A
Resources
Title of Resource Author(s) Publisher Copyright
What Do You Expect? Lappan, Fey, Fitzgerald, Friel
and Phillips
Dale Seymour Pulbications 1998
Strategies for Success in Mathematics: Level
G
Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999
Curriculum and Evaluation Standards for
School Mathematics Addenda Series Grades 5-
8
Geddes, Zawojewski, Reys,
Phillips, Curcio, Bezuk
The National Council of
Teachers of Mathematics
1992
7th Grade Algebra 1A Resources
106
Algebra 1B Math Curriculum
107
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring, or labeling help to make sense of the world around us?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
A. Number Sense
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 8 pertain to these sets of numbers as
well): Rational numbers; Percents;
Exponents; Roots; Absolute Values; Numbers
represented in scientific notation
Discovering Algebra Chapter 7.1, 8,
9, 10
Math Counts
Teacher-created
worksheets/problems
Investigate decimal patterns
using a calculator
Applicable Problems
Recursive Routines
Through the use of geometry of
squares and cubes
Applicable Lesson Investigations
Direct Instruction
Cooperative student exploration
of “undoing” operations of
functions
Teacher-created review
examples
Do Now
Quiz/Test
Teacher Observation
Class Discussions
Written Explanations
2. Demonstrate a sense of the relative
magnitudes of numbers.
National Council of Teachers of
Mathematics, Developing Number
Sense
Spend national debt at a given
rate-how long?
4.1.A 7th Algebra 1B 108
· How do mathematical ideas interconnect and build on one another to produce a coherent whole?
· How can we compare and contrast numbers?
· How can counting, measuring, or labeling help to make sense of the world around us?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
A. Number Sense
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations.
Math Counts
Real-world examples
Problem solving
Collaborative discussions
Do Now
Quiz/Test
Class discussion
Teacher Observation
4. Compare and order numbers of all named
types.
UCSMP Transitions Chapter 12 Graphing on a number line
5. Use whole numbers, fractions, decimals, and
percents to represent equivalent forms of the
same number.
Discovering Algebra Chapter 12
UCSMP Algebra
Spiral of right triangles –
Pythagorean Theorem
4.1.A 7th Algebra 1B 109
· What makes a computational strategy both effective and efficient?
· How do operations affect numbers?
· How do mathematical representations reflect the needs of society across cultures?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
B. Numerical Operations
Lesson Investigations Teacher Observation
Discussion of Lesson
Investigation results
Do Now
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Pencil-and-paper; Mental math;
Calculator.
Developing Skills in Algebra One
Book A & B
Mental Math Warm-Ups
Do Now
Use Applications
Do Now
Quiz/Test
Teacher Observation
2. Find cube roots of numbers and understand
the inverse nature of powers and roots.
Discovering Algebra Chapter 10
Teacher-created problems
Finding the length of the edge of
a cube knowing volume
Do Now
Quiz/Test
Teacher Observation
3. Solve problems involving proportions and
percents.
Discovering Algebra Chapters 7-12
Math Counts
4.1.B 7th Algebra 1B 110
· What makes a computational strategy both effective and efficient?
· How do operations affect numbers?
· How do mathematical representations reflect the needs of society across cultures?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
B. Numerical OperationsEssential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Understand and apply the laws of exponents
to simplify expressions involving numbers and
variables raised to powers.
Discovering Algebra Chapter 7
Developing Skills in Algebra One
Book B
Algebra with Pizzazz!
Lesson Investigations 7.1, 7.5,
7.6, 7.7
Skittle Activity
U.S. Census Activity
Do Now
Quiz/Test
Teacher Observation
4.1.B 7th Algebra 1B 111
C. Estimation
· How can we decide when to use an exact answer and when to use an estimate?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Estimate square and cube roots of numbers. Teacher-Created Problems
Discovering Algebra 10.8
Lesson Investigation 10.8 Mental Practice
Calculator Teacher
Observation
2. Recognize the limitations of estimation and
assess the amount of error resulting from
estimation.
National Council of Teachers of
Mathematics – Data Analysis and
Statistics Addenda series
Physically measure lengths and
discuss why disparities occur
when using π or 3.14 for surface
area and volumes (cones and
cylinders)
Measure/Justify
4.1.C 7th Algebra 1B
112
Standard 4.2 Geometry and Geometrical Properties
· How can spatial relationships be described by careful use of geometric language?
· How do geometric relationships help to solve problems and/or make sense of phenomena?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
A. Geometric Properties
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply the Pythagorean
Theorem.
Navigating through Geometry 9-12
Geometer’s Sketchpad
Discovering Algebra Chapter 11
Math Counts
Real-world application problems Do Now
Teacher Observation
2. Understand and apply the concept of
similarity: Using proportions to find missing
measures; Scale drawings; Models of 3D
objects.
Discovering Algebra Chapter 9
Geometer’s Sketchpad
Lesson Investigations
Manipulatives
Quiz/Test
Do Now
Teacher Observation
3. Use logic and reasoning to make and
support conjectures about geometric objects.
Navigating through Geometry 9-12
Teacher-created problems
Geometer’s Sketchpad
Direct Instruction Teacher Observation
4.2.A 7th Algebra 1B
113
Standard 4.2 Geometry and Geometrical Properties
· What situations can be analyzed using transformations and symmetries?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
B. Transforming Shapes
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
UCSMP Transitions Lesson
Masters
UCSMP Transitions Chapter 8
Navigating through Geometry 9-12
Discovering Algebra Chapters 9 &
11
Lesson Investigation 9.4
Use calculator to compare
graphs of equations that involve
transformations
Geometer’s Sketchpad
Do Now
Quiz/Test
Coordinate grid drawings
Teacher Observation
4.2.B 7th Algebra 1B
114
Standard 4.2 Geometry and Geometrical Properties
· How can geometric/algebraic relationships best be represented and verified?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
C. Coordinate Geometry
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use coordinate geometry to represent and
verify properties of lines.
• Finding the intersection of two lines
• Lines with the same slope are parallel
• Lines that are perpendicular have slopes
whose product is -1
Discovering Algebra Chapter 6 &
11
Geometer’s Sketchpad
More Practice with Yours Skills
Lesson Investigations 11.1, 11.2
Lesson Investigations 6.1, 6.2,
6.3
Graphing Calculator work
Applications in coordinate
geometry
Do Now
Quiz/Test
Teacher Observation
4.2.C 7th Algebra 1B 115
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
D. Units of Measurement
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use appropriate equivalents between
standard and metric systems to estimate
measurements (e.g., kilometers is about 3
miles)
Discovering Algebra Chapters 6-11 Appropriate use throughout
Lesson Investigations
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
2. Recognize that the degree of precision
needed in calculations depends on how the
results will be used and the instruments used
to generate the measurements.
Discovering Algebra Chapters 6-11 Appropriate use throughout
Lesson Investigations
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
3. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
Discovering Algebra Chapters 6-11 Appropriate use throughout
Lesson Investigations
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.2.D 7th Algebra 1B
116
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
D. Units of Measurement
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Recognize that all measurements of
continuous quantities are approximations.
Discovering Algebra Chapters 6-11 Appropriate use throughout
Lesson Investigations
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
5. Solve problems that involve compound
measurement units, such as speed (miles per
hour), air pressure (pounds per square inch),
and population density (persons per square
mile).
Discovering Algebra Chapters 6-11 Appropriate use throughout
Lesson Investigations
Do Now
Teacher-Created problems
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.2.D 7th Algebra 1B
117
Standard 4.2 Geometry and Geometrical Properties
· How can measurements be used to solve problems?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Essential Questions :
E. Measuring Geometric Objects
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Develop and apply strategies for finding
perimeter and area: Impact of a dilation on
the perimeter and area of a 2-dimensional
figure.
Geometer’s Sketchpad
Math Counts
Teacher-created materials
Cooperative Investigations Learnia
NJ ASK Coach
2. Develop and apply strategies and formulas
for finding the volume of a three-dimensional
figure.
Geometer’s Sketchpad
Math Counts
Teacher-created materials
Cooperative Investigations Learnia
NJ ASK Coach
3. Impact of a dilation on the volume of a
three-dimensional figure.
Geometer’s Sketchpad
Math Counts
Teacher-created materials
Cooperative Investigations Learnia
NJ ASK Coach
4. Use formulas to find the volume of a sphere. Geometer’s Sketchpad
Math Counts
Teacher-created materials
Cooperative Investigations Learnia
NJ ASK Coach
5. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height
Geometer’s Sketchpad
Math Counts
Teacher-created materials
Cooperative Investigations Learnia
NJ ASK Coach
4.2.E 7th Algebra 1B 118
· How can change be best represented mathematically?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
A. Patterns Essential Questions :
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize, describe, extend, and create
patterns involving whole numbers, rational
numbers, and integers: Descriptions using
tables, verbal and symbolic rules, graphs,
simple equations or expressions; Finite and
infinite sequences; Arithmetic sequences (i.e.,
sequences generated by repeated addition of a
fixed number, positive or negative); Geometric
sequences (i.e., sequences generated by
repeated multiplication by a fixed positive
ratio, greater than 1 or less than 1);
Generating sequences by using calculators to
repeatedly apply a formula.
Discovering Algebra Chapters 6-11
Teacher-created materials
Navigating through Algebra Grades
9-12
Lesson Investigations 7.1, 7.2,
7.7
Given terms in a pattern,
describe patterns in words
Recursive investigations
Real-world problem solving
U.S. Census Activity
Do Now
Quiz/Test
Teacher Observation
4.3.A 7th Algebra 1B
119
· How are patterns of change related to the behavior of functions?
Resources
Direct Instruction
Lesson Investigation
Real-world problems
Lesson Investigations from
Chapter 8
Do Now
Quiz/Test
Teacher Observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
B. Functions and Relationships
2. Recognize and describe the difference
between linear and exponential growth, using
tables, graphs, and equations.
Discovering Algebra Chapter 7 Lesson Investigations 7.1, 7.2,
7.7
Skittle Activity
Do Now
Quiz/Test
Teacher Observation
Written Explanations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Graph functions, and understand and
describe their general behavior: Equations
involving two variables; Equations involving
two variables; Rates of change (informal
notion of slope).
Discovering Algebra Chapters 5-11
4.3.B 7th Algebra 1B
120
· How can mathematical models be used to describe physical relationships?
· How can physical models be used to clarify mathematical relationships?
Resources
Direct Instruction
Lesson Investigations 8.1, 8.3,
8.4, 8.5, 8.7
Teacher observation
Do Now
Quiz/Test
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
C. Modeling
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations: Using
concrete materials (manipulatives), tables,
graphs, verbal rules, algebraic expressions/
equations/ inequalities; Growth situations,
such as population growth and compound
interest, using recursive (e.g., NOW-NEXT)
formulas (cf. science standards and social
studies standards).
Discovering Algebra Chapter 7 Lesson Investigations 7.1, 7.7
Direct Instruction
Do Now
Quiz/Test
Teacher Observation
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
Discovering Algebra Chapters 6-11
4.3.C 7th Algebra 1B 121
· What makes an algebraic algorithm both effective and efficient?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use graphing techniques on a number line:
Absolute value.
Discovering Algebra Chapter 9 Direct Instruction
Geometer’s Sketchpad
Do Now
Quiz/Test
Teacher Observation
2. Solve simple linear equations informally,
graphically, and using formal algebraic
methods: Multi-step, integer coefficients only
(although answers may not be integers);
Absolute value; Compound inequalities;
Rational expressions; Using paper-and-pencil,
calculators, graphing calculators,
spreadsheets, and other technology.
Discovering Algebra Chapters 5 &
6
Teacher-created material
Direct Instruction
Lesson Investigation 6.5
Do Now
Quiz/Test
Teacher Observation
3. Solve systems of equations:
• Graphically
• Algebraic methods
Discovering Algebra Chapter 6
Developing Skills in Algebra One
Book B
Direct Instruction
Lesson Investigations 6.1, 6.2
Graphing Calculator
Do Now
Quiz/Test
Teacher Observation
Teacher-Created materials
4.3.D 7th Algebra 1B
122
· What makes an algebraic algorithm both effective and efficient?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Direct instruction Do Now
Quiz/Test
Teacher Observation
Teacher-Created materials
6. Evaluate and simplify algebraic
expressions:
• Add and subtract polynomials
• Multiply a polynomial by a monomial or
binomial
• Divide a polynomial by a binomial
• Use laws of exponents
Discovering Algebra Chapters 6-11
Developing Skills in Algebra One
Books B-D
Teacher-Created materials
Direct Instruction
Algebra Tiles
Do Now
Quiz/Test
Teacher Observation
Teacher-Created materials
4. Factor polynomials Discovering Algebra Chapter 10
Developing Skills in Algebra One
Book B
Direct Instruction
Algebra Tiles
Do Now
Quiz/Test
Teacher Observation
5. Rational Expressions
• Add and Subtract
• Multiply and Divide
Developing Skills in Algebra One
Book D
Teacher-Created materials
4.3.D 7th Algebra 1B
123
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can the collection, organization, interpretation, and display of data be used to answer
questions?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode); Finding
the median and mean (weighted average)
using frequency data; Effect of additional data
on measures of central tendency.
Math Counts Graphing Calculator
Teacher-created problems
Class Discussion
Teacher-created problems
Graphing Calculator
Teacher Observation
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data sets.
Navigation through Data Analysis
Grades 6-8
Discovering Algebra Chapters 6-10
Prediction
Using graphing calculator to
show two statistical graphs at the
same time to compare various
statistical averages
Graphing Calculator
Teacher Observation
3. Estimate lines of best fit and use them to
interpolate within the range of the data.
Discovering Algebra Chapter 5
TinkerPlots
Internet Resources
Lesson Investigation 5.6
Class Discussion
Internet Resources
TinkerPlots Activities
Do Now
Graphing Calculator
Quiz/Test
Teacher Observation
Discussion of Lesson
Investigation
4.4.A 7th Algebra 1B 124
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Determine probabilities of compound
events.
Connected Mathematics “What Do
You Expect?"
USCMP Transitions
Manipulatives
Use of collaborative
investigations
Teacher-created problems
2. Explore the probabilities of conditional
events.
Connected Mathematics “What Do
You Expect?"
USCMP Transitions
Manipulatives
Use of collaborative
investigations
Teacher-created problems
3. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
Dealing with Data and Chance –
National Council of Teachers of
Mathematics Addenda Series
Navigating through Data and
Chance Grades 6-8
Graphing calculator probability
simulation programs
Teacher observation
Written explanation of how
the two ideas are related in
given situations
4. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
Dealing with Data and Chance –
National Council of Teachers of
Mathematics Addenda Series
Navigating through Data and
Chance Grades 6-8
Graphing calculator probability
simulation programs
Investigation write-up
4.4.B 7th Algebra 1B 125
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can experimental and theoretical probabilities be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Play and analyze probability-based games,
and discuss the concepts of fairness and
expected value.
Connected Mathematics “What Do
You Expect?"
Math Counts
Analyze size of sections on dart
boards for area versus
probability
Investigation write-up
4.4.B 7th Algebra 1B 126
· What counting strategy works best here?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Direct Instruction
Manipulatives
Investigations
Textbook-generated
quizzes and tests
Essential Questions :
· How can attributes be used to classify data/objects?
· What is the best way to solve this?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
Math Counts
Connected Mathematics “What Do
You Expect?”
Direct Instruction
Manipulatives
Investigations
Textbook-generated
quizzes and tests
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement (e.g., number of possible
license plates) vs. ordered situations without
replacement (e.g., number of possible slates of
3 class officers from a 23 student class).
Math Counts
Connected Mathematics “What Do
You Expect?”
UCSMP Algebra
Direct Instruction
Manipulatives
Investigations
Textbook-generated
quizzes and tests
2. Explore counting problems involving Venn
diagrams with three attributes.
Math Counts
Connected Mathematics “What Do
You Expect?”
4.4.C 7th Algebra 1B 127
· How can visual tools such as networks (vertex-edge graphs) be used to answer questions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
· How can algorithmic thinking be used to solve problems?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use vertex-edge graphs and algorithmic
thinking to represent and find solutions to
practical problems: Finding the shortest
network connecting specified sites; Finding a
minimal route that includes every street (e.g.,
for trash pick-up); Finding the shortest route
on a map from one site to another; Finding the
shortest circuit on a map that makes a tour of
specified sites.
Rutgers workshop on Discrete
Mathematics
Teacher-created materials
Rutgers prepared worksheets
Write a tour guide with map
Teacher-Created
worksheets
Teacher-created quiz
Tour Guide Project
4.4.D 7th Algebra 1B 128
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
Discovering Algebra Chapters 6-11
Website Standards
www.nctm.org
Connected Math Series
Geometer’s Sketchpad
TinkerPlots
Math Counts
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
Question Quest level C
Teacher-Created Materials
Connected Math Series
Geometer’s Sketchpad
Tinkerplots
Math Counts
Students analyze each others
written responses
Share solution methods
Written Explanations
4.5.A 7th Algebra 1B
129
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
Math Counts
Question Quest level C
Connected Math Series
Geometer’s Sketchpad
TinkerPlots
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4. Pose problems of various types and levels of
difficulty.
Math Counts
Question Quest level C
Connected Math Series
Geometer’s Sketchpad
TinkerPlots
4.5.A 7th Algebra 1B
130
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
A. Problem SolvingEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Monitor their progress and reflect on the
process of their problem solving activity.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.A 7th Algebra 1B
131
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.B 7th Algebra 1B
132
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Analyze and evaluate the mathematical
thinking and strategies of others.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4. Use the language of mathematics to express
mathematical ideas precisely.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.B 7th Algebra 1B
133
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.C 7th Algebra 1B 134
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4. Apply mathematics in practical situations
and in other disciplines.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.C 7th Algebra 1B 135
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
C. ConnectionsEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Trace the development of mathematical
concepts over time and across cultures (cf.
world languages and social studies standards).
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Class Discussions
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Class Discussions
4.5.C 7th Algebra 1B 136
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Give examples and
counterexamples
Written Explanations
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.D 7th Algebra 1B 137
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Select and use various types of reasoning
and methods of proof.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Share methods
Students analyze each others’
responses
Written Explanations
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Estimations and predictions Written Explanations
4.5.D 7th Algebra 1B 138
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Test x ^2 > x for all real
numbers
Written Explanations
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
New Jersey Frameworks
National Council of Teachers of
Mathematics: Curriculum and
Evaluation Standards for School
Mathematics
Elementary and Middle School
Mathematics
Strategies for Success Level G
Brainstorming
Journaling
Classroom Discussion
Predictions
Written Explanations
4.5.D 7th Algebra 1B 139
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
E. Representations
Brainstorming
Journaling
Classroom Discussion
Written Explanations
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
Discovering Algebra Chapters 6-11
Math Counts
Algebra Out Loud
Navigating Algebra grades 9-12
Use algebra tiles to show
multiplication of polynomials
Use tables to find algebraic
functions relating quantities
Use area formula and graphing
calculator to predict maximum
area
Graphs
Written Explanations
2. Select, apply, and translate among
mathematical representations to solve
problems.
Discovering Algebra Chapters 6-11
Math Counts
Algebra Out Loud
Navigating Algebra grades 9-12
4.5.E 7th Algebra 1B
140
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
E. Representations Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
Discovering Algebra Chapters 6-11
Math Counts
Algebra Out Loud
Navigating Algebra grades 9-12
Brainstorming
Journaling
Classroom Discussion
Written Explanations
4.5.E 7th Algebra 1B
141
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
Discovering Algebra Chapters 6-11
Geometer's Sketchpad
Use graphing calculator or
computer to compare various
ways of finding “Line of best fit”
Written Explanations
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
Discovering Algebra Chapters 6-11
Geometer's Sketchpad
Compare two teams batting
averages using various graphical
representations
Written Explanations
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
Discovering Algebra Chapters 6-11
Geometer's Sketchpad
Graph rational expressions and
discuss asymptotes
Written Explanations
4.5.F 7th Algebra 1B
142
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
Standard 4.5 Mathematical Processes
F. TechnologyEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
Discovering Algebra Chapters 6-11
Developing Number Sense
Addenda series National Council of
Teachers of Mathematics
Discover patterns from positive
to negative through investigation
with graphing calculator
Written Explanations
5. Use computer software to make and verify
conjectures about geometric objects.
Discovering Algebra Chapters 6-11
Geometer’s Sketchpad
Test Triangle Similarity
Theorem
Written Explanations
6. Use computer-based laboratory technology
for mathematical applications in the sciences.
Core math textbooks
Various workbooks
Teacher-created materials
Use CBL’s to collect data on
motion sensor or temperature
and analyze for algebraic
patterns
Written Explanations
4.5.F 7th Algebra 1B
143
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1B
Pacing Guide
UnitDiscovering Algebra
ChapterNumber of Blocks
Linear Equations 5 8
Graphing, Slope, and Writing the Equation of
a Line
5 8
Systems of Equations and Inequalities 6 10
Exponents and Exponential Models 7 12
Functions 8 10
Transformations 9 11
Polynomials Developing Skills in Algebra
One Books A-D
7
Radicals Developing Skills in Algebra
One Books A-D
6
Quadratics 10 12
Rational Expressions Developing Skills in Algebra
One Books A-D
4
7th Grade Algebra 1B Pacing Guide 144
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1B
Resources
Title of Resource Author(s) Publisher Copyright
Discovering Algebra An Investigative
Approach
Jerald Murdock, Ellen Kamischke,
Eric Kamischke
Key Curriculum Press 2002
Developing Skills in Algebra One - Books A
and B
Harold and Loretta Taylor Dale Seymour Publications 1984
Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
LL Teach, Inc. 2002
Pre-Algebra with Pizzazz! Steve & Janis Marcy McGraw Hill 2002
Algebra Out Loud Pat Mower, PhD Jossey Bass 2003
New Jersey ASK Coach Jerome Kaplan Ed.D Triumph Learning 2005
Question Quest Level C Paul Lawrence
UCSMP Transitions Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
UCSMP Algebra Lesson Masters A and B Zal Usiskin Scott, Foresman 1995
Tinker Plots Clifford Konold & Craig D. Miller Key Curriculum Press 2005
Geometer's Sketchpad 4 Nicholas Jackiw Key Curriculum Press 2006
Algebra Puzzles & Problems Greenes/Findell Creative Publications 1998
7th Grade Algebra 1B Resources
145
Flemington Raritan School District
Mathematics Curriculum
Grades 7-8
7th Grade Algebra 1B
Resources
Title of Resource Author(s) Publisher Copyright
Algebra Teacher's Activities Kit Judith & Robert Muschla Jossey Bass 2003
Explain It Lepore, Fleetwood & Hall Creative Publications 2001
ASK Workout Jerome Kaplan Ed.D Triumph Learning 2008
Hands -On Algebra ! Frances M. Thompson The Center for Applied Research
Education
1998
Teaching Student-Centered Mathematics
Grades 5-8
John A. Van de Walle & LouAnn
H. Lovin
Pearson Education 2006
Key Curriculum Press 2003
NCTM Navigation Series: Algebra Burke, Erickson, Lott, Obert The National Council of
Teachers of Mathematics
2001
Strategies for Success in Mathematics: Level
G
Weisenfeld, Coultas, Swalm Steck-Vaugh Company 1999
Geometry Activities for Middle School
Students
Wyatt, Lawrence, Foletta Key Curriculum Press 2004
Shape Makers: Developing Geometric
Reasoning in Middle School
Michael T. Battista
Curriculum and Evaluation Standards for
School Mathematics Addenda Series Grades 9-
12
Burrill The National Council of
Teachers of Mathematics
1992
7th Grade Algebra 1B Resources
146
8th Grade Curriculum
147
4.1.B.1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation with
integers and all number types named above with: Pencil-
and-paper; Mental math; Calculator.
Science Wave activity
4.1.A.2. Demonstrate a sense of the relative magnitudes
of numbers.
Science
Social Studies
Astronomy Unit
Holocaust Unit - visual representation of
numbers
4.1.A.5. Use computer software to make and verify
conjectures about geometric objects.
Technology Creating models
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
4.1.A.1. Extend understanding of the number system by
constructing meanings for the following (unless
otherwise noted, all indicators for grade 8 pertain to
these sets of numbers as well): Rational numbers;
Percents; Exponents; Roots; Absolute Values; Numbers
represented in scientific notation.
Science Astronomy Unit
4.1.A.3. Understand and use ratios, rates, proportions,
and percents (including percents greater than 100 and
less than 1) in a variety of situations.
Science
Music
Art
Cooking
Genetics - Punnet Squares
Chemistry
Notes (1/4,1/16)
Scale Drawing
Recipes
8th Grade Interdisciplinary Connections 148
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
4.2.A.1. Understand and apply concepts involving lines,
angles, and planes: Complementary and supplementary
angles; Vertical angles; Bisectors and perpendicular
bisectors; Parallel, perpendicular, and intersecting
planes; Intersection of plane with cube, cylinder, cone,
and sphere.
Sewing Creating quilts
4.2.A.4. Understand and apply the concept of similarity:
Using proportions to find missing measures; Scale
drawings; Models of 3D objects.
Technology
Art
Creating Models
Scale drawings, creating lables for cans
4.2.A.3. Understand and apply properties of polygons:
Quadrilaterals, including squares, rectangles,
parallelograms, trapezoids, rhombi; Regular polygons;
Sum of measures of interior angles of a polygon; Which
polygons can be used alone to generate a tessellation and
why.
4.1.B.4. Solve problems involving proportions and
percents.
Science Labs throughout the year
4.1.C.2. Use equivalent representations of numbers such
as fractions, decimals, and percents to facilitate
estimation.
Science Labs throughout the year
Art Polygon project and tessellations
4.1.C.3. Recognize the limitations of estimation and
assess the amount of error resulting from estimation.
Science Labs throughout the year
8th Grade Interdisciplinary Connections 149
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
4.2.B.1. Understand and apply transformations: Finding
the image, given the pre-image, and vice-versa;
Sequence of transformations needed to map one figure
onto another; Reflections, rotations, and translations
result in images congruent to the pre-image; Dilations
(stretching/shrinking) result in images similar to the pre-
image.
Art Reflections and rotations
Science On-going through science labs, metric
system
4.2.C.1. Use coordinates in four quadrants to represent
geometric concepts.
Social Studies Reading a map
4.2.D.2. Use approximate equivalents between standard
and metric systems to estimate measurements (e.g.,
kilometers is about 3 miles).
Science Ongoing through science labs, metric
system
4.2.D.1. Solve problems requiring calculations that
involve different units of measurement within a
measurement system (e.g., 4’3” plus 7’10” equals 12’1”).
4.2.E.1. Develop and apply strategies for finding
perimeter and area: Geometric figures made by
combining triangles, rectangles and circles or parts of
circles; Estimation of area using grids of various sizes;
Impact of a dilation on the perimeter and area of a 2-
dimensional figure; Impact of a dilation on the
perimeter and area of a 2-dimensional figure.
Sewing
Art
Creating a quilt
Polygon project
8th Grade Interdisciplinary Connections 150
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
Science Half-life lab
4.3.C.2. Use patterns, relations, symbolic algebra, and
linear functions to model situations: Using concrete
materials (manipulatives), tables, graphs, verbal rules,
algebraic expressions/ equations/ inequalities; Growth
situations, such as population growth and compound
interest, using recursive formulas.
Social Studies Population growth
4.3.B.1. Graph functions, and understand and describe
their general behavior: Equations involving two
variables; Rates of change (informal notion of slope).
4.3.C.1. Analyze functional relationships to explain how
a change in one quantity can result in a change in
another, using pictures, graphs, charts, and equations.
Science Labs throughout the year
4.3.B.2. Recognize and describe the difference between
linear and exponential growth, using tables, graphs, and
equations.
Social Studies Population growth, immigration information
8th Grade Interdisciplinary Connections 151
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
Social Studies
Science
Current events
Environmental unit
4.3.D.2. Solve simple linear equations informally,
graphically, and using formal algebraic methods:
Multi-step, integer coefficients only (although answers
may not be integers) Simple literal equations (e.g., A =
lw) Using paper-and-pencil, calculators, graphing
calculators, spreadsheets, and other technology.
Science Equation balancing in chemistry
Social Studies Current events
4.4.A.2. Make inferences and formulate and evaluate
arguments based on displays and analysis of data sets.
Social Studies Data analysis from graphs
4.4.A.1. Select and use appropriate representations for
sets of data, and measures of central tendency (mean,
median, and mode): Type of display most appropriate
for given data; Box-and-whisker plot, upper quartile,
lower quartile; Scatter plot; Calculators and computer
used to record and process information; Finding the
median and mean (weighted average) using frequency
data; Effect of additional data on measures of central
tendency.
4.4.A.3. Estimate lines of best fit and use them to
interpolate within the range of the data.
Science Half-life graphs
4.4.A.4. Use surveys and sampling techniques to
generate data and draw conclusions about large groups.
8th Grade Interdisciplinary Connections 152
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
Reading skills
Physical Education
4.4.D.1. Use vertex-edge graphs and algorithmic
thinking to represent and find solutions to practical
problems: Finding the shortest network connecting
specified sites; Finding a minimal route that includes
every street; Finding the shortest route on a map from
one site to another; Finding the shortest circuit on a
map that makes a tour of specified sites; Limitations of
computers.
Science
Social Studies
Circuit labs
Shortest route on a map
4.5.A.2. Solve problems that arise in mathematics and in
other contexts: Open-ended problems; Non-routine
problems; Problems with multiple solutions; Problems
that can be solved in several ways.
Language Arts
Fairness of games
4.4.C.3. Apply techniques of systematic listing, counting,
and reasoning in a variety of different contexts.
All disciplines Discussions throughout
4.4.B.6. Play and analyze probability-based games and
discuss the concepts of fairness and expected value.
All disciplines Discussions throughout4.5.A.4. Pose problems of various types and levels of
difficulty.
4.5.A.5. Monitor their progress and reflect on the
process of their problem solving activity.
All disciplines Discussions throughout
8th Grade Interdisciplinary Connections 153
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
4.5.B.1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Language Arts Ongoing throughout
Ongoing throughout
Scientific method
All disciplines Discussions throughout
4.5.C.4. Apply mathematics in practical situations and
in other disciplines.
All disciplines Discussions throughout
4.5.D.3. Select and use various types of reasoning and
methods of proof.
Discussions and persuasive essays
4.5.C.3. Recognize that mathematics is used in a variety
of contexts outside of mathematics.
4.5.C.5. Trace the development of mathematical
concepts over time and across cultures.
Social Studies
World Languages
Discussions throughout
Discussions throughout
4.5.B.2. Communicate mathematical thinking coherently
and clearly to peers, teachers, and others, both orally
and in writing.
Science
All disciplines Discussions throughout
Language Arts
4.5.D.5. Make and investigate mathematical conjectures:
Counterexamples as a means of disproving conjectures;
Verifying conjectures using informal reasoning or
proofs.
Science
4.5.D.4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of their
problem solutions.
8th Grade Interdisciplinary Connections 154
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard Subject
8th Grade Interdisciplinary Connections
Learning Experience
Science Scientific method
4.5.E.1. Create and use representations to organize,
record, and communicate mathematical ideas: Concrete
representations (e.g., base-ten blocks or algebra tiles);
Pictorial representations (e.g., diagrams, charts, or
tables); Symbolic representations (e.g., a formula);
Graphical representations (e.g., a line graph).
Science Data collection from labs
Creating excel spreadsheets
4.5.F.5. Use computer software to make and verify
conjectures about geometric objects.
Technology Creating models
4.5.F.2. Use computer spreadsheets, software, and
graphing utilities to organize and display quantitative
information.
4.5.D.6. Evaluate examples of mathematical reasoning
and determine whether they are valid.
Software Applications
8th Grade Interdisciplinary Connections 155
Pre-Algebra Curriculum
156
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 8 pertain to these sets of numbers as
well): Rational numbers; Percents;
Exponents; Roots; Absolute Values; Numbers
represented in scientific notation.
- Students calculate relative
change in quantity
- Number line in classroom
- Students use calculators to
work with numbers with more
than 10 digits
McDougal Littell
7.3 - 7.7 (Rational Numbers)
1.4, 4.6, 4.7 (Exponents)
9.1 (Roots)
2.1 (Absolute Value)
4.8 (Scientific Notation)
_______________________
Holt
Ch. 6 (Rational Numbers)
4.1 - 4.3 (Exponents)
4.5 - 4.6 (Roots)
1.3 (Absolute Value)
4.4 (Scientific Notation)
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Students discuss why
numbers are easier to
compare when written in
scientific notation
Essential Questions :
Assessments
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7 - 8
4.1.A 8th Grade Pre-Algebra 157
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Essential Questions :
Assessments
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7 - 8
4. Compare and order numbers of all named
types.
McDougal Littell
2.1 - 2.5
_______________________
Holt
2.3 - 2.5
2. Demonstrate a sense of the relative
magnitudes of numbers.
- Geometer's Sketchpad
- Activity to show integers on a
number line
- Students use real world data to
discover relationships of
numbers
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Ongoing in all investigations
McDougal Littell
7.1 - 7.7, 8.8
_______________________
Holt
5.1 - 5.4, 5.5
McDougal Littell
2.1, 5.5
_______________________
Holt
2.2
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations.
4.1.A 8th Grade Pre-Algebra 158
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Essential Questions :
Assessments
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7 - 8
McDougal Littell
4.3, 4.5, 5.1 - 5.7, 7.3 - 7.7
_______________________
Holt
6.1 - 6.6
Do Now
Written assessments
Teacher Observation
5. Use computer software to make and verify
conjectures about geometric objects.
Classwork Activity/Accuracy
of Student work
7. Construct meanings for common irrational
numbers, such as pi (π) and the square root of
two.
McDougal Littell
9.2
_______________________
Holt
4.5 - 4.6
Students explore irrational
numbers through Pythagorean's
Theorem
Classwork Activity/Accuracy
of Student work
6. Recognize that repeating decimals
correspond to fractions and determine their
fractional equivalents:
5/7 = 0.714285714285...
= 0.714285
McDougal Littell
5.5
_______________________
Holt
2.1 - 2.6
Calculator Exploration
Ongoing in all investigations
4.1.A 8th Grade Pre-Algebra 159
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
Technology exploration
Do Now
Written assessments
Teacher Observation
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Pencil-and-paper; Mental math;
Calculator.
McDougal Littell
2.2 - 2.5
_________________________
Holt
1.4 - 1.6
3. Find square and cube roots of numbers and
understand the inverse nature of powers and
roots.
McDougal Littell
9.1
_________________________
Holt
4.5 - 4.6
2. Use exponentiation to find whole number
powers of numbers.
Technology exploration
McDougal Littell
4.6 - 4.8
_________________________
Holt
4.1 - 4.4
· How can we compare and contrast numbers?
Do Now
Written assessments
Teacher Observation
Ongoing in all investigations
Standard 4.1 Number and Numerical Operations
AssessmentsLearning ExperiencesKnowledge/Skills/Understanding
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Pencil-and-paper; Mental math;
Calculator.
B. Numerical OperationsEssential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4.1.B 8th Grade Pre-Algebra 160
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
· How can we compare and contrast numbers?
Standard 4.1 Number and Numerical Operations
AssessmentsLearning ExperiencesKnowledge/Skills/Understanding
B. Numerical OperationsEssential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
5. Understand and apply the standard
algebraic order of operations, including
appropriate use of parentheses.
McDougal Littell
1.2
_________________________
Holt
1.1
Do Now
Written assessments
Teacher Observation
Ongoing in all investigations
4. Solve problems involving proportions and
percents.
Do Now
Written assessments
Teacher Observation
McDougal Littell
7.2 - 7.7
_________________________
Holt
5.1, 5.4, 6.2 - 6.6
Solving real world problems
4.1.B 8th Grade Pre-Algebra 161
C. Estimation
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
· How can we compare and contrast numbers?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Estimate square and cube roots of numbers. NJ Frameworks Students use the multiplication
function to perform successive
approximations to find
acceptable values for several
square roots (the square roots of
2, 3, 7, 19 and the cube roots of
10 and 100)
Do Now
Written assessments
Teacher Observation
2. Use equivalent representations of numbers
such as fractions, decimals, and percents to
facilitate estimation.
McDougal Littell
7.4
_______________________
Holt
6.1
Ongoing through investigations Do Now
Written assessments
Teacher Observation
4.1.C 8th Grade Pre-Algebra 162
C. Estimation
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
· How can we compare and contrast numbers?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Recognize the limitations of estimation and
assess the amount of error resulting from
estimation.
NJ Frameworks Students make estimates of the
number of times things happen in
a lifetime and compare
estimations to referenced
materials
Do Now
Written assessments
Teacher Observation
4.1.C 8th Grade Pre-Algebra 163
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.2 Geometry and Geometrical Properties
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Geometric Properties
Grades 7 - 8
Essential Questions :
2. Understand and apply the Pythagorean
Theorem.
McDougal Littell
9.3 - 9.4
_______________________
Holt
4.8
- Using manipulatives
- Geometer's Sketchpad
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Understand and apply concepts involving
lines, angles, and planes: Complementary and
supplementary angles; Vertical angles;
Bisectors and perpendicular bisectors;
Parallel, perpendicular, and intersecting
planes; Intersection of plane with cube,
cylinder, cone, and sphere.
McDougal Littell
8.1 - 8.2
_______________________
Holt
7.1 - 7.2
Geometer's Sketchpad Do Now
Written assessments
Teacher Observation
4.2.A 8th Grade Pre-Algebra 164
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.2 Geometry and Geometrical Properties
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Geometric Properties
Grades 7 - 8
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences Assessments
- Direct instruction
- Using manipulatives
McDougal Littell
8.8
_______________________
Holt
5.5
Use proportions to investigate
real world problems
Do Now
Written assessments
Teacher Observation
3. Understand and apply properties of
polygons: Quadrilaterals, including squares,
rectangles, parallelograms, trapezoids,
rhombi; Regular polygons; Sum of measures
of interior angles of a polygon; Which
polygons can be used alone to generate a
tessellation and why.
McDougal Littell
8.3 - 8.4
_______________________
Holt
7.4
4. Understand and apply the concept of
similarity: Using proportions to find missing
measures; Scale drawings; Models of 3D
objects.
Do Now
Written assessments
Teacher Observation
4.2.A 8th Grade Pre-Algebra 165
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.2 Geometry and Geometrical Properties
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Geometric Properties
Grades 7 - 8
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences Assessments
5. Use logic and reasoning to make and
support conjectures about geometric objects.
McDougal Littell
Ch. 8
_______________________
Holt
Ch. 7
Ongoing through Geometry
Investigations
Do Now
Written assessments
Teacher Observation
4.2.A 8th Grade Pre-Algebra 166
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources Assessments
Do Now
Written assessments
Teacher Observation
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
Standard 4.2 Geometry and Geometrical Properties
McDougal Littell
8.6 - 8.8
_______________________
Holt
7.7
- Exploring through Geometer's
Sketchpad
- Rotation art activity
Students describe sizes,
positions, orientation of
shapes such as flips, slides,
turns, and scaling
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding
2. Use iterative procedures to generate
geometric patterns: Fractals (e.g., the Koch
Snowflake); Self-similarity; Construction of
initial stages; Patterns in successive stages
(e.g., number of triangles in each stage of
Sierpinski’s Triangle).
NJ Frameworks - Students explore shapes with
tangrams
- Students build a Sierpinski's
Triangle
B. Transforming Shapes
Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4.2.B 8th Grade Pre-Algebra 167
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.2 Geometry and Geometrical Properties
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
C. Coordinate Geometry
Learning Experiences
1. Use coordinates in four quadrants to
represent geometric concepts.
McDougal Littell
2.8
_______________________
Holt
7.5
Students explore properties of
shapes in a coordinate system
Do Now
Written assessments
Teacher Observation
2. Use a coordinate grid to model and quantify
transformations (e.g., translate right 4 units).
McDougal Littell
8.7
_______________________
Holt
7.7
Students will perform
transformations on a coordinate
grid
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding
4.2.C 8th Grade Pre-Algebra 168
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Essential Questions : Essential Questions :
Standard 4.2 Geometry and Geometrical Properties
Accuracy of student work
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
D. Units of Measurement
Do Now
Written assessments
Teacher Observation
Students plan a new Olympics by
renaming standard events in
different measurement units
Learning Experiences
1. Solve problems requiring calculations that
involve different units of measurement within
a measurement system (e.g., 4’3” plus 7’10”
equals 12’1”).
3. Recognize that the degree of precision
needed in calculations depends on how the
results will be used and the instruments used
to generate the measurements.
Students develop a project, for
example, scale drawing of an
apartment floor plan
Knowledge/Skills/Understanding
McDougal Littell
7.1
_______________________
Holt
5.2
Using real life examples
2. Use approximate equivalents between
standard and metric systems to estimate
measurements (e.g., kilometers is about 3
miles).
NJ Frameworks
NJ Frameworks
Ongoing with all measurement
activities
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Students reflect on close they
are to degree of accuracy and
how it affects results
4.2.D 8th Grade Pre-Algebra 169
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Essential Questions : Essential Questions :
Standard 4.2 Geometry and Geometrical Properties
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
D. Units of Measurement
Learning ExperiencesKnowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Students are asked to find the
height of a tall tree if the
height of a small tree is
known
Using real life examples
6. Solve problems that involve compound
measurement units, such as speed (miles per
hour), air pressure (pounds per square inch),
and population density (persons per square
mile).
Teacher created materials
Various workbooks
Students will use their
knowledge of mathematics to
plan and carry out scientific
experimentation
Reflection on results of
student created experiments
Teacher created materials
Various workbooks
5. Recognize that all measurements of
continuous quantities are approximations.
Teacher created materials
Various workbooks
Using real life examples Do Now
Written assessments
Teacher Observation
4. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
4.2.D 8th Grade Pre-Algebra 170
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
Essential Questions :
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
E. Measuring Geometric Objects
2. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height (e.g.,
use rice to compare volumes of figures with
same base and height).
McDougal Littell
10.7
_______________________
Holt
8.6
Teacher demonstration with
manipulatives
Do Now
Written assessments
Teacher Observation
1. Develop and apply strategies for finding
perimeter and area: Geometric figures made
by combining triangles, rectangles and circles
or parts of circles; Estimation of area using
grids of various sizes; Impact of a dilation on
the perimeter and area of a 2-dimensional
figure; Impact of a dilation on the perimeter
and area of a 2-dimensional figure.
McDougal Littell
1.6, 10.1 - 10.2
_______________________
Holt
8.1 - 8.3
Students investigate the
relationship between perimeter
and area
Do Now
Written assessments
Teacher Observation
Standard 4.2 Geometry and Geometrical Properties
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
4.2.E 8th Grade Pre-Algebra 171
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
Essential Questions :
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
E. Measuring Geometric Objects
Standard 4.2 Geometry and Geometrical Properties
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
4. Use formulas to find the volume and surface
area of a sphere.
McDougal Littell
10.7
_______________________
Holt
8.9
Students will evaluate problems Do Now
Written assessments
Teacher Observation
3. Develop and apply strategies and formulas
for finding the surface area and volume of a
three-dimensional figure: Volume —prism,
cone, pyramid; Surface area —prism
(triangular or rectangular base), pyramid
(triangular or rectangular base); Impact of a
dilation on the surface area and volume of a
three-dimensional figure.
McDougal Littell
10.4 - 10.7
_______________________
Holt
8.5 - 8.8
Students investigate the nets of
three dimensional figures
Students build models and
explain how changes in
surface area and volume are
impacted as lengths are
changed
4.2.E 8th Grade Pre-Algebra 172
· How are patterns of change related to the behavior of functions?
Resources
McDougal Littell
11.1
_______________________
Holt
13.1 - 13.3
- Direct Instruction
- Geometer's Sketchpad
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
1. Recognize, describe, extend, and create
patterns involving whole numbers, rational
numbers, and integers: Descriptions using
tables, verbal and symbolic rules, graphs,
simple equations or expressions; Finite and
infinite sequences; Arithmetic sequences;
Geometric sequences; Generating sequences
by using calculators to repeatedly apply a
formula.
Do Now
Written assessments
Teacher Observation
Standard 4.3 Patterns and Algebra
Assessments
Essential Questions :
Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
A. Patterns
4.3.A 8th Grade Pre-Algebra 173
· How are patterns of change related to the behavior of functions?
Resources
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
B. Functions and Relationships
· How can change be best represented mathematically?
2. Recognize and describe the difference
between linear and exponential growth, using
tables, graphs, and equations.
McDougal Littell
11.6
_______________________
Holt
13.4 - 13.5
Cooperative Learning Activities Do Now
Written assessments
Teacher Observation
1. Graph functions, and understand and
describe their general behavior: Equations
involving two variables; Rates of change
(informal notion of slope).
McDougal Littell
11.3 - 11.7
_______________________
Holt
13.4 - 13.7
Technology Exploration Do Now
Written assessments
Teacher Observation
4.3.B 8th Grade Pre-Algebra 174
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Knowledge/Skills/Understanding Learning Experiences
C. Modeling Essential Questions :
Assessments
Standard 4.3 Patterns and Algebra
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations: Using
concrete materials (manipulatives), tables,
graphs, verbal rules, algebraic expressions/
equations/ inequalities; Growth situations,
such as population growth and compound
interest, using recursive formulas.
Teacher created materials
Various workbooks
Ongoing through all
investigations
Do Now
Written assessments
Teacher Observation
Technology exploration Do Now
Written assessments
Teacher Observation
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
McDougal Littell
11.6
_______________________
Holt
12.2
4.3.C 8th Grade Pre-Algebra 175
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
2. Solve simple linear equations informally,
graphically, and using formal algebraic
methods:
Multi-step, integer coefficients only (although
answers may not be integers) Simple literal
equations (e.g., A = lw) Using paper-and-
pencil, calculators, graphing calculators,
spreadsheets, and other technology.
Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences
1. Use graphing techniques on a number line:
Absolute value; Arithmetic operations
represented by vectors (arrows) (e.g., “-3 + 6”
is “left 3, right 6”).
McDougal Littell
2.1
_______________________
Holt
1.3
Number Line in classroom
McDougal Littell
3.1 - 3.4, 6.1 - 6.4
_______________________
Holt
11.2
- Direct Instruction
- Real world problem solving
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
4.3.D 8th Grade Pre-Algebra 176
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences
Do Now
Written assessments
Teacher Observation
McDougal Littell
3.6 - 3.7, 6.5
_______________________
Holt
11.4
Direct Instruction Do Now
Written assessments
Teacher Observation
3. Solve simple linear inequalities.
4. Create, evaluate, and simplify algebraic
expressions involving variables: Order of
operations, including appropriate use of
parentheses; Distributive property;
Substitution of a number for a variable;
Translation of a verbal phrase or sentence into
an algebraic expression, equation, or
inequality, and vice versa.
McDougal Littell
1.3, 2.6, 2.7
_______________________
Holt
11.1
Applied throughout
investigations
4.3.D 8th Grade Pre-Algebra 177
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Standard 4.3 Patterns and Algebra
D. Procedures Essential Questions :
Knowledge/Skills/Understanding Learning Experiences
5. Understand and apply the properties of
operations, numbers, equations, and
inequalities: Additive inverse; Multiplicative
inverse; Addition and multiplication
properties of equality; Addition and
multiplication properties of inequalities.
McDougal Littell
3.1 - 3.4
_______________________
Holt
1.7 - 1.8
Direct Instruction Do Now
Written assessments
Teacher Observation
4.3.D 8th Grade Pre-Algebra 178
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Graphing project
Essential Questions :
· How can classifying help me in organizing data to solve problems?
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode): Type of
display most appropriate for given data; Box-
and-whisker plot, upper quartile, lower
quartile; Scatter plot; Calculators and
computer used to record and process
information; Finding the median and mean
(weighted average) using frequency data;
Effect of additional data on measures of
central tendency.
McDougal Littell
5.8, 12.1 - 12.3
_______________________
Holt
9.3 -9.4, 9.8
Real world problem solving
4.4.A 8th Grade Pre-Algebra 179
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How can classifying help me in organizing data to solve problems?
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
Knowledge/Skills/Understanding Learning Experiences Assessments
McDougal Littell
5.8, 12.1 - 12.3
_______________________
Holt
9.3 -9.4, 9.8
Do Now
Written assessments
Teacher Observation
Real world problem solving
Student project
3. Estimate lines of best fit and use them to
interpolate within the range of the data.
McDougal Littell
11.2
_______________________
Holt
12.7
Real world problem solving Students produce a scatterplot
to determine line of best fit
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data sets.
4. Use surveys and sampling techniques to
generate data and draw conclusions about
large groups.
Teacher created material
Various worbooks
Real world problem solving
4.4.A 8th Grade Pre-Algebra 180
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
B. Probability
· How can classifying help me in organizing data to solve problems?
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
McDougal Littell
12.8
_______________________
Holt
10.5
Stations in classroom Results from stations
McDougal Littell
7.8, 12.7
_______________________
Holt
10.1
Cooperative Learning activities Do Now
Written assessments
Teacher Observation
2. Determine probabilities of compound
events.
3. Explore the probabilities of conditional
events (e.g., if there are seven marbles in a
bag, three red and four green, what is the
probability that two marbles picked from the
bag, without replacement, are both red).
McDougal Littell
12.7 - 12.8
_______________________
Holt
10.5
Stations in classroom Results from stations
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
1. Interpret probabilities as ratios, percents,
and decimals.
4.4.B 8th Grade Pre-Algebra 181
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
B. Probability
· How can classifying help me in organizing data to solve problems?
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
6. Play and analyze probability-based games
and discuss the concepts of fairness and
expected value.
Teacher created materials
_______________________
Holt
Ch. 10 ending activity
Cooperative Learning activities Do Now
Written assessments
Teacher Observation
4. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
McDougal Littell
12.7 - 12.8
_______________________
Holt
10.4
Stations in classroom Results from stations
5. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
McDougal Littell
7.8
_______________________
Holt
10.2, 10.4
Direct instruction Do Now
Written assessments
Teacher Observation
4.4.B 8th Grade Pre-Algebra 182
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can classifying help me in organizing data to solve problems?
Learning Experiences Assessments
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement vs. ordered situations
without replacement; Factorial notation;
Concept of combinations.
McDougal Littell
12.4 - 12.6
_______________________
Holt
10.8 - 10.9
- Direct instruction
- Ice cream activity
Student projects
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
2. Explore counting problems involving Venn
diagrams with three attributes.
Various workbooks Direct instruction Do Now
Written assessments
Teacher Observation
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
McDougal Littell
12.4
_______________________
Holt
10.8
Ongoing throughout
investigations
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding
4.4.C 8th Grade Pre-Algebra 183
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can classifying help me in organizing data to solve problems?
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use vertex-edge graphs and algorithmic
thinking to represent and find solutions to
practical problems: Finding the shortest
network connecting specified sites; Finding a
minimal route that includes every street;
Finding the shortest route on a map from one
site to another; Finding the shortest circuit on
a map that makes a tour of specified sites;
Limitations of computers.
NJ Frameworks - Students explore common
discrete mathematical models,
explore their properties, and
design them for specific
situations
- Students devise, describe, and
test algorithms for solving
optimization and search options
Do Now
Written assessments
Teacher Observation
4.4.D 8th Grade Pre-Algebra 184
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.A 8th Grade Pre-Algebra 185
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
4. Pose problems of various types and levels of
difficulty.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
5. Monitor their progress and reflect on the
process of their problem solving activity.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.A 8th Grade Pre-Algebra 186
· How can spatial relationships be described by careful use of geometric language?
Resources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
B. Communication
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Assessments
3. Analyze and evaluate the mathematical
thinking and strategies of others.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.B 8th Grade Pre-Algebra 187
· How can spatial relationships be described by careful use of geometric language?
Resources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
B. Communication
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Assessments
4. Use the language of mathematics to express
mathematical ideas precisely.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.B 8th Grade Pre-Algebra 188
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
C. Connections
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.C 8th Grade Pre-Algebra 189
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
C. Connections
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4. Apply mathematics in practical situations
and in other disciplines.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
5. Trace the development of mathematical
concepts over time and across cultures.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
4.5.C 8th Grade Pre-Algebra 190
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
D. Reasoning
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Select and use various types of reasoning
and methods of proof.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.D 8th Grade Pre-Algebra 191
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
D. Reasoning
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
4.5.D 8th Grade Pre-Algebra 192
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
E. Representations
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
2. Select, apply, and translate among
mathematical representations to solve
problems.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.E 8th Grade Pre-Algebra 193
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
E. Representations
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.E 8th Grade Pre-Algebra 194
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
- Technology exploration
- Geometer's Sketchpad
Do Now
Written assessments
Teacher Observation
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
- Technology exploration
- Geometer's Sketchpad
Do Now
Written assessments
Teacher Observation
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
- Technology exploration
- Geometer's Sketchpad
Do Now
Written assessments
Teacher Observation
4.5.F 8th Grade Pre-Algebra 195
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
- Technology exploration
- Geometer's Sketchpad
Do Now
Written assessments
Teacher Observation
6. Use computer-bases laboratory technology
for mathematical applications in the sciences.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
- Technology exploration
- Geometer's Sketchpad
Do Now
Written assessments
Teacher Observation
5. Use computer software to make and verify
conjectures about geometric objects.
McDougal Littell
Chapters. 1 - 12
Holt
Chapters 1 - 14
Various Workbooks
4.5.F 8th Grade Pre-Algebra 196
Algebra with Pizzazz! Steve and Janis Marcy
Fractions, Decimals, and Percents Joke
WorksheetsChristine A. Koers Nasco 2006
Algebra Joke Worksheets Christine A. Koers Nasco 2003
Geo Joke Worksheets Christine A. Koers
McGraw Hill 2002
Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989
Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
2008
Author(s)
McDougall Littell Course 3
and all related resources (differentiation
including ELL)
Ron Larson, Laurie Boswell,
Timothy D. Kanold, and Lee
Stiff
McDougal Littell
Holt Course 3: Pre-Algebra
and all related resources (differentiation
including ELL)
Jeanine M. Bennett, Edward B.
Burger, David J. Chard, Audrey
L. Jackson, Paul A. Kennedy,
Freddie L. Renfro, Janet K.
Scheer, and Bert K. Waits
Holt, Reinhart and Winston
8th Grade Pre-Algebra
Title of ResourceTitle of Resource Publisher Copyright
Resources
2007
Pre-Algebra Joke Worksheets Christine A. Koers Nasco 2003
Nasco 2002
8th Grade Pre-Algebra Resources 197
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Author(s)
8th Grade Pre-Algebra
Title of ResourceTitle of Resource Publisher Copyright
Resources
Frank Schaffer Publications 2002
Teacher Created Resources Inc. 1999Pre-Algebra Brain Teasers Lorin Olschanski
Skills for Success - Algebra Theresa Kane McKell
The 100+ Series - Standard Based Math
Grades 7-8
Mary Lee Vivian and Margaret
Thomas
Frank Schaffer Publications 2003
Carson-Dellosa Publishing
Company, Inc.2003
1998
1996
1996
The 100+ Series - Pre-Algebra Grades 5-8Mary Lee Vivian and Margaret
ThomasFrank Schaffer Publications 2003
The 100+ Series - Intro to GeometryMary Lee Vivian and Margaret
Thomas
The 100+ Series - Math Grades 7-8Mary Lee Vivian and Margaret
ThomasFrank Schaffer Publications 2003
The 100+ Series - Algebra Grades 5-8Mary Lee Vivian and Margaret
ThomasFrank Schaffer Publications 2003
Jossey-Bass 2003Algebra Teacher's Activities Kit Judith and Gary Robert Muschla
Algebra Puzzlers
Pre-Algebra
Masterminds Riddle Math Series - Pre-Algebra
Theresa Kane McKell
Dawn Talluto Jacobi
Brenda Opie and Douglas
McAvinn
Frank Schaffer Publications
Kelley Wingate Publications
Incentive Publications Inc.
8th Grade Pre-Algebra Resources 198
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Author(s)
8th Grade Pre-Algebra
Title of ResourceTitle of Resource Publisher Copyright
Resources
-------NJ Frameworkshttp://www.state.nj.us/education/
frameworks/math/index.html
Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006
Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006
Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006
GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000
Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002
Preparing for the New Jersey GEPA - Grade 8David J. Glatzer and Joyce
GlatzerAmsco School Publications, Inc. 2005
New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008
Adventures with Area Evelyn B. Christensen Nasco 2007
Quadrant Quandries Julie K. Cohen Nasco 2007
The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001
Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005
New Jersey Department of
Education and Rutgers
8th Grade Pre-Algebra Resources 199
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Author(s)
8th Grade Pre-Algebra
Title of ResourceTitle of Resource Publisher Copyright
Resources
Measuring Up - Grade 8 Michael Goodman People's Publishing Group 2003
Skills for Success - GeometryTiffany Moore and Jenae
Hawkins
Carson-Dellosa Publishing
Company, Inc.2007
Plotting Pictures Paula Rozell Dale Seymour Publications 1995
Algebra Puzzles Hank Garcia Creative Teaching Press 2006
Power Practice Geometry Pamela Jennett Creative Teaching Press 2007
Scratch Your Brain AlgebraDoug Brumbaugh and David
RockThe Critical Thinking Co. 2008
Algebra Practice Exercises Thomas E. Campbell
Power Practice Pre-Algebra Wendy Osterman Creative Teaching Press 2004
J. Weston Walch Publisher 1996
8th Grade Pre-Algebra Resources 200
5
11
Integer Operations 2
-----
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Ratio, Proportion, Percent 7
6
-----
Benchmark Assessment -
Midtem
Factors, Fractions, Exponents,
Rational Number Operations
-----
7
Benchmark Assessment -
Pre-Test-----
Equations and Inequalities 3
10
McDougall Littell Mathematics
Course 3 Chapter
4,5
Number of Blocks
8th Grade Pre-Algebra
Unit
Pacing Guide
Variables and Expressions 1
8th Grade Pre-Algebra Pacing Guide 201
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
McDougall Littell Mathematics
Course 3 ChapterNumber of Blocks
8th Grade Pre-Algebra
Unit
Pacing Guide
Multi-Step Equations and
Inequalities5 7
Benchmark Assessment -
Post-Test----- -----
5
Measurement, Area, Volume 10 6
6
Linear Equations and Graphs 12
Polygons and Transformations 8 10
4Real Numbers and Right
Triangles9
Data Analysis and Probability 11
8th Grade Pre-Algebra Pacing Guide 202
Benchmark Assessment -
Pre-Test-----
Holt Course 3 Chapter
2
Variables, Expressions, Integers 1
Ratios, Proportion, Similarity 5
Exponents, Square roots,
Pythagorean Theorem, and
Scientific Notation
Graphs, Functions, and
Sequences
4
10
-----
Number of Blocks
3
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit
8th Grade Pre-Algebra
Pacing Guide
Percents
Fractions, Decimals, and
Percents
11
8
9
10
6 5
8th Grade Pre-Algebra Pacing Guide 203
Holt Course 3 Chapter Number of Blocks
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit
8th Grade Pre-Algebra
Pacing Guide
-----
Measurement, Area, and
Volume8
Benchmark Assessment -
Midterm-----
Probability 10 7
Two Dimensional Geometry 7
4
12
Data and Statistics 9
Benchmark Assessment -
Post-Test----- -----
5
8th Grade Pre-Algebra Pacing Guide 204
Algebra 1B Curriculum
205
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
Do Now
Written assessments
Teacher Observation
· How can we compare and contrast numbers?
Essential Questions :
Assessments
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations.
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 8 pertain to these sets of numbers as
well): Rational numbers; Percents;
Exponents; Roots; Absolute Values.
- Investigate decimal patterns
using a caluclator
- Class discussions
- Written explanations
- Recursive Routines
- Through the use of geometry
and squares and cubes
Teacher created materials
Discovering Algebra
Sections 7.3 - 7.6
Teacher created materials
Various workbooks
2. Demonstrate a sense of the relative
magnitudes of numbers.
Ongoing through problems
- Problem Solving
- Collaborative discussions
- Brainstorming
Teacher created materials
Various workbooks
4.1.A 8th Grade Algebra 1B 206
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Knowledge/Skills/Understanding Learning Experiences
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Essential Questions :
Assessments
5. Use whole numbers, fractions, decimals, and
percents to represent equivalent forms of the
same number.
Teacher created materials
Various workbooks
Ongoing throughout problems
Spiral of Right Triangles
(Pythagorean Theorem)
Circle - develop pi from
circumference formula
Teacher created materials
Various workbooks
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
7. Construct meanings for common irrational
numbers, such as pi (π) and the square root of
two.
4. Compare and order numbers of all named
types.
6. Recognize that repeating decimals
correspond to fractions and determine their
fractional equivalents:
5/7 = 0.714285714285...
= 0.714285
Teacher created materials
Various workbooks
Graphing on a number line
Line-up in classroom
Use equations method
Teacher created materials
Various workbooks
4.1.A 8th Grade Algebra 1B 207
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Standard 4.1 Number and Numerical Operations
Essential Questions :
2. Use exponentiation to find whole number
powers of numbers.
Discovering Algebra
Sections 7.1 - 7.6
Do Now
Written assessments
Teacher Observation
Technology exploration
3. Find square and cube roots of numbers and
understand their inverse relationships.
Mathematics Curriculum
Grades 7 - 8
· How can we compare and contrast numbers?
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Finding the length of the edge of
a cube knowing the volume
Mental Math Warmups
B. Numerical Operations
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding AssessmentsLearning Experiences
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Pencil-and-paper; Mental math;
Calculator.
Teacher created materials
Do Now
Written assessments
Teacher Observation
Teacher created materials
Geometer's Sketchpad
- Technology exploration
- Real world problems
4. Solve problems involving proportions and
percents.
Teacher created packet of percents,
proportion, and interest
4.1.B 8th Grade Algebra 1B 208
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Standard 4.1 Number and Numerical Operations
Essential Questions :
Mathematics Curriculum
Grades 7 - 8
· How can we compare and contrast numbers?
B. Numerical Operations
Knowledge/Skills/Understanding AssessmentsLearning Experiences
Direct Instruction Do Now
Written assessments
Teacher Observation
Pattern investigation Do Now
Written assessments
Teacher Observation
6. Perform operations on matrices (Addition
and Subtraction, Scalar Multiplication,
Multiplication).
Discovering Algebra
Chapter 1 and 8
Teacher created materials
5. Understand and apply the standard
algebraic order of operations, including
appropriate use of parentheses.
Discovering Algebra
Chapter 7
4.1.B 8th Grade Algebra 1B 209
C. Estimation
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Resources
3. Recognize the limitations of estimation and
assess the amount of error resulting from
estimation.
Teacher created problems
Various workbooks
Physically measure lengths and
discuss why disparities occur
Do Now
Written assessments
Teacher Observation
2. Use equivalent representations of numbers
such as fractions, decimals, and percents to
facilitate estimation.
Teacher created problems
Various workbooks
Direct instruction Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Estimate cube roots of numbers. Teacher created problems
Various workbooks
Technology Exploration Do Now
Written assessments
Teacher Observation
· How can we compare and contrast numbers?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
Essential Questions :
4.1.C 8th Grade Algebra 1B 210
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
3. Understand and apply properties of
polygons.
Real world application problems Do Now
Written assessments
Teacher Observation
Assessments
Do Now
Written assessments
Teacher Observation
Exploration and Investigation Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences
Essential Questions :
Teacher created problems
Various workbooks
Teacher created problems
Various workbooks
Direct instruction
2. Understand and apply the Pythagorean
Theorem.
Discovering Algebra
Chapter 11
Various workbooks
1. Understand and apply concepts involving
lines, angles, and planes: Complementary and
supplementary angles; Bisectors and
perpendicular bisectors; Parallel,
perpendicular, and intersecting planes;
Intersection of plane with cube, cylinder, cone,
and sphere.
Geometer's Sketchpad
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.2 Geometry and Geometrical Properties
A. Geometric Properties
4.2.A 8th Grade Algebra 1B 211
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources AssessmentsKnowledge/Skills/Understanding Learning Experiences
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.2 Geometry and Geometrical Properties
A. Geometric Properties
4. Understand and apply the concept of
similarity: Using proportions to find missing
measures; Scale drawings; Models of 3D
objects.
5. Use logic and reasoning to make and
support conjectures about geometric objects.
Geometer's Sketchpad
Teacher created materials
Various workbooks
Exploration and Investigation Do Now
Written assessments
Teacher Observation
Teacher created problems
Various workbooks
Cooperative Learning activity Do Now
Written assessments
Teacher Observation
4.2.A 8th Grade Algebra 1B 212
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
B. Transforming Shapes
2. Use iterative procedures to generate
geometric patterns: Fractals (e.g., the Koch
Snowflake); Self-similarity; Construction of
initial stages; Patterns in successive stages
(e.g., number of triangles in each stage of
Sierpinski’s Triangle).
Discovering Algebra
Chapter 0,1,2,3
Direct instruction Do Now
Written assessments
Teacher Observation
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another;
Reflections, rotations, and translations result
in images congruent to the pre-image;
Dilations (stretching/shrinking) result in
images similar to the pre-image.
Geometer's Sketchpad
Discovering Algebra
Chapter 9 and 11
Use calculator to compare
graphs of equations that involve
transformations
Coordinate grid drawings
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Standard 4.2 Geometry and Geometrical Properties
4.2.B 8th Grade Algebra 1B 213
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.2 Geometry and Geometrical Properties
Learning Experiences
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
AssessmentsKnowledge/Skills/Understanding
C. Coordinate Geometry Essential Questions :
2. Use a coordinate grid to model and quantify
transformations (e.g., translate right 4 units).
Discovering Algebra
Chapter 11
Direct Instruction Coordinate grid drawings
Teacher Observation
1. Use coordinates in four quadrants to
represent geometric concepts.
Discovering Algebra
Chapter 11
Determine if a quadrilateral is a
parallelogram or a rectangle
Do Now
Written assessments
Teacher Observation
4.2.C 8th Grade Algebra 1B 214
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
Standard 4.2 Geometry and Geometrical Properties
2. Use approximate equivalents between
standard and metric systems to estimate
measurements (e.g., kilometers is about 3
miles).
Discovering Algebra
Chapters 6 - 11
Ongoing in all investigations Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
D. Units of Measurement
1. Solve problems requiring calculations that
involve different units of measurement within
the same system.
Discovering Algebra
Chapters 6 - 11
Using real life examples
3. Recognize that the degree of precision
needed in calculations depends on how the
results will be used and the instruments used
to generate the measurements.
Discovering Algebra
Chapters 6 - 11
Students develop a project, for
example, scale drawing of an
apartment floor plan
4.2.D 8th Grade Algebra 1B 215
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.2 Geometry and Geometrical Properties
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
D. Units of Measurement
5. Recognize that all measurements of
continuous quantities are approximations.
Discovering Algebra
Chapters 6 - 11
Using real life examples Do Now
Written assessments
Teacher Observation
4. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
Discovering Algebra
Chapters 6 - 11
Using real life examples Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
6. Solve problems that involve compound
measurement units, such as speed (miles per
hour).
Discovering Algebra
Chapters 6 - 11
Using real life examples
4.2.D 8th Grade Algebra 1B 216
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
2. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height.
Students investigate the
relationship between perimeter
and area
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.2 Geometry and Geometrical Properties
Geometer's Sketchpad
Various workbooks
Teacher demonstration with
manipulatives
E. Measuring Geometric Objects
Do Now
Written assessments
Teacher Observation
1. Develop and apply strategies for finding
perimeter and area: Geometric figures made
by combining triangles, rectangles and circles
or parts of circles; Estimation of area using
grids of various sizes; Impact of a dilation on
the perimeter and area of a 2-dimensional
figure; Impact of a dilation on the perimeter
and area of a 2-dimensional figure.
Geometer's Sketchpad
Various workbooks
Geometer's Sketchpad
Various workbooks
Knowledge/Skills/Understanding Learning Experiences Assessments
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
4.2.E 8th Grade Algebra 1B 217
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.2 Geometry and Geometrical Properties
E. Measuring Geometric Objects
Knowledge/Skills/Understanding Learning Experiences Assessments
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
3. Develop and apply strategies and formulas
for finding the surface area and volume of a
three-dimensional figure: Volume —prism,
cone, pyramid; Surface area —prism
(triangular or rectangular base), pyramid
(triangular or rectangular base); Impact of a
dilation on the surface area and volume of a
three-dimensional figure.
Geometer's Sketchpad
Various workbooks
Students investigate the nets of
three dimensional figures
4. Use formulas to find the volume and surface
area of a sphere.
Geometer's Sketchpad
Various workbooks
Students evaluate problems Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
4.2.E 8th Grade Algebra 1B 218
· How are patterns of change related to the behavior of functions?
Resources
Do Now
Written assessments
Teacher Observation
Standard 4.3 Patterns and Algebra
Assessments
Essential Questions :
Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Discovering Algebra
Chapters 6 - 11
Teacher created materials
- Given terms in a pattern,
describe patterns in words
- Real world problem solving
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
A. Patterns
1. Recognize, describe, extend, and create
patterns involving whole numbers, rational
numbers, and integers: Descriptions using
tables, verbal and symbolic rules, graphs,
simple equations or expressions; Finite and
infinite sequences; Arithmetic sequences;
Geometric sequences; Generating sequences
by using calculators to repeatedly apply a
formula.
4.3.A 8th Grade Algebra 1B 219
· How are patterns of change related to the behavior of functions?
Resources
1. Graph functions, and understand and
describe their general behavior: Equations
involving two variables; Rates of change
(informal notion of slope).
Discovering Algebra
Chapters 5 - 6
- Real world problem solving
- Discussion
Do Now
Written assessments
Teacher Observation
2. Recognize and describe the difference
between linear and exponential growth, using
tables, graphs, and equations.
Discovering Algebra
Chapter 7
- Real world problem solving
- Discussion
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
4.3.B 8th Grade Algebra 1B 220
· How are patterns of change related to the behavior of functions?
Resources
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations:
Growth situations, such as population growth
and compound interest, using recursive
formulas.
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
- Direct instruction
- Collaborative investigations
C. Modeling
Do Now
Written assessments
Teacher Observation
- Reasoning
- Discussions
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Assessments
Standard 4.3 Patterns and Algebra
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Discovering Algebra
Chapter 7
Essential Questions :
Learning Experiences
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
Discovering Algebra
Chapters 6 - 11
4.3.C 8th Grade Algebra 1B 221
· How are patterns of change related to the behavior of functions?
Resources
Discovering Algebra
Chapter 4
Teacher created materials
Direct instruction Do Now
Written assessments
Teacher Observation
3. Solve systems og equations: graphically;
algebraic methods; using matrices.
Discovering Algebra
Chapter 6
Teacher created materials
Direct instruction
2. Solve linear equations and inequalities
informally, graphically, and using formal
algebraic methods:
Multi-step, integer coefficients only (although
answers may not be integers); absolute value;
compound inequalities; rational expressions;
using paper-and-pencil, calculators, graphing
calculators, spreadsheets, and other
technology.
Flemington Raritan School District
Do Now
Written assessments
Teacher Observation
Standard 4.3 Patterns and Algebra
Essential Questions : Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Mathematics Curriculum
Grades 7 - 8
Discovering Algebra
Chapter 8
Teacher created materials
Direct instruction
· How can change be best represented mathematically?
1. Use graphing techniques on a number line:
Absolute value.
D. Procedures
Do Now
Written assessments
Teacher Observation
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
4.3.D 8th Grade Algebra 1B 222
· How are patterns of change related to the behavior of functions?
Resources
Flemington Raritan School District
Standard 4.3 Patterns and Algebra
Essential Questions : Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
Mathematics Curriculum
Grades 7 - 8
· How can change be best represented mathematically?
D. Procedures
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
6. Evaluate and simplify algebraic
expressions: add and subtract polynomials;
multiply a polunomial by a monomial or
binomial; divide a polynomial by a monomial;
use laws of exponents.
Discovering Algebra
Chapter 7
Teacher created materials
Various workbooks
Discovering Algebra
Chapter 10
Teacher created materials
- Algebra tiles
- Investigations
Do Now
Written assessments
Teacher Observation
5. Rational expressions: add and subtract;
mulitply and divide.
Teacher created materials
Various workbooks
Do Now
Written assessments
Teacher Observation
Direct instruction
Direct instruction
Do Now
Written assessments
Teacher Observation
4. Factor polynomials.
4.3.D 8th Grade Algebra 1B 223
· How can spatial relationships be described by careful use of geometric language?
Resources
Discovering Algebra
Chapter 1
Teacher created materials
Essential Questions :
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data sets.
Discovering Algebra
Chapter 1
Teacher created materials
Real world problem solving Do Now
Written assessments
Teacher Observation
· How can statistics help us to understand real world situations?
Assessments
Do Now
Written assessments
Teacher Observation
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode): Finding
the median and mean (weighted average)
using frequency data; Effect of additional data
on measures of central tendency.
· How can classifying help me in organizing data to solve problems?
Real world problem solving
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Learning ExperiencesKnowledge/Skills/Understanding
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.A 8th Grade Algebra 1B 224
· How can spatial relationships be described by careful use of geometric language?
Resources
Discovering Algebra
Chapter 2
Teacher created materials
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
2. Explore the probabilities of conditional
events (e.g., if there are seven marbles in a
bag, three red and four green, what is the
probability that two marbles picked from the
bag, without replacement, are both red).
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Probability stations
- Direct instruction
- Manipulatives
- Probability stations
- Direct instruction
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
3. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
Do Now
Written assessments
Teacher Observation
Essential Questions : Essential Questions :
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can classifying help me in organizing data to solve problems?
- Manipulatives
- Probability stations
- Direct instruction
1. Determine probabilities of compound
events.
Discovering Algebra
Chapter 2
Teacher created materials
4.4.B 8th Grade Algebra 1B 225
· How can spatial relationships be described by careful use of geometric language?
Resources
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can classifying help me in organizing data to solve problems?
Do Now
Written assessments
Teacher Observation
5. Play and analyze probability-based games
and discuss the concepts of fairness and
expected value.
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Probability stations
- Direct instruction
Do Now
Written assessments
Teacher Observation
4. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Probability stations
- Direct instruction
4.4.B 8th Grade Algebra 1B 226
· How can spatial relationships be described by careful use of geometric language?
Resources
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Direct instruction
Do Now
Written assessments
Teacher Observation
2. Explore counting problems involving Venn
diagrams with three attributes.
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Direct instruction
Do Now
Written assessments
Teacher Observation
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement (e.g., number of possible
license plates) vs. ordered situations without
replacement.
Discovering Algebra
Chapter 2
Teacher created materials
- Manipulatives
- Direct instruction
Do Now
Written assessments
Teacher Observation
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
· How can classifying help me in organizing data to solve problems?
Flemington Raritan School District
Mathematics Curriculum
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete MathematicsGrades 7 - 8
4.4.C 8th Grade Algebra 1B 227
Resources
1. Use vertex-edge graphs and algorithmic
thinking to represent and find solutions to
practical problems: Finding the shortest
network connecting specified sites; Finding a
minimal route that includes every street;
Finding the shortest route on a map from one
site to another; Finding the shortest circuit on
a map that makes a tour of specified sites;
Limitations of computers (overwhelming the
capacity).
Teacher created materials - Students explore common
discrete mathematical models,
explore their properties, and
design them for specific
situations
- Students devise, describe, and
test algorithms for solving
optimization and search options
Do Now
Written assessments
Teacher Observation
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can spatial relationships be described by careful use of geometric language?
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
· How can classifying help me in organizing data to solve problems?
Flemington Raritan School District
Mathematics Curriculum
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete MathematicsGrades 7 - 8
4.4.D 8th Grade Algebra 1B 228
· How can spatial relationships be described by careful use of geometric language?
Resources
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
Discovering Algebra
Chapters 6 - 11
Question Quest
Level D
Various workbooks
- Students analyze their own
written response compared to
teacher created examples
- Students analyze each other's
written responses
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
Discovering Algebra
Chapters 6 - 11
Question Quest
Level D
Various workbooks
- Brainstorming
- Journaling
- Classroom discussion
- Predictions
Do Now
Written assessments
Teacher Observation
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
A. Problem Solving
Grades 7 - 8
4.5.A 8th Grade Algebra 1B 229
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
A. Problem Solving
Grades 7 - 8
4. Pose problems of various types and levels of
difficulty.
Discovering Algebra
Chapters 6 - 11
Question Quest
Level D
Various workbooks
- Brainstorming
- Journaling
- Classroom discussion
- Predictions
Do Now
Written assessments
Teacher Observation
3. Select and apply a variety of appropriate
problem-solving strategies to solve problems.
Discovering Algebra
Chapters 6 - 11
Question Quest
Level D
Various workbooks
- Brainstorming
- Journaling
- Classroom discussion
- Predictions
Do Now
Written assessments
Teacher Observation
4.5.A 8th Grade Algebra 1B 230
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
A. Problem Solving
Grades 7 - 8
5. Monitor their progress and reflect on the
process of their problem solving activity.
Discovering Algebra
Chapters 6 - 11
Question Quest
Level D
Various workbooks
- Brainstorming
- Journaling
- Classroom discussion
- Predictions
Do Now
Written assessments
Teacher Observation
4.5.A 8th Grade Algebra 1B 231
· How can spatial relationships be described by careful use of geometric language?
Resources
3. Analyze and evaluate the mathematical
thinking and strategies of others.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
B. Communication
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
Essential Questions :
Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
4.5.B 8th Grade Algebra 1B 232
· How can spatial relationships be described by careful use of geometric language?
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
B. Communication
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
Essential Questions :
Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
4. Use the language of mathematics to express
mathematical ideas precisely.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.B 8th Grade Algebra 1B 233
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
Do Now
Written assessments
Teacher Observation
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
C. Connections
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.C 8th Grade Algebra 1B 234
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
C. Connections
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4. Apply mathematics in practical situations
and in other disciplines.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
5. Trace the development of mathematical
concepts over time and across cultures.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.C 8th Grade Algebra 1B 235
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Select and use various types of reasoning
and methods of proof.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
Do Now
Written assessments
Teacher Observation
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
D. Reasoning
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.D 8th Grade Algebra 1B 236
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
D. Reasoning
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.D 8th Grade Algebra 1B 237
· How can spatial relationships be described by careful use of geometric language?
Resources
2. Select, apply, and translate among
mathematical representations to solve
problems.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
E. Representations
Grades 7 - 8
4.5.E 8th Grade Algebra 1B 238
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
E. Representations
Grades 7 - 8
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
4.5.E 8th Grade Algebra 1B 239
· How can spatial relationships be described by careful use of geometric language?
Resources
Do Now
Written assessments
Teacher Observation
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
Do Now
Written assessments
Teacher Observation
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.F 8th Grade Algebra 1B 240
· How can spatial relationships be described by careful use of geometric language?
ResourcesKnowledge/Skills/Understanding Learning Experiences Assessments
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
5. Use computer software to make and verify
conjectures about geometric objects.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Incorporated throughout
investigations
Do Now
Written assessments
Teacher Observation
Do Now
Written assessments
Teacher Observation
6. Use computer-bases laboratory technology
for mathematical applications in the sciences.
Discovering Algebra
Chapters 6 - 11
Teacher created materials
Various workbooks
Incorporated throughout
investigations
4.5.F 8th Grade Algebra 1B 241
8th Grade Algebra 1B
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Title of Resource Publisher Copyright
Discovering AlgebraJerald Murdock, Ellen
Kamischke, and Eric KamischkeKey Curriculum Press 2002
Author(s)
Pre-Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002
Middle School Math with Pizzazz! Steve and Janis Marcy McGraw Hill 1989
Algebra Joke Worksheets Christine A. Koers Nasco 2003
Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002
Geo Joke Worksheets Christine A. Koers Nasco 2002
Pre-Algebra Joke Worksheets Christine A. Koers Nasco 2003
Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003
Fractions, Decimals, and Percents Joke
WorksheetsChristine A. Koers Nasco 2006
The 100+ Series - Pre-AlgebraMary Lee Vivian and Margaret
ThomasMcGraw Hill 2003
The 100+ Series - AlgebraMary Lee Vivian and Margaret
ThomasMcGraw Hill 2003
8th Grade Algebra 1B Resources 242
8th Grade Algebra 1B
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Title of Resource Publisher CopyrightAuthor(s)
Carson-Dellosa Publishing
Company, Inc.
Teacher Created Resources Inc.
Frank Schaffer Publications
Kelley Wingate Publications
2003
1999
1998
1996
Skills for Success - Algebra
Pre-Algebra Brain Teasers
Algebra Puzzlers
Pre-Algebra
Theresa Kane McKell
Lorin Olschanski
Theresa Kane McKell
Dawn Talluto Jacobi
NJ Frameworkshttp://www.state.nj.us/education/f
rameworks/math/index.html
New Jersey Department of
Education and Rutgers-------
Masterminds Riddle Math Series - Pre-AlgebraBrenda Opie and Douglas
McAvinnIncentive Publications Inc. 1996
Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006
Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005
Punchline Algebra Book A and Book B Steve and Janis Marcy Marcy Mathworks 2006
Punchline Problem Solving Steve and Janis Marcy Marcy Mathworks 2006
Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002
GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000
8th Grade Algebra 1B Resources 243
8th Grade Algebra 1B
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Title of Resource Publisher CopyrightAuthor(s)
New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008
Preparing for the New Jersey GEPA - Grade 8David J. Glatzer and Joyce
GlatzerAmsco School Publications, Inc. 2005
Quadrant Quandries Julie K. Cohen Nasco 2007
Adventures with Area Evelyn B. Christensen Nasco 2007
Scratch Your Brain AlgebraDoug Brumbaugh and David
RockThe Critical Thinking Co. 2008
The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001
Developing Skills in Algebra 1: Book C Harold and Loretta Taylor Dale Seymour Publications 1984
Algebra Practice Exercises Thomas E. Campbell J. Weston Walch Publisher 1996
The Univeristy of Chicago School Mathematics
Project - AlgebraScott Foresman Harper Collins Publishers 1996
What's My Rule? (Using Problem Solving
Strategies Grades 6 - 12)Dave and Teddy Logothetti Dale Seymour Publications 1983
Geometry Reproducibles Sara Freeman Milliken Publishing Company 2004
Test Time Algebra Maureen Steddin J. Weston Walch Publisher 2003
8th Grade Algebra 1B Resources 244
-----
Polynomials
10 7
Linear Equations
5 16
Systems of Equations and Inequalities
Graphing, Slope, and Writing the Equation of
a Line
Benchmark Assessment - Midterm
----- -----
Exponents and Exponential Models
7
8th Grade Algebra 1B
Discovering AlgebraDiscovering Algebra
6 10
Pacing Guide
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit Number of Blocks
Benchmark Assessment - Pretest -----
5 10
8
8th Grade Algebra 1B Pacing Guide 245
8th Grade Algebra 1B
Discovering AlgebraDiscovering Algebra
Pacing Guide
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit Number of Blocks
Benchmark Assessment - Final
----- -----
13
Rational Expressions and Functions
9 4
Radicals
11 4
Quadratics
10
8th Grade Algebra 1B Pacing Guide 246
Advanced Algebra Curriculum
247
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Essential Questions :
· How can spatial relationships be described by careful use of geometric language?
Assessments
Written assessments
Class discussions
Teacher observations
Do now
Written assessments
Teacher observation
Teacher created materials
Various Workbooks
Discovering Advanced Algebra
Chapter 1
Written classwork2. Demonstrate a sense of the relative
magnitudes of numbers.
Resources
1. Extend understanding of the number system
by constructing meanings for the following
(unless otherwise noted, all indicators for
grade 8 pertain to these sets of numbers as
well): Roots of monomials, Variables in
exponents, Roots, Know the meaning on
square/cubic roots, Understand the inverse
relationship between powers and roots.
- Use of geometry connections
through squares and cubes
- Direct instruction
Knowledge/Skills/Understanding Learning Experiences
4.1.A 8th Grade Advanced Algebra 248
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
· How can we compare and contrast numbers?
Essential Questions :
· How can spatial relationships be described by careful use of geometric language?
AssessmentsResourcesKnowledge/Skills/Understanding Learning Experiences
Do now
Written assessments
Teacher observation
Class discussion
3. Understand and use ratios, rates,
proportions, and percents (including percents
greater than 100 and less than 1) in a variety
of situations. Solving ratios and proportions
involving polynomials.
Teacher created materials
Various Workbooks
5. Construct meanings for common irrational
numbers, such as pi (π) and the square root of
two. Prove the square root of two is irrational.
Teacher created mateirals Direct instruction
Do now
Written assessments
Teacher observation
Solving real world problems
Graphing on a number line4. Compare and order rational and irrational
numbers.
Teacher created materials
Various Workbooks
Do now
Written assessments
Teacher observation
4.1.A 8th Grade Advanced Algebra 249
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
· How can we compare and contrast numbers?
Essential Questions :
2. Perform operations on Matrices. 2. Perform operations on Matrices. Discovering Advanced Algebra
Section 6.2
Do now
Written assessments
Teacher observation
Students investigate weekly
movement of rental cars between
cities and analyze results
- Various workbooks
- Teacher created materials
Do now
Written assessments
Teacher observation
- Mental Math classwork
worksheets
- Ongoing throughout
investigations
ResourcesKnowledge/Skills/Understanding AssessmentsLearning Experiences
1. Use and explain procedures for performing
calculations involving addition, subtraction,
multiplication, division, and exponentiation
with integers and all number types named
above with: Mental math.
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
B. Numerical Operations
4.1.B 8th Grade Advanced Algebra 250
C. Estimation
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
1. Recognize the limitations of estimation and
assess the amount of error resulting from
estimation.
- Various workbooks
-Teacher created materials
Take results of experiments done
in class and make conclusions
for a larger/smaller group or
time.
Do now
Written assessments
Teacher observations
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
· How can we compare and contrast numbers?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
Essential Questions :
4.1.C 8th Grade Advanced Algebra 251
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
Solve real world problems Do now
Written assessments
Teacher observation
Assessments
1. Understand and apply the concept of
similarity using:
Models of 3D objects
Polynomials used sometimes as dimensions.
Geometer's Sketchpad
Teacher created materials
Various workbooks
- Use Geometer's Sketchpad to
investigate the effects of rotating
a triangle around a fixed point
- Cooperative learning activity
- Solve real world problems
Knowledge/Skills/Understanding Learning Experiences
3. Use geometric models to represent real
world situations and to solve problems.
Various workbooks Solve real world problems
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Resources
Do now
Written assessments
Teacher observation
Do now
Written assessments
Teacher observation
2. Use logic and reasoning to make and
support conjectures about geometric objects.
Various workbooks
Teacher created materials
Essential Questions :
Standard 4.2 Geometry and Geometrical Properties
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Geometric Properties
Grades 7 - 8
4.2.A 8th Grade Advanced Algebra 252
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Grades 7 - 8
Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding
1. Understand and apply transformations:
Finding the image, given the pre-image, and
vice-versa; Sequence of transformations
needed to map one figure onto another.
Discovering Advanced Algebra
Chapter 4, pg. 219
Geometer's Sketchpad
Various workbooks
Flemington Raritan School District
B. Transforming Shapes
Mathematics Curriculum
Assessments
Do now
Written assessments
Teacher observations
- Graphing activities
- Geometer's Sketchpad
investigations
- Cooperative learning activities
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Resources Learning Experiences
Standard 4.2 Geometry and Geometrical Properties
Do now
Written assessments
Teacher observations
Essential Questions :
2. Use iterative procedures to generate
geometric patterns: Fractals (e.g., the Koch
Snowflake); Self-similarity; Construction of
initial stages; Patterns in successive stages
(e.g., number of triangles in each stage of
Sierpinski’s Triangle).
Discovering Advanced Algebra
pgs. 9, 32-33, 369-397, 642
- Investigations
- Cooperative learning activities
- Students investigate the
Mandelbot set.
4.2.B 8th Grade Advanced Algebra 253
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Grades 7 - 8
Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding
Flemington Raritan School District
B. Transforming Shapes
Mathematics Curriculum
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Resources Learning Experiences
Standard 4.2 Geometry and Geometrical Properties
Essential Questions :
Direct instruction Do now
Written assessments
Teacher observations
3. Determine whether two or more given
shapes can be used to generate a tessellation.
Discovering Advanced Algebra
pg. 208
4.2.B 8th Grade Advanced Algebra 254
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Students perform investigations Do now
Written assessments
Teacher observation
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Do now
Written assessments
Teacher observation
AssessmentsResources
Discovering Advanced Algebra
pgs. 129-130, 186-189, 455,
Chapter 4
Various workbooks
Teacher created materials
- Direct instruction
- Students investigate and
explore what happens to the
equation of a linear function
when they translate the graph of
a line
- Students use motion detectors,
graphing calculators, fathom
software to investigate parallel
lines
Standard 4.2 Geometry and Geometrical Properties
C. Coordinate Geometry
2. Show position and represent motion in the
coordinate plane using vectors.
Discovering Advanced Algebra
pg. 455
Essential Questions : Essential Questions :
1. Use coordinate geometry to represent and
verify properties of lines; distances between
two points; midpoint and slope of a line
segment; finding the intersection of two lines;
lines with the same slope are parallel; lines
that are perpendicular have slopes whose
product is -1.
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences
4.2.C 8th Grade Advanced Algebra 255
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
AssessmentsResources
Standard 4.2 Geometry and Geometrical Properties
C. Coordinate Geometry Essential Questions : Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences
3. Understand and apply properties of
polygons. Quadrilaterals, including squares,
rectangles, parallelograms, trapezoids and
rhombi; regular polygons; sum of measures of
interior angles of a polygon.
Various workbooks
Teacher created materials
- Solving real world problems
- Direct instruction
Do now
Written assessments
Teacher observation
4. Use logic and reasoning to make and
support conjectures and geometric objects.
Various workbooks
Teacher created materials
Ongoing throughout
investigations
Do now
Written assessments
Teacher observation
4.2.C 8th Grade Advanced Algebra 256
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
1. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem solving
situation.
Various workbooks Direct instruction Do now
Written assessments
Teacher observation
2. Understand and use the concept of
significant digits.
Teacher created materials Direct instruction Do now
Written assessments
Teacher observation
Assessments
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning ExperiencesResources
Essential Questions : Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
D. Units of Measurement
Standard 4.2 Geometry and Geometrical Properties
4.2.D 8th Grade Advanced Algebra 257
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Standard 4.2 Geometry and Geometrical Properties
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Do now
Written assessments
Teacher observation
1. Develop and apply strategies for finding
perimeter and area:
Impact of a dilation on the perimeter and are
of a two dimensional figure.
Discovering Advanced Algebra
pg. 309
Various workbooks
Students investigate using
models
Do now
Written assessments
Teacher observation
Class discussion
2. Recognize that the volume of a pyramid or
cone is one-third of the volume of the prism or
cylinder with the same base and height (e.g.,
use rice to compare volumes of figures with
same base and height).
E. Measuring Geometric Objects
Discovering Advanced Algebra
pg. 523
Various workbooks
-Students explore the volume of
cones and pyramids by
constructing
- Solve real world problems
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
4.2.E 8th Grade Advanced Algebra 258
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Standard 4.2 Geometry and Geometrical Properties
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
E. Measuring Geometric Objects
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
4. Use formulas to find the volume and surface
area of a sphere.
Various workbooks
Teacher created materials
Direct Instruction Do now
Written assessments
Teacher observation
3. Develop and apply strategies and formulas
for finding the surface area and volume of a
three-dimensional figure: Volume —prism,
cone, pyramid; Surface area —prism
(triangular or rectangular base), pyramid
(triangular or rectangular base); Impact of a
dilation on the surface area and volume of a
three-dimensional figure.
Various workbooks
Teacher created materials
- Cooperative learning
- Investigations
Do now
Written assessments
Teacher observation
4.2.E 8th Grade Advanced Algebra 259
· How are patterns of change related to the behavior of functions?
Do now
Written assessments
Teacher observation
Standard 4.3 Patterns and Algebra
Assessments
Essential Questions :
Knowledge/Skills/UnderstandingKnowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
1. Use models and algebraic formulas to
represent and analyze sequences and series:
Explicit formulas for nth terms, sums of finite
arithmetic series, sums of finite and infinite
geometric series, develop and informal notion
of limit, use inductive reasoning to form
generalizations.
Discovering Advanced Algebra
pgs. 45-48, 114, 630, 637-640, 650-
651
- Students investigate, compare
and contrast formulas: three
recursive, three graphs, three
linear equations
- Students investigate arithmetic
number sequences and find the
partial sum formula
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Resources
A. Patterns
4.3.A 8th Grade Advanced Algebra 260
· How are patterns of change related to the behavior of functions?
Learning Experiences Assessments
2. Understand and perform transformations
on commonly used functions; translations,
reflections, dilations; effects on linear and
quadratic graphs of parameter changes in
equations.
Discovering Advanced Algebra
pgs. 186, 188, 202, 309
Students investigate using a
graphing calculator what
happens to the equation of a
linear function when you
translate the graph of a line
Do now
Written assessments
Teacher observations
· How can change be best represented mathematically?
Resources
Standard 4.3 Patterns and Algebra
Essential Questions :
1. Analyze and explain the general properties
and behavior of functions of one variable,
using appropriate graphing technologies:
Slope of a line or curve, domain and range,
intercepts, maximum/minimum, estimating
roots of an equation, intersecting points as
solutions of systems of equations, rates of
change.
Discovering Advanced Algebra
pgs. 121-124, 151-152
Various workbooks
- Students use motion sensor to
calculate the speed of a balloon
rocket
- Cooperative learning graphing
activities
Do now
Written assessments
Teacher observations
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
B. Functions and Relationships
4.3.B 8th Grade Advanced Algebra 261
· How are patterns of change related to the behavior of functions?
Learning Experiences Assessments
· How can change be best represented mathematically?
Resources
Standard 4.3 Patterns and Algebra
Essential Questions :
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
B. Functions and Relationships
- Cooperative learning graphing
activities
- Direct instruction
- Graphing calculator
Do now
Written assessments
Teacher observations
3. Understand and compare the properties of
classes of functions, including exponential,
polynomial, rational, and trigonometric
functions; linear vs. non-linear.
Various workbooks
4.3.B 8th Grade Advanced Algebra 262
· How are patterns of change related to the behavior of functions?
· How can change be best represented mathematically?
- Students solve real world
problems to understand finite
differences/functions using
physical representations
- Students investigate cost of
living growth exponentially
Do now
Written assessments
Teacher observation
Discovering Advanced Algebra
Chapter 5
2. Use patterns, relations, symbolic algebra,
and linear functions to model situations: Using
concrete materials (manipulatives), tables,
graphs, verbal rules, algebraic expressions/
equations/ inequalities; Growth situations,
such as population growth and compound
interest, using recursive formulas.
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Assessments
Do now
Written assessments
Teacher observation
Standard 4.3 Patterns and Algebra
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
C. Modeling Essential Questions :
Knowledge/Skills/Understanding Learning Experiences
1. Analyze functional relationships to explain
how a change in one quantity can result in a
change in another, using pictures, graphs,
charts, and equations.
Resources
Students investigate using
exponential functions to model
real world growth and decay
scenarios
Discovering Advanced Algebra
Chapter 5
4.3.C 8th Grade Advanced Algebra 263
· How are patterns of change related to the behavior of functions?
· How can change be best represented mathematically?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Assessments
Standard 4.3 Patterns and Algebra
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
C. Modeling Essential Questions :
Knowledge/Skills/Understanding Learning ExperiencesResources
- Direct instruction
- Cornering the Market
investigation: students simulate
what happens when a popular
new product enters the Market
- Students investigate the
breaking point of spaghetti
- Students use recursion to
explore loan balances and
payment opt
Cooperative learning activities
using the graphing calculator
Do now
Written assessments
Teacher observation
Do now
Teacher observation
3. Use functions to model real-world
phenomena and solve problems that involve
varying quantities: Linear, quadratic,
exponential, periodic (sine, cosine), and step
functions (e.g. price of mailing a first class
letter over the past 200 years), direct and
inverse variation, absolute value, expressions,
equations and inequalities, same function can
model variety of phenomena, growth/decay
and change in the natural world, application
in mathematics, biology, and economics
(including compound interest).
4. Analyze and describe how a change in an
independent variable leads to change in a
dependent one.
Discovering Advanced Algebra
Chapter 5 pgs. 38-41, 52-54, 62-
63, 67-70, 178, 180, 185, 537
Teacher created materials
4.3.C 8th Grade Advanced Algebra 264
· How are patterns of change related to the behavior of functions?
· How can change be best represented mathematically?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Assessments
Standard 4.3 Patterns and Algebra
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
C. Modeling Essential Questions :
Knowledge/Skills/Understanding Learning ExperiencesResources
Investigation on the Tower of
Hanoi.
Do now
Written assessments
Teacher observation
5. Convert recursive formulas to linear or
exponential functions (e.g. Tower of Hanoi
and doubling).
Discovering Advanced Algebra
Chapter 1
4.3.C 8th Grade Advanced Algebra 265
· How are patterns of change related to the behavior of functions?
1. Solve simple linear inequalities. Teacher created materials
Various workbooks
- Direct Instruction
- Investigations through graphing
Do now
Written assessments
Teacher observation
Teacher created materials
Various workbooks
- Direct Instruction
- Investigations using the
graphing calculator
- Geometer's Sketchpad activity
Do now
Written assessments
Teacher observation
2. Evaluate and simplify expressions, add and
subtract polynomials, multiply a polynomial
by a monomial or binomial, divide a
polynomial by a monomial.
Discovering Advanced Algebra
pgs. 414 - 416
Various workbooks
- Cooperative learning activities
using the algebra tiles
- Investigations using the column
method and area method
Do now
Written assessments
Teacher observation
3. Select and use appropriate methods to solve
equations and inequalities: Linear equations -
algebraically, Quadratic equations - factoring
(when the coefficient of x2 is 1) and using the
quadratic formula, All types of equations
using graphing, computer, and graphing
calculator techniques.
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Resources
Standard 4.3 Patterns and Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
D. Procedures
Grades 7 - 8
4.3.D 8th Grade Advanced Algebra 266
· How are patterns of change related to the behavior of functions?
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Resources
Standard 4.3 Patterns and Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
D. Procedures
Grades 7 - 8
4. Judge the meaning, utility and
reasonableness of the results of symbol
manipulations, including those carried out by
technology.
Teacher created materials
Various workbooks
Investigations using the graphing
calculator
Do now
Written assessments
Teacher observation
- Direct Instruction
- Cooperative learning activites
Do now
Written assessments
Teacher observation
5. Students perform arithmetic operations on
rational expressions.
Teacher created materials
Various workbooks
4.3.D 8th Grade Advanced Algebra 267
· How can spatial relationships be described by careful use of geometric language?
Do now
Written assessments
Teacher observation
Assessments
Teacher created problems based on
real world situations
Discovering Advanced Algebra
pgs. 77 - 81, Chapter 13
Do now
Written assessments
Teacher observation
Projects
Learning Experiences
- Students investigate pulse rates
and practice making box plots
- Students analyze data about
backpacks and determine how
much the typical backpack
weighs
- Graphing calculator
investigations
Cooperative learning activities
using the graphing calculator
1. Select and use appropriate representations
for sets of data, and measures of central
tendency (mean, median, and mode): Type of
display most appropriate for given data; Box-
and-whisker plot, upper quartile, lower
quartile; Scatter plot; Calculators and
computer used to record and process
information; Finding the median and mean
(weighted average) using frequency data;
Effect of additional data on measures of
central tendency.
2. Make inferences and formulate and
evaluate arguments based on displays and
analysis of data sets.
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
ResourcesKnowledge/Skills/Understanding
· How can classifying help me in organizing data to solve problems?
· How can statistics help us to understand real world situations?
4.4.A 8th Grade Advanced Algebra 268
· How can spatial relationships be described by careful use of geometric language?
AssessmentsLearning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Essential Questions :
ResourcesKnowledge/Skills/Understanding
· How can classifying help me in organizing data to solve problems?
· How can statistics help us to understand real world situations?
Investigations Do now
Written assessments
Teacher observation
Do now
Written assessments
Teacher observation
5. Evaluate the use of data in real world
context.
Various workbooks Cooperative learning activities Do now
Written assessments
Teacher observation
4. Use surveys and sampling techniques to
generate data and draw conclusions about
large groups.
3. Estimate lines of best fit and use them to
interpolate within the range of the data.
Discovering Advanced Algebra
pg. 131
Students investigate and extend
"The Wave" activity
Discovering Advanced Algebra
pg. 128
4.4.A 8th Grade Advanced Algebra 269
· How can spatial relationships be described by careful use of geometric language?
Resources
2. Determine probabilities of compound
events.
Do now
Written assessments
Teacher observation
- Direct Instruction
- Cooperative learning activities
· How can statistics help us to understand real world situations?
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
1. Interpret probabilities as ratios, percents,
and decimals.
Discovering Advanced Algebra
pg. 687
"Dieing for a Four"
investigation: students conduct
and analyze playing a board
game in which they must roll a 4
on the die before taking the first
turn
Cooperative learning activities
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding
Do now
Written assessments
Teacher observation
3. Explore the probabilities of conditional
events (e.g., if there are seven marbles in a
bag, three red and four green, what is the
probability that two marbles picked from the
bag, without replacement, are both red).
Do now
Written assessments
Teacher observation
Discovering Advanced Algebra
pg. 672
Teacher created materials
Various Workbooks
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Learning Experiences Assessments
Essential Questions : Essential Questions :
· How can classifying help me in organizing data to solve problems?
B. Probability
4.4.B 8th Grade Advanced Algebra 270
· How can spatial relationships be described by careful use of geometric language?
Resources
· How can statistics help us to understand real world situations?
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Learning Experiences Assessments
Essential Questions : Essential Questions :
· How can classifying help me in organizing data to solve problems?
B. Probability
6. Play and analyze probability-based games,
and discuss the concepts of fairness and
expected value.
Teacher created materials
Do now
Written assessments
Teacher observation
Class discussion
Cooperative learning activities
used to solve real life problems
4. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models:
Frequency, relative frequency.
Do now
Written assessments
Teacher observation
Discovering Advanced Algebra
pg. 659
Teacher created materials
Students will play a variety of
probability games
Do now
Written assessments
Teacher observation
5. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
Teacher created materials
Various workbooks
Students use the multiplication
rule for independent events and
calculate the theoretical
probability of rolling a sum of 6
with 2 dice
4.4.B 8th Grade Advanced Algebra 271
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
1. Apply the multiplication principle of
counting: Permutations: ordered situations
with replacement (e.g., number of possible
license plates) vs. ordered situations without
replacement (e.g., number of possible slates of
3 class officers from a 23 student class);
Factorial notation; Concept of combinations
(e.g., number of possible delegations of 3 out
of 23 students).
Discovering Advanced Algebra
pgs. 694-698, 703- 707
Various workbooks
- Investigation when students
explore the placements of jigsaw
puzzle pieces to determine
placement possibilities
-Students determine the number of
handshakes in a social setting
- Students analyze a simulated
lottery game to determine
probability of winn
Do Now
Written assessments
Teacher observation
2. Explore counting problems involving Venn
diagrams with three attributes.
Various workbooks
Teacher created materials
Students use Venn diagrams to
solve problems
Do Now
Written assessments
Teacher observation
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.C 8th Grade Advanced Algebra 272
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
C. Systematic Listing and Counting
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
3. Apply techniques of systematic listing,
counting, and reasoning in a variety of
different contexts.
Various workbooks
Teacher created materials
Direct instruction Do Now
Written assessments
Teacher observation
4.4.C 8th Grade Advanced Algebra 273
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
1. Use vertex-edge graphs and algorithmic
thinking to represent and find solutions to
practical problems: Finding the shortest
network connecting specified sites; Finding a
minimal route that includes every street;
Finding the shortest route on a map from one
site to another; Finding the shortest circuit on
a map that makes a tour of specified sites;
Limitations of computers.
Teacher created materials
Various workbooks
Cooperative learning activities Do now
Written assessments
Teacher observation
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
4.4.D 8th Grade Advanced Algebra 274
· How can spatial relationships be described by careful use of geometric language?
2. Solve problems that arise in mathematics
and in other contexts: Open-ended problems;
Non-routine problems; Problems with
multiple solutions; Problems that can be
solved in several ways.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
4.5.A 8th Grade Advanced Algebra 275
· How can spatial relationships be described by careful use of geometric language?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
4. Pose problems of various types and levels of
difficulty.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
5. Monitor their progress and reflect on the
process of their problem solving activity.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.A 8th Grade Advanced Algebra 276
· How can spatial relationships be described by careful use of geometric language?
Resources
3. Analyze and evaluate the mathematical
thinking and strategies of others.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
B. Communication
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
1. Use communication to organize and clarify
mathematical thinking: Reading and writing;
Discussion, listening, and questioning.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
AssessmentsKnowledge/Skills/Understanding
4.5.B 8th Grade Advanced Algebra 277
· How can spatial relationships be described by careful use of geometric language?
Resources
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Flemington Raritan School District
Mathematics Curriculum
B. Communication
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences AssessmentsKnowledge/Skills/Understanding
4. Use the language of mathematics to express
mathematical ideas precisely.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.B 8th Grade Advanced Algebra 278
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
number, algebra, and geometry).
Do now
Written assessments
Teacher observation
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Resources
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
C. Connections
4.5.C 8th Grade Advanced Algebra 279
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences AssessmentsResources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
C. Connections
Do now
Written assessments
Teacher observation
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4. Apply mathematics in practical situations
and in other disciplines.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
5. Trace the development of mathematical
concepts over time and across cultures.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.C 8th Grade Advanced Algebra 280
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences Assessments
1. Recognize that mathematical facts,
procedures, and claims must be justified.
Do now
Written assessments
Teacher observation
3. Select and use various types of reasoning
and methods of proof.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Resources
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
D. Reasoning
4.5.D 8th Grade Advanced Algebra 281
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences AssessmentsResources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
D. Reasoning
Do now
Written assessments
Teacher observation
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
5. Make and investigate mathematical
conjectures: Counterexamples as a means of
disproving conjectures; Verifying conjectures
using informal reasoning or proofs.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.D 8th Grade Advanced Algebra 282
· How can spatial relationships be described by careful use of geometric language?
2. Select, apply, and translate among
mathematical representations to solve
problems.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Create and use representations to organize,
record, and communicate mathematical ideas:
Concrete representations (e.g., base-ten blocks
or algebra tiles); Pictorial representations
(e.g., diagrams, charts, or tables); Symbolic
representations (e.g., a formula); Graphical
representations (e.g., a line graph).
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Resources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
E. Representations
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
4.5.E 8th Grade Advanced Algebra 283
· How can spatial relationships be described by careful use of geometric language?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
E. Representations
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.E 8th Grade Advanced Algebra 284
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
Do now
Written assessments
Teacher observation
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Resources
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
F. Technology
4.5.F 8th Grade Advanced Algebra 285
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences AssessmentsResources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Knowledge/Skills/Understanding
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
F. Technology
Do now
Written assessments
Teacher observation
6. Use computer-based laboratory technology
for mathematical applications in the sciences.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
5. Use computer software to make and verify
conjectures about geometric objects.
Discovering Advanced Algebra
Chapters 1 - 13
Various workbooks
Teacher created materials
Ongoing through all
investigations, activities and
class discussions
Do now
Written assessments
Teacher observation
4.5.F 8th Grade Advanced Algebra 286
Algebra Warm-Ups Scott McFadden
Algebra Teacher's Activities Kit Judith and Gary Robert Muschla
Skills for Success - Algebra
Jossey-Bass 2003
Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999
Dale Seymour 1987
Geo Joke Worksheets Christine A. Koers Nasco 2002
Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002
Algebra Joke Worksheets Christine A. Koers Nasco 2003
Clever CountingLappan, Fey, Fitzgerald, Friel, and
PhillipsPrentice Hall 2002
GeometryMary Lee Vivian, Tammy Bohn-
Voepel, and Margaret ThomasMcGraw Hill 2003
Title of Resource Publisher Copyright
Discovering Advanced AlgebraJerald Murdock, Ellen and Eric
KamischkeKey Curriculum Press 2004
Author(s)
8th Grade Advanced Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
2004
1986
2003
Milliken
Houghton Mifflin
Carson-Dellosa Publishing
Company, Inc.Theresa Kane McKell
Geometry
Algebra
Sara Freeman
Dolciani, Brown, and Cole
8th Grade Advanced Algebra Resources 287
Title of Resource Publisher CopyrightAuthor(s)
8th Grade Advanced Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Preparing for the New Jersey GEPA - Grade 8 David J. Glatzer and Joyce Glatzer Amsco School Publications, Inc. 2005
Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002
GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000
Navigating through ProbabilityShaughnessy, Barrett, Billstein,
Kranendonk, and Peck
The National Council of
Teachers of Mathematics, Inc.2004
80 Activities to Make Basic Algebra Easier Robert S. Graflund Walch Publishing 2001
Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006
McGraw Hill 2003
Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005
GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000
Algebra Puzzlers Theresa Kane McKell Frank Schaffer Publications 1998
Algebra IIChad Helgeson and Margaret
ThomasMcGraw Hill 2003
AlgebraMary Lee Vivian and Margaret
Thomas
Algebra and Trigonometry 1986Houghton MifflinDolciani, Sorgenfrey, Brown, and
Kane
8th Grade Advanced Algebra Resources 288
Title of Resource Publisher CopyrightAuthor(s)
8th Grade Advanced Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Algebra Practice Exercises Thomas E. Campbell J. Weston Walch Publisher 1996
The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001
Navigating through Data AnalysisBurrill, Franklin, Godbold, and
Young
The National Council of
Teachers of Mathematics, Inc.2003
Navigating through GeometryDay, Kelley, Krussel, Lott, and
Hirstein
The National Council of
Teachers of Mathematics, Inc.2001
New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008
8th Grade Advanced Algebra Resources 289
Exponents and Exponential Models
5 8
Quadratics
7
Linear Equations
3 8
Systems of Equations and Inequalities
3, 6 5
Graphing, Slope, and Writing the Equation of
a Line
8th Grade Advanced Algebra
Discovering Advanced AlgebraDiscovering Advanced Algebra
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit
Pacing Guide
Number of Blocks
12
Polynomials
7 6
3 6
Functions
4, 5 4
8th Grade Advanced Algebra Pacing Guide 290
8th Grade Advanced Algebra
Discovering Advanced AlgebraDiscovering Advanced Algebra
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Unit
Pacing Guide
Number of Blocks
Radical Expressions
4 8
Benchmark Assessment - Midterm
----- -----
Benchmark Assessment - Final
----- -----
Probability and Discrete Math
Other resources 7
Rational Expressions
9 11
8th Grade Advanced Algebra Pacing Guide 291
Algebra 2 Curriculum
292
A. Number Sense
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Quiz 1.1-1.2, Unit Test 1
Quiz 1.1-1.2, Unit Test 1
Algebra 2
pgs. 3, 4, 7, 17, 39, 58
2. Compare and order rational and irrational
numbers.
Written classwork
Students use linear equations to
solve real life problems such as
how much fuel a car consumes
over various distances
3. Develop conjectures and informal proofs of
properties of number systems and sets of
numbers.
Algebra 2
pgs. 5, 13, 19-24, 201
AssessmentsKnowledge/Skills/Understanding Learning Experiences
Quiz 1.1-1.2, Unit Test 11. Extend understanding of the number system
to all real numbers.
Students graph real numbers on a
number line and problem solve
using algebraic models
Algebra 2
pgs. 3, 5-6, 8, 14, 49-55, 58, 60,
401
Resources
· How can we compare and contrast numbers?
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.1 Number and Numerical Operations
4.1.A 8th Grade Algebra 2 293
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Quiz 4.1-4.3, Unit Test 4
4. Understand and apply the laws of exponents
to simplify expressions involving numbers
raised to powers.
Algebra 2
pgs. 323-328, 388, 401-404, 480,
483
Quiz 6.1-6.3, Unit Test 6,
Quiz 7.1-7.2, Unit Test 7
Direct instruction
- Students use a graphing
calculator to perform matrix
operations
- Direct instruction
- Students use matrices to find
the number of calories burned
3. Perform operations on matrices.
· Addition and subtraction
· Scalar multiplication
Algebra 2
pgs. 200-206, 207, 209, 240
Graphing calculator
Quiz 1.1-1.2, Unit Test 1Algebra 2
pgs. 5-9, 13, 19-24, 58, 201
· How can we compare and contrast numbers?
Quiz 6.1-6.3, Quiz 6.4-6.6,
Unit Test 6, Quiz 7.1-7.2,
Quiz 7.3-7.4, Unit Test 7
2. Develop, apply, and explain methods for
solving problems involving rational and
negative exponents.
Standard 4.1 Number and Numerical Operations
Essential Questions :
Knowledge/Skills/Understanding Assessments
B. Numerical Operations
Algebra 2
pgs. 323-328, 345-350, 352-357,
401-413, 415-420, 437-442, 456
Ongoing throughout
investigations
1. Extend understanding and use of operations
to real numbers and algebraic procedures.
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Students use exponents to solve
finding the per capita GDP of
Denmark
Learning ExperiencesResources
4.1.B 8th Grade Algebra 2 294
C. Estimation
· How can problems in the real world be solved with Mathematics?
· How can estimation be useful to us to reason out solutions to problems?
· How can spatial relationships be described by careful use of geometric language?
Standard 4.1 Number and Numerical Operations
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can we compare and contrast numbers?
Resources
3. Recognize the limitations of estimation,
assess the amount of error resulting from
estimation, and determine whether the error is
within tolerance limits.
Algebra 2
pg. 103
Students employ the skill of
estimation in prediction of
outcomes when solving real-life
mathematical problems
Teacher observation
Student solutions to practice
exercises
4.1.C 8th Grade Algebra 2 295
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Standard 4.2 Geometry and Geometrical Properties
Essential Questions :
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
AssessmentsResources
A. Geometric Properties
1. Draw perspective views of 3D objects on
isometric dot paper, given 2D representations
(e.g. nets or projective views).
Algebra 2
pgs. 194-195
Students write a system of linear
equations to model real-life
situations
Teacher observation
Student solutions to practice
exercises
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Knowledge/Skills/Understanding Learning Experiences
4.2.A 8th Grade Algebra 2 296
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Resources
Essential Questions : Essential Questions :
b. Outcome of extending iterative process
indefinitely
Algebra 2
pgs. 275-276, 482
Students use real-life problem
solving (e.g. finding the balance
of an account; using an
exponential model to study and
analyze endangered species)
Teacher observation
Whole class discussions of
examples
Student solutions to practice
problems
1. Generate and analyze iterative geometric
patterns.
a. Fractals (e.g. Sierpinski's Triangle)
Standard 4.2 Geometry and Geometrical Properties
Students apply complex numbers
to fractal geometry
Teacher observation
Student solutions to practice
exercises
Algebra 2
pgs. 274-276
B. Transforming Shapes
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Knowledge/Skills/Understanding Learning Experiences Assessments
4.2.B 8th Grade Algebra 2 297
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
C. Coordinate Geometry
Standard 4.2 Geometry and Geometrical Properties
AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources
1. Use coordinates in geometry to represent
and verify properties of lines.
a. Distance between two points
Algebra 2
pgs. 589-594, 642
Students derive the distance
formula
Quiz 10.1-10.3, Unit Test 10
b. Midpoint and slope of a line segment Algebra 2
pgs. 75-78, 92, 590-594, 642
Students use the distance and
midpoint formulas in finding the
diameter of a broken dish
Quiz 2.1-2.3, Unit Test 2,
Quiz 10.1-10.3, Unit Test 10
Quiz 3.1-3.2, Unit Test 3
d. Lines with the same slope are parallel Algebra 2
pgs. 77-140, 143
Students examine systems with
many or no solutions
Quiz 2.1-2.3, Unit Test 2,
Quiz 3.1-3.2, Unit Test 3
c. Finding the intersection of two lines Algebra 2
pgs. 139-146, 186
Students use linear systems to
solve the real-life problem of
choosing the least expensive
long distance phone system
4.2.C 8th Grade Algebra 2 298
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
C. Coordinate Geometry
Standard 4.2 Geometry and Geometrical Properties
AssessmentsKnowledge/Skills/Understanding Learning ExperiencesResources
e. Lines that are perpendicular have slopes
whose product is -1
Algebra 2
pgs. 77, 79-80, 89
Students examine and analyze
real-life examples of slope (e.g.
slope as a geometrical use; slope
as a rate of change)
Quiz 2.1-2.3, Unit Test 2
4.2.C 8th Grade Algebra 2 299
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences
Do Now
Written Assessments
Teacher Observation
AssessmentsKnowledge/Skills/Understanding
Algebra 2
Chapters 1 - 10
1. Solve problems requiring calculations that
involve different units of measurement within
a measurement system (e.g., 4’3” plus 7’10”
equals 12’1”).
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
D. Units of Measurement
Standard 4.2 Geometry and Geometrical Properties
3. Recognize that the degree of precision
needed in calculations depends on how the
results will be used and the instruments used
to generate the measurements.
Resources
Appropriate use throughout
lessons
Do Now
Written Assessments
Teacher Observation
2. Use approximate equivalents between
standard and metric systems to estimate
measurements (e.g., kilometers is about 3
miles).
Algebra 2
Chapters 1 - 10
Appropriate use throughout
lessons
Do Now
Written Assessments
Teacher Observation
Algebra 2
Chapters 1 - 10
Appropriate use throughout
lessons
4.2.D 8th Grade Algebra 2 300
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences AssessmentsKnowledge/Skills/Understanding
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
D. Units of Measurement
Standard 4.2 Geometry and Geometrical Properties
Resources
Do Now
Written Assessments
Teacher Observation
Appropriate use throughout
lessons
Do Now
Written Assessments
Teacher Observation
Appropriate use throughout
lessons
Do Now
Written Assessments
Teacher Observation
Appropriate use throughout
lessons
6. Recognize that repeating decimals
correspond to fractions and determine their
fractional equivalents:
5/7 = 0.714285714285...
= 0.714285
Algebra 2
Chapters 1 - 10
4. Select and use appropriate units and tools to
measure quantities to the degree of precision
needed in a particular problem-solving
situation.
Algebra 2
Chapters 1 - 10
5. Recognize that all measurements of
continuous quantities are approximations.
Algebra 2
Chapters 1 - 10
4.2.D 8th Grade Algebra 2 301
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Learning Experiences AssessmentsKnowledge/Skills/Understanding
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
D. Units of Measurement
Standard 4.2 Geometry and Geometrical Properties
Resources
Do Now
Written Assessments
Teacher Observation
7. Construct meanings for common irrational
numbers, such as pi (π) and the square root of
two.
Algebra 2
Chapters 1 - 10
Appropriate use throughout
lessons
4.2.D 8th Grade Algebra 2 302
· How can knowledge of geometric properties help in problem solving situations?
· How can coordinate grid systems help us analyze situations?
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Teacher observation
Student solutions to class
exercises and homework
problems
Standard 4.2 Geometry and Geometrical Properties
Learning Experiences AssessmentsResources
Essential Questions :
Knowledge/Skills/Understanding
E. Measuring Geometric Objects
b. Estimation of area, perimeter, volume, and
surface area.
Algebra 2
pgs. 28, 375
Cooperative learning Teacher observation
Student solutions to class
exercises and homework
problems
· How does the mathematics of geometry enable us to wonder and understand our natural
and physical world?
1. Use a variety of strategies to determine
perimeter and area of plane figures and
surface area and volume of 3D figures.
a. Finding which shape has minimal (or
maximal) area, perimeter, volume, or surface
area under given conditions using graphing
calculators, dynamic geometric software,
and/or spreadsheets.
Algebra 2
pg. 375
Graphing calculator
Students use the graph of
polynomial functions to solve
real-life problems such as
maximizing the volume of a box
4.2.E 8th Grade Algebra 2 303
· How are patterns of change related to the behavior of functions?
Conclusions drawn from
activity
Student written explanations
· How can change be best represented mathematically?
1. Use models and algebraic formulas to
represent and analyze sequences and series.
a. Explicit formulas for nth terms.
Algebra 2
pgs. 659, 661, 656, 681
Students evaluate and write
recursive rules for sequences
Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Resources
Standard 4.3 Patterns and Algebra
Assessments
Class discussion of calculator
activity
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
2. Develop an informal notion of limit. Teacher created materials Investigation Cooperative activity
Class discussion
Do Nows
Teacher observation
Student solutions to practice
exercises
Geometer's Sketchpad Geometer's Sketchpad
Students evaluate and write
recursive rules for sequences.
c. Sums of finite and infinite geometric series.
b. Sums of finite arithmetic series. Algebra 2
pg. 675
Essential Questions :
Knowledge/Skills/Understanding
A. Patterns
4.3.A 8th Grade Algebra 2 304
· How are patterns of change related to the behavior of functions?
· How can change be best represented mathematically?
Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Resources
Standard 4.3 Patterns and Algebra
Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
Essential Questions :
Knowledge/Skills/Understanding
A. Patterns
Cooperative work/graphic
organizers
Unit Test 11
3. Use inductive reasoning to form
generalizations.
Algebra 2
pgs. 689-690
Students use mathematical
induction to prove statements
about all positive integers
4.3.A 8th Grade Algebra 2 305
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources
1. Understand relations and functions and
select, convert flexibility among, and use
various representations for them, including
equations or inequalities, tables and graphs.
Algebra 2
pgs. 19, 41-43, 67, 72, 82-88, 108-
113, 114-121, 131-132, 139-146,
156-162, 249-255, 300-302, 306-
312, 314, 316, 331-332, 373-388,
390, 466, 475, 524, 601-608, 609-
614, 615-620, 643-644, 595-596
Graphing calculator
- Students use piecewise
functions to model real-life
quantities
- Students graph and solve
systems of linear equations and
linear inequalities
- Students write quadratic
functions given characteristics of
their graphs
- Students analyze the graph of a
polynomial function
- Students graph and write
equations of circles
- Students graph and write
equations of ellipses
- Students graph and write
equations of hyperbolas
Unit Test 1
Quiz 2.1-2.3, Unit Test 2
Quiz 3.1-3.2, Quiz 3.4, Unit
Test 3
Quiz 5.1-5.3,Unit Test 5
Quiz 6.1-6.3, Unit Test 6
Quiz 8.1-8.3, Unit Test 8
Quiz 10.1-10.3, Quiz 10.4-
10.5, Unit Test 10
4.3.B 8th Grade Algebra 2 306
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources
2. Analyze and explain the general properties
and behavior of functions of one variable,
using appropriate graphing technologies.
a. Slope of a line or curve
Algebra 2
pgs. 75-81
Students find slopes of lines and
classify parallel and
perpendicular lines
Teacher observation
Student solutions to practice
problems
b. Domain and range Algebra 2
pg. 453
Students use a graphing
calculator to find and draw
statistical graphs (e.g. NBA foul
shooting percentages).
Do Now
Teacher observation
Classwork activities
4.3.B 8th Grade Algebra 2 307
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources
c. Intercepts Graphing calculator Students use the graphing
calculator to find the real
solution to equations (e.g.
quadratic equations, polynomial
equations, an equation with an
extraneous solution)
Teacher observation
Solutions to classwork and
homework exercises
d. Continuity Algebra 2
pgs. 271, 372, 439
Direct instruction Teacher observation
Solutions to classwork and
homework exercises
e. Maximum/minimum Algebra 2
pgs. 121, 372, 546
Graphing calculator
- Students use technology to find
quadratic models
- Students examine and analyze
turning points corresponding to
local minimum and maximum
values
- Students use rational functions
to find a local minimum
Do Now
Teacher observation
Student solutions to practice
exercises
4.3.B 8th Grade Algebra 2 308
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources
Students find and use the
discriminant of quadratic
equations
Student oral and written
solutions
3. Understand and perform transformations
on commonly used functions.
· Effects on linear and quadratic graphs of
parameter changes in equations
Algebra 2
pg. 293
i. Rate of change Algebra 2
pgs. 90
Graphing calculator
Students use a graphing
calculator to graph equations of
the form y=f(x)
Teacher observation
Student graphs
f. Estimating roots of equations. Algebra 2
pgs. 252, 290, 308, 374-375, 549
Graphing calculator
- Students use technology to
approximate zeros
- Students find the rational
zeroes of a polynomial function
Quiz 5.1-5.3, Unit Test 5
g. Intersecting points as solutions of systems of
equations
Algebra 2
pgs. 146, 149, 154, 300
Graphing calculator Teacher observation
Student graphs
4.3.B 8th Grade Algebra 2 309
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Essential Questions :
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
B. Functions and Relationships
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources
4. Understand and compare the properties of
classes of functions, including exponential,
polynomial, rational, and trigonometric
functions.
a. Linear vs. non-linear
Algebra 2
pgs. 19-22, 329-335, 465-471,
481-485, 509-516, 524-526, 595
Graphing calculator
- Students evaluate/graph
polynomial functions
- Students graph and use
exponential growth functions
- Students evaluate and graph
logistic growth functions
- Students graph and write
equations of parabolas
Quiz 1.3-1.5, Unit Test 1,
Quiz 6.1-6.3, Unit Test 6,
Quiz 8.1-8.3, Unit Test 8
Direct instruction Teacher observation
Student solutions to class
examples
c. Increasing/decreasing on an interval Algebra 2
pgs. 374, 518
Graphing calculator activity Do Nows
Teacher observation
Students solutions to practice
exercises
b. Symmetry Algebra 2
pgs. 249, 595-596
4.3.B 8th Grade Algebra 2 310
· How are patterns of change related to the behavior of functions?
Quiz 2.4-2.5
Unit Test 2
Quiz 9.1-9.3
Unit Test 9
Students use absolute value in
real-life situations (e.g. Path of a
golf ball; graph functions of the
path of sunlight)
Standard 4.3 Patterns and Algebra
Unit Test 1
Unit Test 2
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
C. Modeling
Knowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
b. Direct and inverse variation
1. Use functions to model real-world
phenomena and solve problems that involve
varying quantities.
a. Linear, quadratic, exponential, periodic
(sine and cosine), and step functions (e.g.,
price of mailing a first class letter over the
past 200 years)
Algebra 2
pgs. 70, 115-121, 266, 361, 468-
471, 510, 512
Graphing calculator
Algebra 2
pgs. 94, 97-98, 534-539
c. Absolute value Algebra 2
pgs. 52-55, 121, 126-127
Graphing calculator
Resources
- Exploration
- Direct instruction
Unit Test 2
Quiz 8.1-8.3
Unit Test 8
Assessments
- Students write linear equations
- Students write direct variation
equations by analyzing real-life
mathematical models
4.3.C 8th Grade Algebra 2 311
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
C. Modeling
Knowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources Assessments
Students examine and analyze
models of exponential decay.
(e.g. Descending value of an
automobile.) Students analyze
models with power functions
Quiz 8.1-8.3
Unit Test 8
- Exploration
- Direct instruction
e. Same function can model a variety of
phenomena
Algebra 2
pgs. 284, 288, 294, 297, 300, 303,
519, 521
f. Growth/decay and change in the natural
world
Text pages: 325, 467-471, 476-479,
482, 509-516, 519
Graphing calculator
d. Expressions, equations and inequalities Algebra 2
pgs. 21, 27, 44, 46-47, 93, 110,
112-113, 158, 165, 169, 172, 294-
297, 300, 302-305, 325
- Exploration
- Direct instruction
Do Nows
Class discussion of examples
and exploration
Teacher observation
Unit Test 1, Unit Test 2
Quiz 3.3-3.4
Unit Test 3, Unit Test 5
4.3.C 8th Grade Algebra 2 312
· How are patterns of change related to the behavior of functions?
Standard 4.3 Patterns and Algebra
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions :
C. Modeling
Knowledge/Skills/Understanding Learning Experiences
· How can patterns, relations, and functions be used as tools to best describe and
help explain real – life situations?
· How can change be best represented mathematically?
Resources Assessments
g. Applications in mathematics, biology, and
economics (including compound interest)
Algebra 2
pgs. 21, 24, 28, 78, 101, 254, 275,
277-278, 288, 325, 332, 391, 399,
410, 413, 417, 419, 433, 436, 468-
471, 482, 497, 521-522, 527, 535,
551, 559, 563, 572
Students solve real-life models
mathematically (e.g. Number of
households owning a VCR; US
GDP and logistic growth; focal
lengths)
Teacher observation
Student written work and
solutions to examples
Students evaluate functions in
real-life models (E.g. Domain
and range of the Piccard/Jones
balloon flight; Boston Marathon
finishers as related to age;
domain and range examining cap
sizes)
2. Analyze and describe how a change in an
independent variable leads to change in a
dependent one.
Teacher observation
Oral and written explanations
Algebra 2
pgs. 69-73
4.3.C 8th Grade Algebra 2 313
· How are patterns of change related to the behavior of functions?
c. Divide a polynomial by a monomial Algebra 2
pgs. 556, 559
Direct instruction Quiz 9.4-9.6
Unit Test 9
b. Multiply a polynomial by a monomial or
binomial
Algebra 2
pgs. 251, 253-254, 338-343, 389
Direct instruction Quiz 5.1-5.3
Unit Test 5
Quiz 6.1-6.3
Unit Test 6
Resources
Standard 4.3 Patterns and Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
D. Procedures
Grades 7 - 8
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
1. Evaluate and simplify expressions.
a. Add and subtract polynomials
Algebra 2
pgs. 338, 340-343, 389
Students use polynomials in real-
life situations (E.g. Finding net
farm income; finding total
revenue from the sale of
softbound books; ratio of heat
release to size of a long-distance
runner; value of gold mined in a
year)
Quiz 6.1-6.3
Unit Test 6
4.3.D 8th Grade Algebra 2 314
· How are patterns of change related to the behavior of functions?
Resources
Standard 4.3 Patterns and Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
D. Procedures
Grades 7 - 8
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
- Direct instruction
- Exploration
Quiz 2.1-2.3, Unit Test 2
Quiz 3.1-3.2, Unit Test 3
Quiz 5.1-5.3, Quiz 5.4-5.6,
Unit Test 5
Quiz 6.1-6.3, Unit Test 6
Quiz 8.1-8.3, Unit Test 8
Quiz 10.1-10.3, Quiz 10.4-
10.5, Unit Test 10
b. Quadratic equations - factoring (when the
coefficient of x^2 is 1) and using the quadratic
formula
Algebra 2
pgs. 256-263, 281-283, 291-298,
314-316
Students factor with: special
patterns; monomials first;
finding zeros of a quadratic
function; solving quadratic
inequalities.
Quiz 5.1-5.3
Quiz 5.4-5.6
Unit Test 5
2. Select and use appropriate methods to solve
equations and inequalities.
a. Linear equations - algebraically
Algebra 2
pgs. 5, 19-24, 41-47, 139, 177-
183, 186-188, 201
Direct instruction Quiz 1.3-1.5
Unit Test 1
Quiz 3.1-3.2
Unit Test 3
c. All types of equations using graphing,
computer, and graphing calculator techniques
Algebra 2
pgs. 69-70, 82-88, 131, 139-146,
170-176, 186, 188, 249-255, 291,
306-316, 331-332, 373-390, 466,
475, 524, 595-600, 601-608, 609-
614, 615-620, 643
Graphing calculator
4.3.D 8th Grade Algebra 2 315
· How are patterns of change related to the behavior of functions?
Resources
Standard 4.3 Patterns and Algebra
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
D. Procedures
Grades 7 - 8
Essential Questions :
Knowledge/Skills/Understanding Learning Experiences Assessments
· How can patterns, relations, and functions be used as tools to best describe and
help explain real-life situations?
· How can change be best represented mathematically?
Teacher observation
Oral and written explanations
3. Judge the meaning, utility, and
reasonableness of the results of symbol
manipulations, including those carried out by
technology.
Algebra 2
pgs. 25, 146, 149, 259, 271, 300,
360, 368, 372, 439
Incorporated in all real-life
models
4.3.D 8th Grade Algebra 2 316
· How can spatial relationships be described by careful use of geometric language?
b. Correlation coefficient Algebra 2
pgs. 100 - 105
Direct Instruction Quiz 2.4-2.5
Unit Test 2
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete MathematicsGrades 7 - 8
Assessments
1.Estimate or determine lines of best fit (or
curves of best fit if appropriate) with
technology, and use them to interpolate within
the range of data.
Algebra 2
pgs. 103, 107, 307-308, 311
Exploration Teacher observation
Discussion of exploration
Resources
Essential Questions :
· How can classifying help me in organizing data to solve problems?
2. Analyze data using technology, and use
statistical terminology to describe conclusions.
a. Measures of dispersion: variance, standard
deviation, outliers
Algebra 2
pgs. 453-454
Graphing calculator
Students use a graphing
calculator to find statistics and
draw statistical graphs (e.g. The
number of calories in a
sandwich)
Teacher observation
Discussion of exploration
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
Knowledge/Skills/Understanding Learning Experiences
4.4.A 8th Grade Algebra 2 317
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
A. Data Analysis
Standard 4.4 Data Analysis, Probability and Discrete MathematicsGrades 7 - 8
AssessmentsResources
Essential Questions :
· How can classifying help me in organizing data to solve problems?
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
· How can statistics help us to understand real world situations?
Knowledge/Skills/Understanding Learning Experiences
c. Normal distribution (e.g., approximately
95% of the sample lies between two standard
deviations on either side of the mean)
Algebra 2
pg. 453-454
Exploration Teacher observation
Discussion of exploration
4.4.A 8th Grade Algebra 2 318
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
2. Use concepts and formulas of area to
calculate geometric probabilities.
3. Model situations involving probability with
simulations (using spinners, dice, calculators
and computers) and theoretical models, and
solve problems using these models.
Various workbooks Cooperative learning
Algebra 2
pgs. 718 - 757
· How can statistics help us to understand real world situations?
1. Calculate the expected value of a
probability based game, given the
probabilities and payoffs of the various
outcomes, and determine whether the game is
fair.
Algebra 2
pgs. 734 - 738, 708 - 709, 715 -
716, 724 - 725
Direct instruction Unit 12 Tests
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Teacher observation
Oral and written explanations
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Students use area to find
probability
Unit 12 Tests
4.4.B 8th Grade Algebra 2 319
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
· How can statistics help us to understand real world situations?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
4. Determine probabilities in complex
situations.
a. Conditional events
Algebra 2
pgs. 732-733, 736
5. Estimate probabilities and make predictions
based on experimental and theoretical
probabilities.
Algebra 2
pgs. 753-754
c. Dependent and independent events
b. Complementary events Algebra 2
pgs. 726
Algebra 2
pg. 736
Students explore randomly
selecting two cards from a
standard 52 count deck
Unit 12 Tests
Exploration Unit 12 Tests
Unit 12 TestsExploration
Unit 12 TestsStudents use two six-sided dice
to find the probability of a given
event
4.4.B 8th Grade Algebra 2 320
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
· How can statistics help us to understand real world situations?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Essential Questions : Essential Questions :
B. Probability
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
6. Understand and use the "law of numbers"
(that experimental results tend to approach
theoretical probabilities after a large number
of trials).
Algebra 2
pgs. 717, 757
Unit 12 TestsStudents use length (video
cassette recording-probability of
over-recording)
4.4.B 8th Grade Algebra 2 321
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
Direct instruction Unit 12 Test
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
C. Systematic Listing and Counting
Algebra 2
pgs. 701-752
Real world problem solving Unit 12 Test
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
1. Calculate combinations with replacement
and without replacement.
Algebra 2
pgs. 730-736
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
2. Apply the multiplication rule of counting in
complex situations, recognize the difference
between situations with replacement and
without replacement, and recognize the
difference between ordered and unordered
counting situations.
Algebra 2
pgs. 701-707, 756
Students use permutations to
count the number of ways an
event happens
Unit 12 Test
3. Justify solutions to counting problems.
4.4.C 8th Grade Algebra 2 322
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
C. Systematic Listing and Counting
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
Students use the binomial
theorem to discover the
relationship between Pascal's
triangle and the coefficients of a
binomial expansion
Unit 12 Test4. Recognize and explain relationships
involving combinations and Pascal's Triangle,
and apply those methods to situations
involving probability.
Algebra 2
pg. 701
4.4.C 8th Grade Algebra 2 323
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
- Exploration
- Cooperative learning activities
Included in probability2. Explore strategies for making fair decisions.
a. Combining individual preferences into a
group decision (e.g., determining winner of a
election or selection process)
Various workbooks
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
1. Use vertex-edge graphs and algorithmic
thinking to represent and solve practical
problems.
· Circuits that include every edge in a graph
· Circuits that include every vertex in a graph
Various workbooks - Exploration
- Cooperative learning activities
Teacher made tests
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
4.4.D 8th Grade Algebra 2 324
· How can classifying help me in organizing data to solve problems?
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How can statistics help us to understand real world situations?
Essential Questions : Essential Questions :
D. Vertex-Edge Graphs and Algorithms
Standard 4.4 Data Analysis, Probability and Discrete Mathematics
· How can experimental and theoretical probability be used to make predictions or draw
conclusions?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
b. Determining how many Student Council
representatives each class gets when the
classes have unequal sizes (apportionment)
Teacher created resources Exploration Do Now
4.4.D 8th Grade Algebra 2 325
· How can spatial relationships be described by careful use of geometric language?
Quiz 3.1-3.2, Unit Test 3,
Quiz 5.1-5.3, Unit Test 5
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Assessments
1. Learn mathematics through problem
solving, inquiry, and discovery.
Algebra 2
pgs. 12, 21, 27, 33-39, 52, 60, 85,
93, 110, 141, 151, 258, 355, 361,
375, 533, 542
Incorporated in all mathematical
content.
Teacher observation
Oral and written explanations
ResourcesKnowledge/Skills/Understanding Learning Experiences
2. Solve problems that arise in mathematics
and in other contexts.
a. Open-ended problems
Algebra 2
pgs. 46, 72, 105, 113, 154, 206,
269, 328
Incorporated in all mathematical
content
b. Non-routine problems Algebra 2
pgs. 170-176, 177-183, 229, 254-
255, 272, 279-280, 289, 312, 412,
533
Incorporated in all mathematical
content
c. Problems with multiple solutions
Teacher observation
Student written explanations
Unit Test 3
Quiz 5.5-5.6
Unit Test 5
Algebra 2
pgs. 140, 150, 179, 250-254, 272,
277-278, 550
Incorporated in all mathematical
content
4.5.A 8th Grade Algebra 2 326
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
AssessmentsResourcesKnowledge/Skills/Understanding Learning Experiences
d. Problems that can be solved in several ways Incorporated in all mathematical
content
3. Select and apply a variety of appropriate
problem-solving strategies (e.g., “try a simpler
problem” or “make a diagram”) to solve
problems.
Algebra 2
pgs. 12, 21, 27, 33-39, 52, 60, 85,
93, 110, 141, 151, 258, 355, 361,
375, 533, 542
Incorporated in all mathematical
content.
Students use of problem
solving strategies in oral and
written work
Algebra 2
pgs. 82-83, 91, 148-154, 177-183,
186-187, 216-220, 230-235, 237-
238, 241-242, 282-288, 290-297,
353, 373
Quiz 2.1-2.3, Quiz 2.4-2.5,
Unit Test 2, Quiz 3.1-3.2,
Unit Test 3, Unit Test 4, Quiz
5.4-5.6, Unit Test 5
4. Pose problems of various types and levels of
difficulty.
Algebra 2
pgs. Found throughout text. See,
for example, 46, 72, 105, 113, 154,
170-176, 177-183, 206, 229, 237-
238, 254-255, 269, 272, 279-280,
289, 312, 328, 412, 533, 639
Incorporated in all mathematical
content
Teacher observation
Student solutions to practice
exercises
4.5.A 8th Grade Algebra 2 327
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions :
A. Problem Solving
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
AssessmentsResourcesKnowledge/Skills/Understanding Learning Experiences
5. Monitor their progress and reflect on the
process of their problem solving activity.
Algebra 2
pgs. 2, 66, 138, 198, 248, 322,
400, 464, 532, 588
Incorporated in all mathematical
content
Continual student to student
feedback
Teacher to student feedback
Student self reflection
4.5.A 8th Grade Algebra 2 328
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
b. Discussion, listening, and questioning Algebra 2
pgs. 1, 49, 65, 82, 108, 137, 147,
195, 197, 222, 281, 321, 345, 379,
397
Incorporated in all mathematical
content
Incorporated in all mathematical
content
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning Experiences
1. Use communication to organize and clarify
mathematical thinking.
a. Reading and writing
Algebra 2
pgs. Found throughout the text.
See, for example, 2, 57, 129, 138,
185, 198, 239, 248, 313, 322, 387,
400, 421, 455, 464, 523, 532, 575,
588, 641
Teacher observation based on
whole class and small group
discussions
Student explanation and
mathematical reasoning in
written work
Resources
4.5.B 8th Grade Algebra 2 329
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning ExperiencesResources
2. Communicate mathematical thinking
coherently and clearly to peers, teachers, and
others, both orally and in writing.
Algebra 2
pgs. 1, 2, 47, 49, 57, 63, 65, 72,
82, 108, 129, 137, 138, 145, 147,
153, 185, 191, 195, 197, 198, 206,
222, 239, 248, 281, 305, 313, 321,
322, 345, 379, 387, 393, 397, 399,
400, 406, 421, 455, 463-465, 473,
507, 517, 523, 531-533, 560, 575,
Incorporated in all mathematical
content
Clarity of mathematical logic
in student oral and written
work
Teacher observation
3. Analyze and evaluate the mathematical
thinking and strategies of others.
Algebra 2
pgs. 153, 206, 266, 268, 305, 312,
350, 383
Incorporated in all mathematical
content
Student to student oral and
written work
Teacher observation
4.5.B 8th Grade Algebra 2 330
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
B. CommunicationEssential Questions :
Assessments
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Learning ExperiencesResources
4. Use the language of mathematics to express
mathematical ideas precisely.
Algebra 2
pgs. 6, 13, 21,28, 36, 44, 70, 78,
85, 94, 102, 110, 141, 151, 175,
180, 217, 226, 232, 259, 266, 276,
294, 302, 308, 347, 361, 368, 375,
386, 403, 410, 417, 425, 433, 440,
448, 468, 489, 495, 504, 512, 557,
570
Incorporated in all mathematical
content
Student use of mathematical
language in oral and written
work
Teacher observation
4.5.B 8th Grade Algebra 2 331
· How can spatial relationships be described by careful use of geometric language?
Integrated throughout problem
solving examples
Resources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
2. Use connections among mathematical ideas
to explain concepts (e.g., two linear equations
have a unique solution because the lines they
represent intersect at a single point).
Algebra 2
Chapters 1 - 10
Integrated throughout problem
solving examples
Standard 4.5 Mathematical Processes
Do Nows
Teacher observation
Oral and written explanations
C. Connections
Student written and oral work
Assessments
1. Recognize recurring themes across
mathematical domains (e.g., patterns in
numbers, algebra, and geometry).
3. Recognize that mathematics is used in a
variety of contexts outside of mathematics.
Algebra 2
pgs. 82-82, 91, 145, 213, 282-288,
290-297, 353
Integrated throughout problem
solving examples
Teacher observation
Student oral and written
explanations
Algebra 2
pgs. 153, 206, 266, 268, 305, 312,
350, 383
4.5.C 8th Grade Algebra 2 332
· How can spatial relationships be described by careful use of geometric language?
Resources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
C. Connections
Assessments
Art, music, economics, etc.,
history incorporated throughout
mathematical models, examples
and problem solving
Teacher observation; Student
use of abstract math models
to solve "science," "social
studies," "art" and "music"
models
Teacher observation
Class discussions
4. Apply mathematics in practical situations
and in other disciplines.
Algebra 2
pgs. 9, 16, 80, 87-88, 93, 105,
127, 133, 151, 161, 172-173, 183,
204, 212, 217, 220, 235, 254, 262,
263, 266, 268, 279, 284, 288, 296,
308, 327, 342, 347, 355, 405, 410,
412, 414, 428, 433, 435, 450, 451,
452, 459, 471, 472, 483, 495, 506, 5
Integrated throughout problem
solving examples
5. Trace the development of mathematical
concepts over time and across cultures.
Algebra 2
pgs. 40, 89, 169, 236, 270, 351,
444, 499, 574
4.5.C 8th Grade Algebra 2 333
· How can spatial relationships be described by careful use of geometric language?
Resources
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
C. Connections
Assessments
6. Understand how mathematical ideas
interconnect and build on one another to
produce a coherent whole.
Algebra 2
pgs. 57, 129, 185, 239, 313, 387,
455, 523, 575, 641
Integrated throughout problem
solving examples
Teacher observation
Student oral and written
explanations
4.5.C 8th Grade Algebra 2 334
· How can spatial relationships be described by careful use of geometric language?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Teacher observation; Oral
and written explanations
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Incorporated in all mathematical
content
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Incorporated in all mathematical
content
Teacher observation; Oral
and written explanations
1. Recognize that mathematical facts,
procedures, and claims must be justified.
Algebra 2
pgs. 396-397, 439, 504
Incorporated in all mathematical
content
Teacher observation; Student
oral and written work
2. Use reasoning to support their
mathematical conclusions and problem
solutions.
Algebra 2
pg. 439
3. Select and use various types of reasoning
and methods of proof.
Algebra 2
Chapters 1 - 10
4. Rely on reasoning, rather than answer keys,
teachers, or peers, to check the correctness of
their problem solutions.
Algebra 2
pgs. 101, 379, 439, 568
Incorporated in all mathematical
content
Teacher observation; Oral
and written explanations
4.5.D 8th Grade Algebra 2 335
· How can spatial relationships be described by careful use of geometric language?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Standard 4.5 Mathematical Processes
D. ReasoningEssential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Incorporated in all mathematical
content
5. Make and investigate mathematical
conjectures.
a. Counterexamples as a means of disproving
conjectures
Algebra 2
pgs. 565, 622
Incorporated in all mathematical
content
Teacher observation
Student oral and written work
6. Evaluate examples of mathematical
reasoning and determine whether they are
valid.
Algebra 2
pg. 19
Incorporated in all mathematical
content
Teacher observation; Oral
and written explanations
Teacher observation
Student oral and written work
b. Verifying conjectures using informal
reasoning or proofs
Algebra 2
pgs. 235, 439
4.5.D 8th Grade Algebra 2 336
· How can spatial relationships be described by careful use of geometric language?
Algebra 2
pgs. 25, 345
Incorporated in all mathematical
content
1. Create and use representations to organize,
record, and communicate mathematical ideas.
a. Concrete representations (e.g., base-ten
blocks or algebra tiles)
c. Symbolic representations (e.g., a formula)
b. Pictorial representations (e.g., diagrams,
charts, or tables)
Algebra 2
pgs. 24, 28-29, 72, 266, 291, 440,
468, 482, 494, 589-590, 642
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Algebra 2
pgs. 49, 99, 281, 421, 533, 622
Incorporated in all mathematical
content
Teacher observation
Student solutions to practice
exercises
E. Representations
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Incorporated in all mathematical
content
Teacher observation
Student solutions to practice
exercises
Teacher observation
Student solutions to practice
exercises
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
4.5.E 8th Grade Algebra 2 337
· How can spatial relationships be described by careful use of geometric language?
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
E. Representations
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
Algebra 2
pgs. 291, 304, 239, 448, 453, 473
Incorporated in all mathematical
content
Teacher observation
Student solutions to practice
exercises
Algebra 2
pgs. 82-88, 91, 139-146, 148-154,
235
Incorporated in all mathematical
content
d. Graphical representations (e.g., a line
graph)
Teacher observation
Student solutions to practice
exercises
3. Use representations to model and interpret
physical, social, and mathematical
phenomena.
Algebra 2
pgs. 25, 49, 99, 220, 281, 294,
297, 345, 421, 512, 533, 622
Incorporated in all mathematical
content
Teacher observation
Student solutions to practice
exercises
2. Select, apply, and translate among
mathematical representations to solve
problems.
4.5.E 8th Grade Algebra 2 338
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences Assessments
1. Use technology to gather, analyze, and
communicate mathematical information.
Algebra 2
pgs. 25, 48, 90, 107, 121, 146,
154, 176, 207, 271, 290, 308, 337,
372, 382, 453-454, 500, 510, 546,
561, 608
Incorporated in all mathematical
content
Do Now
Written Assessments
Teacher Observation
Resources
2. Use computer spreadsheets, software, and
graphing utilities to organize and display
quantitative information.
Algebra 2
pgs. 18, 172, 234, 336
Incorporated in all mathematical
content
Do Now
Written Assessments
Teacher Observation
3. Use graphing calculators and computer
software to investigate properties of functions
and their graphs.
Algebra 2
pgs. 90, 121, 146, 231, 254, 259,
265, 271, 304, 331, 336, 439, 482,
500, 596
Graphing calculator
Incorporated in all mathematical
content
Do Now
Written Assessments
Teacher Observation
4.5.F 8th Grade Algebra 2 339
· How can spatial relationships be described by careful use of geometric language?
Flemington Raritan School District
Mathematics Curriculum
Grades 7 - 8
· How does the use of technology enable us to have a deeper understanding of
mathematics?
Standard 4.5 Mathematical Processes
Essential Questions : Essential Questions :
F. Technology
· How will learning to “think” mathematically enable us to make a life, make a living,
and make a difference?
Knowledge/Skills/Understanding Learning Experiences AssessmentsResources
4. Use calculators as problem-solving tools
(e.g., to explore patterns, to validate solutions).
Algebra 2
pgs. 48, 176, 224, 231-232, 234,
259, 265, 271, 283, 290, 372, 374-
376, 482, 546, 561, 563, 566, 569-
570, 608
Graphing calculator
Incorporated in all mathematical
content
Do Now
Written Assessments
Teacher Observation
5. Use computer software to make and verify
conjectures about geometric objects.
Algebra 2
Chapters 1 - 10
Incorporated in all mathematical
content
Do Now
Written Assessments
Teacher Observation
4.5.F 8th Grade Algebra 2 340
Algebra Dolciani, Brown, and Cole Houghton Mifflin 1986
Geometry Sara Freeman Milliken 2004
Algebra Teacher's Activities Kit Judith and Gary Robert Muschla Jossey-Bass 2003
Algebra Warm-Ups Scott McFadden Dale Seymour 1987
Geo Joke Worksheets Christine A. Koers Nasco 2002
Applying Algebra from A to Z Margaret Thomas Instructional Fair 1999
Algebra Joke Worksheets Christine A. Koers Nasco 2003
Algebra with Pizzazz! Steve and Janis Marcy McGraw Hill 2002
GeometryMary Lee Vivian, Tammy Bohn-
Voepel, and Margaret ThomasMcGraw Hill 2003
Clever CountingLappan, Fey, Fitzgerald, Friel,
and PhillipsPrentice Hall 2002
Algebra 2Ron Larson, Laurie Boswell,
Timothy Kanold, and Lee StiffMcDougall Littell 2001
Title of Resource Publisher CopyrightAuthor(s)
8th Grade Algebra 2
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Skills for Success - Algebra Theresa Kane McKellCarson-Dellosa Publishing
Company, Inc.2003
8th Grade Algebra 2 Resources 341
Title of Resource Publisher CopyrightAuthor(s)
8th Grade Algebra 2
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Algebra and Trigonometry
Algebra Puzzlers
Algebra
Dolciani, Sorgenfrey, Brown,
and Kane
Theresa Kane McKell
Mary Lee Vivian and Margaret
Thomas
Houghton Mifflin
Frank Schaffer Publications
McGraw Hill
1986
1998
2003
GEPA Success in Mathematics Richard Crowe Steck-Vaughn/Berrent 2000
Algebra IIChad Helgeson and Margaret
ThomasMcGraw Hill 2003
Geometer's Sketchpad Nicholas Jackiw Key Curriculum Press 2006
Tinkerplots Clifford Konold, Craig D. Miller Key Curriculum Press 2005
Navigating through ProbabilityShaughnessy, Barrett, Billstein,
Kranendonk, and Peck
The National Council of
Teachers of Mathematics, Inc.2004
Question Quest - Level D Mathematics Paul Lawrence LL Teach, Inc. 2002
GEPA Success in Mathematics - Level H Richard Crowe Steck-Vaughn/Berrent Company 2000
New Jersey ASK 8 Coach Jerome D. Kaplan Triumph Learning 2008
Preparing for the New Jersey GEPA - Grade 8David J. Glatzer and Joyce
GlatzerAmsco School Publications, Inc. 2005
8th Grade Algebra 2 Resources 342
Title of Resource Publisher CopyrightAuthor(s)
8th Grade Algebra 2
Flemington Raritan School DistrictFlemington Raritan School District
Mathematics Curriculum
Resources
Grades 7 - 8
Navigating through Data AnalysisBurrill, Franklin, Godbold, and
Young
The National Council of
Teachers of Mathematics, Inc.2003
Navigating through GeometryDay, Kelley, Krussel, Lott, and
Hirstein
The National Council of
Teachers of Mathematics, Inc.2001
Algebra Practice Exercises Thomas E. Campbell J. Weston Walch Publisher 1996
The Complete Book of Graphing Douglas C. McBroom J. Weston Walch Publisher 2001
Joke Worksheets for Algebra 2 and Precalculus Christine A. Koers NASCO 2002
Algebra 2 Word Problems Anita Harnadek The Critical Thinking Company 2001
Algebra 2Barbara Sandall and Melfried
OlsonMark Twain Media 2005
Algebra 2 Sara Freeman Milliken 2002
8th Grade Algebra 2 Resources 343
Powers, Roots, and Radicals7
5
9
Polynomials and Polynomial Function6 10
Mathematics Curriculum
Grades 7 - 8
8th Grade Algebra 2
2
4
Quadratic Functions
Flemington Raritan School District
4
Algebra 2
Pacing Guide
Matrices
Unit Number of Blocks
Equations and Inequalities1 6
5
----- -----
Systems of Equations and Inequalities3
Benchmark Assessment - Midterm
10
Linear Equations and Functions6
8th Grade Algebra 2 Pacing Guide 344
Mathematics Curriculum
Grades 7 - 8
8th Grade Algebra 2
Flemington Raritan School District
Algebra 2
Pacing Guide
Unit Number of Blocks
9
Quadratic Relations and Conic Sections10 8
Exponential and Logarithmic Functions8 9
Rational Equations and Functions
Benchmark Assessment - Final
----- -----
7
8th Grade Algebra 2 Pacing Guide 345