LEARNING GUIDELINE · Web view2006/05/16 · Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three

Brockton Public Schools

MathematicsCurriculum, Pre-K-8

2006-2007

Brockton Public SchoolsMathematics Curriculum, Pre-K-8

2006-2007Basan Nembirkow, SuperintendentCatherine F. Brine, Executive Director, Office of Teaching and Learning, K-6John J. Jerome, Executive Director of Office of Teaching and Learning, 7-8Linda A. Santry, Coordinator of Math and Science, K-8Barbara M. Lee, Coordinator of Early Childhood EducationMary H. Sundstrom, Department Head for Math, Pre-K-8

Mathematics CommitteeLinda Jordan Math Coach–Central Office Courtney Vasquez Teacher, Brookfield

ElementaryMarguerite Masson Math Coach–Central Office Richard Webb Teacher, Brookfield

ElementaryMaxine Richardson Math Coach–Central Office Michael Sheehan Teacher, Hancock

ElementaryGlenn Young Math Coach–Central Office Amy Simon Teacher, Hancock

ElementaryDavid Cournoyer IRS, Arnone Elementary Joan White Teacher, Hancock

ElementaryPatricia Medis IRS, Gilmore Elementary Michelle Bernstein Teacher, Goddard

KindergartenKathleen Flaherty-Sites IRS, Franklin Elementary Susan Silva Teacher, Kennedy

ElementaryKathryn McMenamy Teacher, East Junior High Joyce Meaden Teacher, East Junior HighJocelyn Young Teacher, Angelo

Elementary Joan Farrington IRS, South Junior High

Violet LeMar Ass’t. Princ., Arnone Elementary Judith Green Teacher, South Junior High

Diane Tarbet Teacher, Ashfield School Diane Behan Teacher, North Junior HighJennifer Giannaros Teacher, Belmont

Elementary Richard Castle Teacher, West Junior HighChanda Lavigne Teacher, Brookfield Linda Monkevicz Teacher, South Junior High

ElementaryMatthew Murphy Teacher, South Junior High

TABLE OF CONTENTS Mathematics Program Philosophy 1 Strand: Patterns, Relations, and

Algebra78

Best Practices in Mathematics 3 Strand: Geometry 80Pre-Kindergarten Mathematics Strand: Measurement 82

Number Sense 5 Strand: Data Analysis, Statistics, and Probability

84

Patterns & Relations 10 Grade 5Shapes and Spatial Sense 12 Strand: Number Sense and Operations 88Measurement 15 Strand: Patterns, Relations, and

Algebra92

Data Analysis, Statistics, and Probability 16 Strand: Geometry 94Kindergarten Strand: Measurement 96

Strand: Number Sense and Operations 18 Strand: Data Analysis, Statistics, and Probability

98

Strand: Patterns, Relations, and Algebra 23 Grade 6Strand: Geometry 26 Strand: Number Sense and Operations 100Strand: Measurement 29 Strand: Patterns, Relations, and

Algebra108

Strand: Data Analysis, Statistics, and Probability

30 Strand: Geometry 111

Grade 1 & 2 Strand: Measurement 115Strand: Number Sense and Operations 32 Strand: Data Analysis, Statistics, and 119

ProbabilityStrand: Patterns, Relations, and Algebra 41 Grade 7Strand: Geometry 47 Strand: Number Sense and Operations 122Strand: Measurement 51 Strand: Patterns, Relations, and

Algebra126



Grade 3 Strand: Measurement 131Strand: Number Sense and Operations 59 Strand: Data Analysis, Statistics, and

Probability133

Strand: Patterns, Relations, and Algebra 64 Grade 8Strand: Geometry 66 Strand: Number Sense and Operations 135Strand: Measurement 68 Strand: Patterns, Relations, and

Algebra139



Grade 4 Strand: Measurement 148Strand: Number Sense and Operations 72 Strand: Data Analysis, Statistics, and

Probability150

5/16/06 1

PROGRAM PHILOSOPHY

The Brockton Public Schools’ Mathematics Program, PreK-8, will provide all students access to the richness of mathematical and technological resources. Through hands-on learning, students will be able to apply mathematical principles to solve problems in their daily lives.

The program goals are to promote excellence in the teaching and learning of mathematics. implement the Massachusetts Mathematics Curriculum Framework. increase awareness and use of technology in the learning process. enhance systemic change in the school district by implementing methodologies and strategies to embrace all learning styles.

In mathematics, students concentrate on making connections and using principles of mathematics to communicate, reason, and solve problems. Students engage in projects that require them to apply number systems, operations, and forms in real-world contexts. The use of manipulatives and technology further supports student learning. Brockton’s Mathematics Program allows students to explore the world of numbers, algorithms, patterns, shapes, data, and spatial sense. Students engage in activities that require them to make sense of real-world data, use manipulatives as representative objects, conceptualize the symbolic value of numbers in various forms, perform operations with numbers, and articulate and justify solutions to problems. The program emphasizes the need for students to make connections and use mathematical principles to communicate, reason, and solve problems.

The Brockton Public Schools Mathematics Program, PreK-8, adopts the vision of the Massachusetts Mathematics Curriculum Framework that “all students in the Commonwealth will achieve mathematical power through problem solving, communication, reasoning, and connections.” The program also embraces the Framework’s Guiding Principles.

Guiding Principles Students will explore mathematical ideas in ways that maintain their enjoyment of and curiosity about mathematics and that help

them develop a depth of understanding. Students will also reflect on real world applications of mathematical principles. All students will have access to high quality mathematics programs. Mathematics learning is a lifelong process that begins and continues in the home and extends to school and community settings. Mathematics instruction will connect with other disciplines and move toward integration of mathematical domains. Students will work together in teams and groups to enhance mathematical learning, communicate effectively, and develop social

and mathematical skills. Technology will be used as an essential tool for effective mathematics education.

5/16/06 2 Mathematics assessment will monitor student performance, improve instruction, enhance learning, and encourage student self

reflection.

Students as Active LearnersIn order to encourage students to take an active role in their mathematics learning, teachers must establish an environment in which students can investigate and experiment with mathematics in authentic ways. Teachers will, therefore, provide students of all ages and learning styles a wide variety of models, materials, activities, demonstrations, games, investigations, interesting problems and conversations in the mathematical content being explored. Thus, students will spend daily-sustained time engaged in authentic mathematical activities. Students will work cooperatively to share ideas, solutions and strategies and confirm that there are multiple ways to solve problems. Learning Centers will be set up accordingly. An appreciation of the importance of learning from one another and the importance of reflection, guided by the teacher, will enhance the learning process.

Instructional GroupingsIn order to achieve the goals of the mathematics curriculum, a multiplicity of grouping strategies—including whole group, small group and individual work—must be utilized. Teachers will use a variety of grouping practices, including cooperative and flexible groupings, to meet the differences in their students’ learning styles and rates. The reconfiguration of groups should be based on teachers’ ongoing assessment of students’ needs. Learning Centers will be designed to meet the needs of diverse learners as well as facilitate the mathematics program.

Importance of ManipulativesActive learning necessitates the extensive and thoughtful use of physical materials to foster the development of abstract ideas, encouraging less teacher direction and more student involvement. Manipulatives and activity-based lessons are necessary to address the different learning styles of our students. Their use will help connect mathematics to the real world. All students, PreK-8, should have frequent, ongoing opportunities to use manipulatives to develop an understanding of mathematical concepts and content.

Assessment and EvaluationAssessment and evaluation are an integral part of the teaching of mathematics and, therefore, should be a daily occurrence within the mathematics classroom. Assessment and evaluation determine instructional decisions and must incorporate teacher observation of the students at work, both individually and in groups. The classroom culture should reinforce the belief that errors are opportunities for learning and that students should be encouraged to take risks without fear of embarrassment or failure.

Traditionally, quizzes and tests have been administered at regular intervals to ascertain student mastery. Today’s battery of assessment devices will also include the teacher’s daily observation of student performance. Teachers must look at the strategies students use to solve problems as well as the solutions they generate. Teachers will also develop rubrics and other assessment techniques and tools which are based on current research, the National Council of Teachers of Mathematics Standards and the

5/16/06 3Massachusetts Mathematics Curriculum Framework. Additional student assessments include interviews, daily journal writing, other forms of writing about mathematics, student/teacher conferencing, student self assessment and work samples.

TechnologyThe Brockton Public Schools’ Five Year Plan for Instructional Technology calls for the phasing in of instructional learning systems and software in all schools. Initially, each student will be assessed to determine an accurate instructional level. Thereafter, students will work on their individualized mathematics programs. Research indicates that students will show significant gain in specific skill areas when the software is used appropriately and consistently. Documentation of student progress provided through this software thus becomes part of each student’s ongoing assessment as well as that of the Brockton Public Schools’ Mathematics Program.

Calculators will also be used in the mathematics program. Neither calculators nor computers replace the need to learn basic facts, to compute mentally or to do paper and pencil computation. Rather, they enhance the learning process and allow the student the opportunity to use technology intelligently to become a confident and knowledgeable decision maker.

Best Practices in MathematicsTeachers at each grade level, K-6, will begin each day with The Every Day Counts calendar program from Houghton Mifflin. In grades 7 and 8 each mathematics class will begin with a dialogue, which will bring the lesson of the day into a real life situation. The core program must be utilized to ensure that prior knowledge, developmental and ongoing assessment options are included in each lesson. In addition, writing about mathematical processes and the use of hands-on, activity-based strategies should be incorporated into lessons to ensure that all learning styles are addressed.

Each daily K-8 mathematics lesson should include the following components: objective(s) a stated purpose for achieving the objective core program materials with appropriate page numbers other materials/manipulatives authentic and engaging independent/group work vocabulary/reading/writing strategies assessment, when applicable

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Students will

engage in authentic mathematics activities daily. write daily. participate in small group discussions several times a

week. participate in cooperative learning several times a

week. engage in group problem solving, negotiation and

consensus development several times a week. engage in solving multi-step problems several times a

week. engage in “hands on” learning activities (e.g., lab

assignments, manipulatives) several times a week. respond to open-ended and open response questions

several times a week. participate in various forms of assessment weekly. use calculators as part of lessons several times a

month. take multiple choice/short answer tests several times a

month. work on group projects monthly. work on share projects with the rest of the school

several times a year.

make oral presentations. use computers and other technology as part of lessons.

Teachers will

directly teach and model mathematics strategies daily. engage students in authentic mathematics activities

daily. engage students in solving multi-step problems. function as coach and facilitator daily. emphasize the practical real world application of

course materials daily. use interdisciplinary teaching materials. use alternative, performance based assessments

weekly. use rubrics as part of all assessments. use portfolios of students’ work as indicators of

student success several times a year. plan and implement strategies to increase parent

involvement several times a year.

5/16/06

LEARNING GUIDELINE

STATE STANDARD

PRE-KProgress Indicators LEARNING EXPERIENCE RESOURCES

1. Listen to and say

the names of numbers in meaningful contexts.

K.N.1 Count by ones to at least 20.

Count by ones orally from 1-10.

Play games and listen to stories and poems that contain numbers and counting sequences.

Use concrete objects to practice one-to-one correspondence (e.g., say the name of objects while placing an object in each space in an egg carton; distributing a musical instrument to each child in a group; putting pegs in each hole of a pegboard).

Count concrete objects for a meaningful purpose (e.g., three crackers for snack; two eyes to glue on the bunny; three steps down to the playground).

Follow visual or rebus recipes (e.g., for making play dough or cookies).

Point to numbers displayed in the preschool setting (e.g., labels on objects, projects, activity areas; children's bus numbers, children's ages)

Everyday Counts: September-JuneMathematics Their Way: 92-105Young Children in Action: 232-237

LAP-D Cognitive Counting 15

LAP-D Cognitive Counting: 13, 14, 16, 18, 24Young Children in Action: 232-237

Young Children in Action: 232-237


Brockton Public Schools NUMBER SENSE: PRE-KINDERGARTEN

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LEARNING GUIDELINE

STATE STANDARD


2. Connect many kinds/quantities of concrete objects and actions to numbers.

K.N.2 Match quantities up to at least 10 with numerals and words.

Create sets of objects to repre-sent quantities from 1-5.

Recognize numeric symbols for quantities from 1-5.

Arrange and count a variety of different kinds of objects to explore the consistency of quantities (e.g., to build understanding of what "3" looks like, whether you are counting blocks, beads or pinecones).

Participate in finger plays and action rhymes that associate number concepts with concrete actions (e.g., Five Little Monkeys Jumping on the Bed).

Use concrete objects, actions, or drawings to represent quantities (e.g., jump two times; stack four unit blocks; string three beads, hold up two fingers, get three blocks on request).

Everyday Counts: September –JuneMathematics Their Way: 166-178Workjobs: 130-179

LAP-D Cognitive Counting: 13, 14Workjobs: 130-179

LAP-D Cognitive Counting: 15


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3. Use positional language and ordinal numbers (first, second, third) in everyday activities.

K.N.3 Identify position of objects in sequences (e.g., first, second) up to fifth.

Use ordinal numbers 1st, 2nd, 3rd verbally to identify position.

Place concrete objects such as nesting or stacking cups, boxes, or dolls in a row and identify their position as first, second, third.

Arrange materials in order (seriate) from small to large; short to long, etc

Use ordinal numbers and positional words (e.g., before/after; first, second, third) to describe the order of daily activities.

Arrange illustrations from a story or photographs of class events or daily routines in sequence.

Everyday Counts: January - JuneYoung Children in Action: 222-224


Everyday Counts January - JuneYoung Children in Action: 222-224

Workjobs: 21


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LEARNING GUIDELINE

STATE STANDARD


4. Use concrete objects to solve simple addition and subtraction problems using comparative language (more than, fewer than, same number of).

K.N.4 Compare sets of up to at least 10 concrete objects using appropriate language (e.g., none, more than, fewer than, some number of, one more than) and order numbers.

K.N.7Use objects and drawings to model and solve related addition and subtraction problems to ten.

Order the numerals 1-5.

Determine whether a group of objects being changed is getting “more” or “less”.

Distribute and compare concrete objects in meaningful ways (e.g., which bucket has more rocks in it; how many more napkins are needed for everyone at the table).

Sing songs and do finger plays that involve adding and taking away (e.g., Two Little Blackbirds).

Use pictorial recipes and discuss how many more cups of cups of flour need to be added to the cookie dough.

Make pictorial menus or shopping lists; identify the amount of money needed to "buy products" in various play areas.

Figure out how many blocks they have altogether when they join two sets or how many blocks are needed to make two towers the same size.

See and discuss meaningful examples of the concept of

Everyday Counts: November, December, January, March, JuneMathematics Their Way: 116-118LAP-D Cognitive Concepts 10, 20, 26, 27, 29

LAP-D Cognitive Counting 10Young Children in Action: 230-232

Mathematics Their Way: 116-118





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LEARNING GUIDELINE

STATE STANDARD


"none" (e.g., you have two cookies left, I have none).

5. Observe and manipulate concrete examples of whole and half.

K.N.5 Understand the concepts of whole and half.

Identify if something cut into two pieces has created equal parts or “fair share”.

Cut food into two equal parts for snacks.

Match whole objects to similar objects that have been broken or cut in half.

Divide a set of objects into two equal parts (e.g., two for you and two for me).

Everyday Counts: November



6. Examine, manipulate, and identify familiar U.S. coins (penny, nickel, dime, quarter) in play activities.

K.N.6 Identify U.S. coins by name.

Identify pennies and count them by ones, (1-5).

Match and label “penny”, “nickel”, “dime”, and “quarter”.

Use the word “add” as a synonym for “getting more”.

Identify the “+” sign to indicate

Create a grocery store or shoe store in the dramatic play area and use play money to pay for items.

Listen to age appropriate books about money and identify the coins.

Separate coins by color and size.

Everyday Counts: September – February

Everyday Counts: September – February

Everyday Counts: September - February


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LEARNING GUIDELINE

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“getting more”.

Draw a model to represent simple addition problems to 5.


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7. Explore and describe a wide variety of concrete objects by their attributes.

K.P.1Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).

Identify objects by color, shape, and size that are the same or different.

Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).

Describe the size, shape, color, and texture of everyday materials such as pasta, rocks, shells, unit blocks, attribute blocks, parquetry blocks, and crackers.

Play games that include identifying (pointing to, selecting, or naming) a specified object from a group of objects (e.g., lotto, concentration cards).

Listen to and use words that describe the characteristics of objects (e.g., big, small, tall, short, narrow, thick, thin, deep, shallow, round, flat, straight, crooked, heavy, light).

Everyday Counts: November - June

LAP-D Cognitive Counting 4, 7


8. Sort, categorize, or classify objects by more than one attribute.

K.P.2Sort and classify objects by color, shape, size, number, and other properties.

Sort and classify objects, giving reasons why they are alike or different.

Sort parquetry blocks or string beads by size, shape, color, or texture (e.g., big circles/small circles; blue squares/blue circles; big yellow squares/ small yellow squares).

Everyday Counts: December - JuneMathematics Their Way: 60-87Young Children in Action: 200-206

Brockton Public Schools PATTERNS AND RELATIONS: PRE-KINDERGARTEN

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LEARNING GUIDELINE

STATE STANDARD


9. Recognize, describe, reproduce, extend, create, and compare repeating patterns of concrete materials.

K.P.3Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).

Reproduce and extend a color, rhythmic, shape, number, and letter simple repeating pattern (ABAB).

Repeat clapping or drumbeat patterns.

Use pattern cards to reproduce patterns with concrete objects such as beads, colored cubes, mosaic tiles with pattern cards.

Find patterns in their everyday environment (plaid, stripes, checks on clothing, floors or walls).

Repeat a pattern/sequence in a variety of ways (e.g., an ABAB pattern with stickers, blocks, or stamps).

Manipulate objects in and out of patterns.

recognize and predict word patterns in familiar rhythms, music or stories.

Note: The ability to recognize and create patterns generally develops over time. The ability to distinguish multiple attributes also grows over time.

Everyday Counts: October – June

Mathematics Their Way: 21-2-42LAP-D Cognitive Matching 7, 10

Everyday Counts: November, December, April, May – June

Everyday Counts: November-June

Everyday Counts: February, April, June

Everyday Counts: November - February

Brockton Public Schools PATTERNS AND RELATIONS: PRE-KINDERGARTEN

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LEARNING GUIDELINE

STATE STANDARD


10. Investigate and identify materials of various shapes, using appropriate language.

K.G.1 Name, describe, sort, and draw simple, two-dimensional shapes.

K.G.2 Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners).

Name and sort simple two-dimensional shapes.

Count the number of sides and corners on a triangle, square, and rectangle.

Sort parquetry blocks by one or more attributes.

Place unit blocks on top of their silhouettes.

Feel and describe parquetry blocks, then try to identify them without looking.

Eat snacks cut in various shapes; cut cookie dough into basic shapes.

Create/represent shapes (e.g., using popsicle sticks, pipe cleaners, unit blocks).

Find examples of basic shapes such as circle, square, triangle, and rectangle in the environment (e.g., go on a "shape walk" indoors or outdoors to find examples of basic shapes in buildings, in the classroom, in nature).

Locate individual objects in pictures composed of overlapping shapes or find shapes in magazine illustrations, picture books (e.g., I Spy books).

Everyday Counts: September - JuneMathematics Their Way: 58-60

LAP-D Cognitive Matching 1, 2, 4LAP-D Cognitive Counting 5, 16

Everyday Counts: December-April


LAP-D Cognitive Matching 7



Brockton Public School SHAPES & SPATIAL SENSE: PRE-KINDERGARTEN

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LEARNING GUIDELINE

STATE STANDARD


11. Explore and identify space, direction, movement, relative position, and size using body movement and concrete objects.

K. G. 4Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions.

Identify positions of objects in space and use appropriate language (e.g., inside, outside, under, over, next to) to describe and compare their relative positions.

Illustrate position and relative distance among objects/ locations using classroom materials or outdoor equipment (e.g., up, down, high, low, above, below, in front of, behind, beside, near, far, next to, apart, together).

Move their bodies in space by following verbal instructions through an obstacle course (e.g., crawl under the table, walk around the jungle gym; jump over the block). Follow or use directional language

related to daily routines and activities or in dance recordings (e.g., "Put your hands up, down, over your head.").

Locate objects based on directional words (e.g., it's next to the ball; under the basket).

Play with puzzles of increasing complexity as skills develop.

Figure out how much space is needed for a task (e.g., to build a construction using large interlocking panels, or whether two children can fit inside a cardboard box).

Identify shapes in different orientations (a triangle is still a triangle even though it's turned in

Everyday Counts: September – JuneEveryday Counts: LAP-D Cognitive Counting 2, 9LAP-D Cognitive Matching 11, 14








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LEARNING GUIDELINE

STATE STANDARD


different directions).

12. Listen to and use comparative words to describe the relationships of objects to one another.

K.M.1Recognize and compare the attributes of length, volume/capacity, weight, area, and time using appropriate language, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds less, holds the same amount.

Use words that describe amounts appropriately, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds, less, holds the same amount.

Compare and describe objects according to a single attribute (e.g., which is bigger, smaller, taller, longer, shorter, same length, wider, narrower, thicker, thinner, deeper, shallower, lighter, heavier, holds less, or holds the same amount).

Measure sand, water, or rice using variety of containers and compare the amounts.

Make objects of play dough and compare their size.

Build structures with blocks and compare their length or height.

String beads and compare the length of two necklaces.

Use simple balance scales to compare the weight of classroom materials.

Compare the size of various everyday objects (e.g., put various people's shoes side by side to see which is longest.

Note: Younger preschool children

Everyday Counts March – JunMathematics Their Way: 116-139LAP-D Cognitive Counting 11Young Children in Action: 135-136








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LEARNING GUIDELINE

STATE STANDARD


should focus on a single attribute at a time.


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LEARNING GUIDELINE

STATE STANDARD


13. Use estimation in meaningful ways and follow up by verifying the accuracy of estimations.

K.M.2 Make and use estimates of measurements from everyday experiences.

Make and use estimates of measurements from everyday experiences.

Estimate how many steps it will take to cross the room or the sandbox; how many small containers it will take to fill a larger one, how many mosaic tiles it will take to fill the board; which cup contains more beans.

Experiment to verify whether their estimates were accurate.

Everyday Counts: March – June

14. Use nonstandard units to measure length, weight, and amount of content in familiar objects.

K.M.3 Use non-standard units to measure length, area, weight, and capacity.

Use non-standard units to measure length, area, weight, and capacity.

Measure the circumference of a pumpkin or watermelon using a piece of string.

Measure the length of a table using their hands.

Measure the width of the sandbox with footsteps.

Measure a child's height using large cardboard blocks.

Compare the length of two play dough snakes or the height of two block towers using their hands.

Compare the capacity of two different containers in the sand or water table.

Everyday Counts: March – June

Brockton Public Schools MEASUREMENT: PRE-KINDERGARTEN

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LEARNING GUIDELINE

STATE STANDARD


15. Organize and draw conclusions from facts they have collected.

K.D.1Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.

Collect and sort concrete objects, pictures, or shapes to create a simple bar graph.

Construct simple graphs and charts to describe concrete materials (e.g., after sorting leaves, children create a graph illustrating the various kinds of leaves, marking the number of leaves in each category, and describing how they sorted the leaves).

Take part in creating and discussing surveys (e.g., survey children's food preferences to decide what snack to serve, with children placing marks on graphs indicating their choice).

Everyday Counts: December – JuneMathematics Their Way: 142-163

Everyday Counts: December – JuneMathematics Their Way: 142-163Everyday Counts: December – JuneMathematics Their Way: 142-163

PRE KINDERGARTEN CURRICULUM RESOURCES

Every Day Counts: Every Day in Pre-K Math. 2002/Great Source Education Group.

LAP-D (Learning Accomplishment Profile) Planning Cards 1996/Kaplan Early Learning Company

Mathematics Their Way Barrata-Lorton, Mary. 1995/Dale Seymour Publications

Workjobs II: Number Activities for Early Childhood. Barrata-Lorton, Mary 1987/Pearson Learning.

Brockton Public Schools DATA ANALYSIS, STATISTICS, AND PROBABILITY: PRE-KINDERGARTEN

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Young Children in Action: A Manual for Preschool Educators. Hohman, Mary. 1983/High Scope Press.

Brockton Public Schools DATA ANALYSIS, STATISTICS, AND PROBABILITY: PRE-KINDERGARTEN

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Additional ResourcesThe following are Pre K – 8 Resources to be used to supplement the core programs where needed

Question of the Day, Lakeshore Publishing – K onlyEvery Day Counts Pattern Games – K-3 only – Great SourceGames for Number Sense – Great Source – K OnlyPlaying Math Games – Teacher Resource Center – K OnlyDeveloping Number Concepts: Counting, Comparing and Patterns – Dale Seymour Publications – K OnlySuper Source K-8 – All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes TangramsHundred Chart – ETA CuisenaireAnalog Clocks – ETA CuisenaireEqua Beam – ETA CuisenaireHands-On Equations – ETA CuisenaireFraction Strips – ETA Cuisenaire

Math to Learn – Grades 1&2 – Great Source Educational GroupMath to Know – Grades 3&4 – Great Source Educational GroupMath at Hand – Grades 5&6 – Great Source Educational GroupMath on Call – Grades 6-8 – Great Source Educational GroupAlgebra to Go – Grade 8 – Great Source Educational Group

Brockton Public Schools PRE-KINDERGARTEN: ADDITIONAL RESOURCES

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STRAND: NUMBER SENSE AND OPERATIONS

DOEStandard number

State Standard Pre-KindergartenProgress Indicators

KindergartenProgress Indicators Resources

K.N.1 Count by ones to at least 20. Count by ones orally from 1-10.

Count by ones orally beginning from any number in the sequence from 0-20.

Mathematical Thinking in KindergartenInvestigation 1, 4-2Investigation 2, 26-39Collecting, Counting, and MeasuringInvestigation 1, 2-21Investigation 2, 22-35Investigation 3, 36-51, Investigation 4, 52-65Investigation 5, 66-77Investigation 6, 78-97Counting Ourselves and OthersInvestigation 1, 2-35Investigation 4, 76-91How Many In All?Investigation 1, 2-27Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Super Source – Snap Cubes Counting Colors – p. 18- Developing Number Sense Book 1, pp. 52-56

Brockton Public Schools NUMBER SENSE AND OPERATIONS: KINDERGARTEN

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DOEStandard number



K.N.2 Match quantities up to at least 10 with numerals and words.

Create sets of objects to represent quantities from 1-5.

Recognize numeric symbols for quantities from 1-5.

Create sets of objects to represent quantities from 0-10.

Recognize and write numeric symbols for quantities from 0-10.

Represent an empty set with the numeral “0”.

Mathematical Thinking in KindergartenInvestigation 1, 4-23Investigation 2, 26-39Collecting, Counting, and MeasuringInvestigation 1, 2-21Investigation 2, 22-35Investigation 3, 36-51Investigation 4, 52-65Investigation 5, 66-77Investigation 6, 78-97Counting Ourselves and OthersInvestigation 1, 2-35Investigation 4, 76-91How Many In All?Investigation 1, 2-27Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Super Source – Color Tiles Creating Patterns, p. 22- Developing Number Sense Book 1, pp. 50-52


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DOEStandard number



K.N.3 Identify position of objects in sequences (e.g., first, second) up to fifth.

Use ordinal numbers 1st, 2nd, 3rd verbally to identify position.


Use ordinal numbers, 1st, 2nd, 3rd, 4th, and 5th

verbally to identify positions.


Collecting, Counting, and MeasuringInvestigation 5, 66-77Investigation 6, 78-97Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Super Source – Color Tiles Line Up Four, pg. 62 - Super Source – Snap Cubes Make A Copy, pg. 38

K.N.4 Compare sets of up to at least 10 concrete objects using appropriate language (e.g., none, more than, fewer than, some number of, one more than) and order numbers.

Determine whether a group of objects being changed is getting “more” or “less”.

Determine whether a group of objects being changed is getting “more,” “less” or “staying the same.”

Represent two equal sets containing up to 10.

Compare sets of at least 10 objects using appropriate language.

Mathematical Thinking in KindergartenInvestigation 4, 54-60Collecting, Counting, and MeasuringInvestigation 4, 52-65Investigation 5, 66-77Investigation 6, 78-97; Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Developing Number Concepts Book 1, pp. 45-46, 48


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DOEStandard number



K.N.5 Understand the concepts of whole and half.

Identify if something cut into two pieces has created equal parts or “fair share”.

Identify if something cut in 2 pieces has been fairly cut in half.

Tell or show how to cut something equally in half.

May be used in conjunction with the Making Shapes and Building Block s UnitEvery Day CountsNone

Supplement with:- Super Source – Color Tiles Half and Half, pg. 46 - Super Source – Snap Cubes Make A Copy, pg. 38

K.N.6 Identify U.S. coins by name. Identify pennies and count them by ones, (1-5)

Match and label “penny”, “nickel”, “dime”, and “quarter”.

Identify U.S. coins by name.

Match coins to their correct value (i.e. a nickel = 5 cents)

See Grade 1Number Games and Story ProblemsInvestigation 2, p. 69.Every Day CountsFebruary-April

Supplement with:- Games for Number Sense pp. S27-S28- Math By All Means (Gr. 1 & 2), Menu Activities


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DOEStandard number



K.N.7 Use objects and drawings to model and solve related addition and subtraction problems to ten.

Use the word “add” as a synonym for “getting more”.

Identify the “+” sign to indicate “getting more”.

Draw a model to represent simple addition problems to 5.

Interpret number sentences for addition and subtraction problems using numbers 0-10 with manipulatives (e.g., with number tiles, counters).

Create and interpret simple stories that can be solved using addition or subtraction.

Use objects and drawings to model and solve related addition and subtraction problems to ten.

How Many In All? Investigation 2, 28-51Investigation 3, 52-73Investigation 4, 74-95Every Day CountsFebruary-AprilDigi-Blocks

Supplement with:- Games for Number Sense – Domino sums – pg. 57 - Super Source – Color Tiles Very Busy Animals, pg. 78

K.N.8 Estimate the number of objects in a group and verify results.

Put sets of objects in order from least to greatest, shortest to longest, etc., using visual clues.

Use the strategy of “guess and check” to estimate with like objects from 0-10 and verify results.

Counting Ourselves and Others Investigation 1, 2-35Every Day CountsNoneDigi-Blocks

Supplement with:- Developing Number Concepts Book 1, pg. 62


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STRAND: PATTERNS, RELATIONS, AND ALGEBRA

DOEStandard number



K.P.1 Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).

Given a set of objects, tell how they are all alike (e.g., all red, all round, etc.).

Identify objects by color, shape, and size that are the same or different.

Identify the attributes of objects as a foundation for sorting and classifying (e.g., a red truck, a red block, and a red ball share the attributes of being red; a square block, a square cracker, and a square book share the attribute of being square shaped).

Mathematical Thinking in KindergartenInvestigation 1, 4-23Pattern Trains and Hopscotch PathsInvestigation 1, 2-23Counting Ourselves and OthersInvestigation 1, 2-35Investigation 2, 36-55Investigation 3, 56-75Every Day CountsOctober, December, MarchDigi-Blocks

Supplement with:- Developing Number Concepts Book 1, pg. 65

K.P.2 Sort and classify objects by color, shape, size, number, and other properties.

Sort objects by matching color, shape, and size.

Sort and classify objects, giving reasons why they are alike or different.

Mathematical Thinking in KindergartenInvestigation 1, 4-23Pattern Trains and Hopscotch PathsInvestigation 1, 2-23Counting Ourselves and OthersInvestigation 1, 2-35Investigation 2, 36-55Investigation 3, 56-75Every Day CountsSeptember-JuneDigi-Blocks

Brockton Public Schools PATTERNS, RELATIONS, & ALGEBRA: KINDERGARTEN

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DOEStandard number



Supplement with:- Developing Number Concepts Book 1, pg. 67- Games and Number Sense, pp. 46-47

K.P.3 Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).

Reproduce and extend a color, rhythmic, shape, number, and letter simple repeating pattern (ABAB).

Identify, reproduce, describe, extend, and create color, rhythmic, shape, number, and letter repeating patterns with simple attributes (e.g., ABABAB).

Mathematical Thinking in KindergartenInvestigation 1, 4-23Pattern Trains and Hopscotch PathsInvestigation 1, 2-23Counting Ourselves and OthersInvestigation 1, 2-35Investigation 2, 36-55Investigation 3, 56-75Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Super Source, Pattern Blocks, Antwalks p.18, Sping to Win p.88, Who Caught the Biggest Fish? p.86 - Developing MathConcepts Book 1, pg. 91-124- Games and Number Sense, pp. 46-47


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DOEStandard number



K.P.4 Count by fives and tens at least up to 50.

Count by tens to 50. Count by fives and tens at least up to 50.

Mathematical Thinking in KindergartenInvestigation 1, 4-23; Pattern Trains and Hopscotch PathsInvestigation 1, 2-23Counting Ourselves and Others

Supplement with:- Games for Number Sense, p.26-27,88-89Investigation 1, 2-35Investigation 2, 36-55Investigation 3, 56-75Every Day CountsNovember, February, March May/June Digi-Blocks


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STRAND: GEOMETRY

DOEStandard number



K.G.1 Name, describe, sort, and draw simple, two-dimensional shapes.

Name and sort simple two-dimensional shapes.

Name, describe, sort, and draw simple, two-dimensional shapes (e.g. Square, circle, triangle…).

Making Shapes and Building BlocksInvestigation 1, 2-25Investigation 2, 26-37 Investigation 3, 38-59Investigation 4, 60-81Every Day CountsSeptember, March, April

Supplement with:- Math By All Means – Geometry Gr. 1&2 Menu Activities- Super Source – Geoboards All About squares, p. 18

K.G.2 Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners).

Count the number of sides and corners on a triangle, square, and rectangle.

Describe the attributes of two-dimensional shapes (e.g., number of sides, number of corners).

Mathematical Thinking in KindergartenInvestigation 1, 4-23Making Shapes and Building BlocksInvestigation 1, 2-25Investigation 2, 26-37Investigation 3, 38-59Investigation 4, 60-81Every Day CountsSeptember, March, AprilDigi-Blocks

Supplement with:- Super Source – Geoboards Four in a Row, p. 30

Brockton Public Schools GEOMETRY: KINDERGARTEN

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STRAND: GEOMETRY

K.G.3 Name and compare three-dimensional shapes.

Match and sort three-dimensional shapes.

Name and compare three-dimensional shapes (e.g., sphere, cube).

Mathematical Thinking in KindergartenInvestigation 1, 4-23Making Shapes and Building BlocksInvestigation 1, 2-25Investigation 2, 26-37Investigation 3, 38-59Investigation 4, 60-81Every Day CountsSeptember, December, May/JuneDigi-Blocks

Supplement with:- Super Source – Geoboards Farm Fences, p. 26

K.G.4 Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions.

Identify positions of objects in space and use appropriate language (e.g., inside, outside, under, over, next to) to describe and compare their relative positions.

Identify positions of objects in space, and use appropriate language (e.g., beside, inside, next to, close to, above, below, apart) to describe and compare their relative positions. See Math Frameworks, Nov. 2000, p. 37.

Mathematical Thinking in KindergartenInvestigation 1, 4-23Making Shapes and Building BlocksInvestigation 1, 2-25Investigation 2, 26-37Investigation 3, 38-59Investigation 4, 60-81Every Day CountsNoneDigi-Blocks

Supplement with:- Super Source – Geoboards Inside, Outside, p. 42

Brockton Public Schools GEOMETRY: KINDERGARTEN

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STRAND: MEASUREMENT

DOEStandard number



K.M.1 Recognize and compare the attributes of length, volume/capacity, weight, area, and time using appropriate language, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds less, holds the same amount.

Use words that describe amounts appropriately, e.g., longer, taller, shorter, same length, heavier, lighter, same weight, holds more, holds, less, holds the same amount.

Recognize and compare the attributes of length (longer, shorter), of volume or capacity holds (more, less), weight (heavier, lighter), area (more, less), time (yesterday, today, tomorrow), and temperature (hotter, colder).

Collecting, Counting, and MeasuringInvestigation 3, 36-51How Many In All? Investigation 1, 2-27Every Day CountsNovember-JuneDigi-Blocks

Supplement with:- Super Source – Geobards- Two Line Design, p. 82- Path finder, p.50- Make the Other Half, p. 46

K.M.2 Make and use estimates of measurements from everyday experiences.

Demonstrate a strategy. Make and use estimates of measurements from everyday experiences.

Collecting, Counting, and MeasuringInvestigation 3, 36-51How Many In All?Investigation 1, 2-27; Every Day CountsNovember, December, JanuaryDigi-Blocks

Supplement with:- Super Source – Shape Cubes How Long Is It? p. 30 Puzzles, p. 54 - Super Source – Geoboards Tell Me About That p. 70

Brockton Public Schools MEASUREMENT: KINDERGARTEN

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K.M.3 Use non-standard units to measure length, area, weight, and capacity.



Collecting, Counting, and MeasuringInvestigation 3, 36-51How Many In All? Investigation 1, 2-27Every Day CountsNovember-JanuaryDigi-Blocks

Supplement with:- Super Source – Geoboards From A to Z p. 34

Brockton Public Schools MEASUREMENT: KINDERGARTEN

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STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITY

DOEStandard number



K.D.1 Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.

Collect and sort concrete objects, pictures, or shapes to create a simple bar graph.

Use counters to represent data from a simple survey.

Sort a variety of objects (fruit, toy animal, etc.) and place them on a graphic mat to create a concrete graph using numbers to 10.

Demonstrate an understanding of at least one fact shown by first-hand data (e.g., count the number of students who stand in each line to show their favorite kind of ice cream).

Verbally state a reason for the results shown on one part of a pictorial table, chart, or graph.

Collect, sort, organize, and draw conclusions about data using concrete objects, pictures, numbers, and graphs.

Mathematical Thinking in KindergartenInvestigation 4, 54-64Counting Ourselves and OthersInvestigation 2, 36-55Investigation 3, 56-75Investigation 4, 76-91Every Day CountsSeptember-JuneDigi-Blocks

Supplement with:- Math By All means - Probability and Statistics – Grades 1 & 2 Menu Activities - Developing Number Sense Book 1 p. 152- Super Source – Geoboards Things that Fly p. 74- Super Source – Color Tiles Counting Colors p. 18 - Super Source – Snap Cubes Red or Blue p. 58 The Disappearing Train p. 78

Brockton Public Schools DATA ANALYSIS, STATISTICS, AND PROBABILITY: KINDERGARTEN

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Brockton Public Schools ADDITIONAL RESOURCES: KINDERGARTEN

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DOEStandard Number

State Standard Grade 1Progress Indicators

Grade 2Progress Indicators Resources

2.N.1 Name and write (in numerals) whole numbers to 1000, identify the place values of the digits, and order the numbers.

Create and label sets of objects from 0 to100.

Demonstrate an understanding of the concepts of tens and

ones (e.g., base ten blocks, number lines) using a variety of manipulatives.

Recognize dictated numbers from 0-100.

Create and label sets of objects from 0 to 1000.

Demonstrate an understanding of the concepts of place value—ones, tens, and hundreds to 1,000 using manipulatives (e.g., base ten blocks, number lines).

Write dictated whole numbers from 0 to 1,000 with correct place value.

Grade 1Mathematical Thinking at Grade 1Investigation 2, 24-59Investigation 5, 114-140Building Number SenseInvestigation 1, 2-35Investigation 3, 92-111Survey Questions and Secret RulesInvestigation 4, 74-99Investigation 2, 32-53Number Games and Story ProblemsInvestigation 2, 49-98Every Day CountsAll monthsDigi-Blocks

Grade 2Mathematical Thinking at Grade 2Investigation 1, 2-19Investigation 2, 20-51Investigation 3, 2-75 Investigation 4, 76-99Investigation 5, 100-123Coins, Coupons, and CombinationsInvestigation 4, 108-124Every Day CountsAll monthsDigi-Blocks

Brockton Public Schools NUMBER SENSE AND OPERATIONS: GRADE 1 & 2

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DOEStandard Number



2.N.2 Identify and distinguish among multiple uses of numbers including cardinal (to tell how many) and ordinal (to tell which one in an ordered list), and numbers as labels and as measurement.

Distinguish between cardinal (“there are 2”) and ordinal (“it’s the second one”) numbers verbally.

Use ordinal numbers(1st-10th).

Measure common objects using non-standards units of measure.

Measure common objects using a ruler to nearest inch.

Identify and distinguish among multiple uses of numbers including cardinal (to tell how many, 1-1000) and ordinal (to tell which one in an ordered list, to 1000th), and numbers as labels and as measurement.

Use a standard ruler to measure to nearest half-inch.

Grade 1Mathematical Thinking at Grade 1 Investigation 2, 24-59Bigger, Taller, Heavier, SmallerInvestigation 3, 60-81Every Day CountsSept., Oct., Nov., Dec., Feb., March, April, May, JuneDigi-BlocksCCC Lab – Ordinal NumbersGrade 2Mathematical Thinking at Grade 2Investigation 1, 2-19 Investigation 2, 20-51Every Day CountsAll monthsDigi-Blocks


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DOEStandard Number



2.N.3 Identify and represent common fractions (1/2, 1/3, 1/4) as parts of wholes, parts of groups, and numbers on the number line.

Identify fair shares in halves, thirds and fourths.

Describe one unit of a fraction as “one-half”, “one-third” or “one-fourth” (1/2, 1/3, 1/4).

Identify and represent common fractions (1/2 to 7/8) as parts of wholes, parts of groups, and numbers on the number line.

Use the terms “numerator” or “denominator” correctly.

Add simple fractions with like denominators using manipulatives(1/4 + 2/4 +3/4).

Grade 1Additional resources neededEvery Day CountsFeb.CCC Lab- Super Source – Pattern Blocks

Grade 2Shapes, Halves, and SymmetryInvestigation 3, 72-93Every Day CountsOct., March

2.N.4 Compare whole numbers using terms and symbols (e.g., less than, equal to, greater than [<,=,>]

Compare whole numbers to 100 using terms and symbols (e.g. less than, equal to, greater than [<,=,>]

Read, write, compare(>, <, =, odd, even), and order whole numbers to 1,000.

Grade 1Readiness: Mathematical Thinking at Grade 1Investigation 2, 24-59Investigation 4, 82-113Investigation 5, 114-135

Survey Questions and Secret RulesInvestigation 4, 74-99Every Day Counts


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DOEStandard Number



Oct., Nov., AprilCCC Lab – SymbolsGrade 2Every Day CountsSept.

2.N.5 Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.

Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.

Identify odd and even numbers and determine whether a set of objects has an odd or even number of elements.

Predict whether a simple addition problem will have an even or odd answer.

Grade 1Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsABAB Patterns in Calendar

Grade 2Coins, Coupons, and CombinationsInvestigation 1 2-52Every Day CountsSept.

2.N.6 Identify the value of all U.S. coins and $1, $5, $10, and $20 bills. Find the value of a collection of coins and dollar bills and different ways to represent an amount of money up to $.50. Use appropriate notation, e.g., $.69, $1.35.

Identify the value of all U.S. coins and $1, $5, $10, and $20 bills.

Find the value of a collection of coins and dollar bills and give appropriate ways to represent an amount of money up to $0.50.

Identify the value of all U.S. coins and $1, $5, $10, and $20 bills.

Find the value of a collection of coins and dollar bills and give appropriate ways to represent an amount of money up to $0.50.

Grade 1Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsNov., Dec., Feb., March, AprilCCC Lab

Grade 2Mathematical Thinking at Grade 2Investigation 4, 76-99Coins, Coupons, and Combinations


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DOEStandard Number



Use appropriate notation, e.g., $0.69, $1.35.

Use appropriate notation, e.g., $0.69, $1.35.

Investigation 2, 54-85Every Day CountsAll months

2.N.7 Demonstrate an understanding of various meanings of addition and subtraction (e.g., addition as combination [plus combined with, more]; subtraction as comparison [how much less, how much more], equalizing [how many more are needed to make these equal], and separation [how much remaining]).

Represent visually presented addition or subtraction problems (acted out or in pictures) (0-20) with a number sentence.

Solve addition and subtraction number sentences up to 20 using manipulatives.

Write a number sentence to represent visually presented addition or subtraction problems (acted out or in pictures) (0-100’s).

Use mental math to add and subtract whole numbers to 20.

Add or subtract one-, two-, and three-digit numbers using penciland paper, and an appropriate algorithm (with and without regrouping).

Grade 1Mathematical Thinking at Grade 1Investigation 2, 24-59Investigation 4, 82-113Investigation 5, 114-144Building Number Sense Investigation 2, 36-79 Investigation 4, 114-171Number Games and Story ProblemsInvestigation 1, 2-45Investigation 3, 100-165Every Day CountsOct., Nov., Feb., March, AprilDigi-Blocks

Grade 2Mathematical Thinking at Grade 2Investigation 2, 20-51Investigation 4, 76-99Coins, Coupons, and CombinationsInvestigation 1, 2-53


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DOEStandard Number



Investigation 3, 86-107Investigation 4, 108-124Putting Together and Taking ApartInvestigation 1, 2-39Every Day CountsOct., Dec., Jan., Feb., March, AprilDigi-Blocks

2.N.8 Understand and use the inverse relationship between addition and subtraction (e.g., 8 + 6 = 14 is equivalent to 14 - 6 = 8 and is also equivalent to 14 - 8 = 6) to solve problems and check solutions.

Use numbers to solve real problems 0-20. (How many cartons of milk do we need if everyone needs one?)

Show a basic understanding of how to reverse a simple addition or subtraction problem.

Explain and demonstrate the relationship between addition and subtraction (fact families).

Use the appropriate operation (addition or subtraction) to solve single-step problems.

Grade 1Number Games and Story ProblemsInvestigation 1, 2-45Investigation 3, 100-165Every Day CountsOct., Nov., March, AprilDigi-Blocks

Grade 2Coins, Coupons, and CombinationsInvestigation 3, 86-107Putting Together and Taking ApartInvestigation 1,2-39Investigation 5, 104-134Every Day CountsOct., Dec., Jan., Feb., April


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DOEStandard Number



2.N.9 Know addition facts (addends to 10) and related subtraction facts, and use them to solve problems.

Know the concepts of addition and subtraction of single digit numbers 0-10.

Demonstrate an understanding of addition and subtraction of numbers 10-20.

Know addition facts (addends to 10) and related subtraction facts, and use them to solve problems.

Grade 1Mathematical Thinking at Grade 1 Investigation 2, 24-59Building Number SenseInvestigation 2, 36-79Investigation 3, 80-113Investigation 4, 114-171Number Games and Story ProblemsInvestigation 1, 2-45Investigation 3, 100-165Every Day CountsOct., Nov., March, April

Grade 2Mathematical Thinking at Grade 2Investigation 3, 20-51


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DOEStandard Number



Coins, Coupons, and CombinationsInvestigation 1, 2-53Investigation 3, 86-107Investigation 4, 108-124Putting Together and Taking ApartInvestigation 1, 2-39Investigation 2, 40-71Investigation 5, 104-134Every Day CountsDec., Jan., Feb., March, April

2.N.10 Demonstrate the ability to add and subtract three-digit numbers accurately and efficiently.

Combine and separate sets of objects 0-20.

Demonstrate an understanding of the concepts of addition and subtraction of any two- and three-digit numbers 0-999 by adding and subtracting 3 digit numbers accurately (with and without regrouping).

Grade 1Readiness:Mathematical Thinking at Grade 1 Investigation 2, 24-59Investigation 4, 82-113Building Number SenseInvestigation 2, 36-79, Investigation 4, 114-171Number Games and Story ProblemsInvestigation 1, 2-45Investigation 3, 100-165Investigation 2, 49-98Every Day Counts


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DOEStandard Number



2.N.11 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for addition (two 3- digit numbers and three 2digit numbers) and subtraction (two, 3 digit numbers).

Combine and separate sets of objects 0-20.

Demonstrate an understanding of the concepts of addition and subtraction of any two- and three-digit numbers 0-999 by adding and subtracting 3 digit numbers accurately (with and without regrouping).

None

Grade 2Readiness:Mathematical Thinking at Grade 2Investigation 4, 76-99Putting Together and Taking ApartInvestigation 1, 2-39Investigation 2, 40-71Investigation 5, 104-134Every Day CountsDec., Jan., Feb., March, April

Grade 1Number Games and Story Problems Investigation 3, p. 102-149

2.N.12 Estimate, calculate, and


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DOEStandard Number



solve problems involving addition and subtraction of 2-digit numbers. Describe differences between estimates and calculations.


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STRAND: PATTERNS, RELATIONS, AND ALGEBRADOEStandard Number



2.P.1 Identify, reproduce, describe, extend, and create simple rhythmic, shape, size, number, color, and letter repeating patterns.

Identify, extend, and create a variety of rhythmic, visual, shape, size, color, letter, number, and verbal two- and three-element patterns (e.g., ABBABB, ABCABC, etc.).

Identify, extend, and construct a variety of rhythmic, shape, size, color, letter, number, verbal, and visual patterns up to five elements.

Identify and extend a two-element numerical pattern up to 100.

Grade 1Mathematical Thinking at Grade 1 Investigation 3, 60-81Investigation 4, 82-113Building Number SenseInvestigation 3, 80-113Investigation 4, 163Quilt Squares and Block TownsInvestigation 1, 2-61Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsSept., Oct., Nov., Dec., Jan., Feb., March, AprilDigi-Blocks

Grade 2Mathematical Thinking at Grade 2Investigation 3, 52-75Coins, Coupons, and CombinationsInvestigation 1, 2-53Shapes, Halves, and SymmetryInvestigation 3, 72-93Putting Together and Taking ApartInvestigation 2, 40-71Timelines and Rhythm PatternsInvestigation 2, 34-6Every Day CountsAll months

Brockton Public Schools PATTERNS, RELATIONS, AND ALGEBRA: GRADE 1 & 2

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Digi-Blocks2.P.2 Identify different patterns on

the hundreds chart. Describe various simple

patterns on a number chart 1 -100.

Describe various patterns on a number chart 1 – 100.

Grade 1Building Number SenseInvestigation 3, 80-113Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsOct., Nov., April

Grade 2Putting Together and Taking ApartInvestigation 1, 2-39Investigation 2, 40-71Every Day CountsNov., Dec., Jan., Feb., March, May/June


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2.P.3 Describe and create addition and subtraction number patterns (e.g., 1, 4, 7, 1,… or 25, 23, 21,…).

Describe and create addition and subtraction number patterns (e.g., 2, 4, 6 or 5, 10, 15, or 100, 90, 80).

Describe and create addition and subtraction number patterns (e.g., 1, 4, 7, 10 …; or 25, 23, 21).

Grade 1Mathematical Thinking at Grade 1 Investigation 3, 60-81Investigation 4, 82-113Building Number SenseInvestigation 3, 80-113Quilt Squares and Block TownsInvestigation 1, 2-61Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsMarch, April

Grade 2Coins, Coupons, and CombinationsInvestigation 2, 54-85Every Day CountsOct., Dec., Jan.-June


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2.P.4 Skip count by twos, fives, and tens up to at least 50, starting at any number.

Skip count by twos to 50; fives and tens to 100, starting at any number.

Skip count by twos, fives, and tens to 100, starting at any number.

Grade 1Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsOctober-JuneBuilding Number SenseInvestigation 3, 60-81

Grade 2Mathematical Thinking at Grade 2Investigation 1, 2-19Investigation 3, 52-75Investigation 5, 76-99Coins, Coupons, and CombinationsInvestigation 2, 54-85Putting Together and Taking ApartInvestigation 2, 40-71Every Day CountsSept., Nov., Jan., Feb., March, May/June


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2.P.5 Construct and solve open sentences that have variables (e.g., + 7 = 100).

Construct and solve open sentences that have missing addends and subtrahends (up to 20).

Construct and solve open sentences that have missing addends and subtrahends (up to 1,000).

Grade 1Readiness:Building Number SenseInvestigation 4, 114-171Investigation 2, 36-79Every Day CountsOct., Nov.

Grade 2Putting Together and Taking ApartInvestigation 3, 72-85Investigation 4, 86-103Every Day CountsNone

2.P.6 Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations.

Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations( up to 100 i.e. 22<80).

Write number sentences using +, -, <, =, and/or > to represent mathematical relationships in everyday situations(up to 1,000).

Grade 1Building Number SenseInvestigation 4, 114-117Number Games and Story ProblemsInvestigation 1, 5-40Investigation 3, 102-149Every Day CountsOct., Nov.

Grade 2Putting Together and Taking ApartInvestigation 5, 104-134Every Day Counts


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Oct., Nov., Dec. Jan. March

2.P.7 Describe functions related to trading, including coin trades and measurement trades (e.g., five pennies make one nickel or four cups make a quart).

Describe functions related to trading, including coin trades (e.g., five pennies make one nickel. …).

Describe functions related to trading, including 2c = 1pint, 4 c =1 qt., 1 ft. = 12 in., 4 quarters = $1.00., 7 days = 1 week

Grade 1Number Games and Story ProblemsInvestigation 2, 46-99Every Day CountsSept., Oct., Nov., Dec., Feb., March

Grade 2Putting Together and Taking ApartInvestigation 2, 0-71Every Day CountsApril, May/June


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STRAND: GEOMETRY

DOEStandard Number



2.G.1 Describe attributes and parts of two- and three-dimensional shapes (e.g., length of sides, and number of corners, edges, faces, and sides).

Describe attributes and parts of two- and three-dimensional shapes (e.g., faces and sides).

Describe attributes and parts of two- and three-dimensional shapes (e.g., corners, edges, faces and sides).

Grade 1Mathematical Thinking at Grade 1 Investigation 1, 2-23Survey Questions and Secret RulesInvestigation 1, 2-31Quilt Squares and Block TownsInvestigation 1, 2-61Investigation 2, 62-97Investigation 3, 98-126Every Day CountsOct., Nov., Dec., Jan.,

Grade 2Mathematical Thinking at Grade 22-19, 52-75Shapes, Halves, and SymmetryInvestigation 1, 2-43Investigation 2, 36-57Investigation 3, 72-93Investigation 4, 94-115Every Day CountsOct., Nov., Dec., Jan., March, April, May/June

Brockton Public Schools GEOMETRY: GRADE 1 & 2

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STRAND: GEOMETRY

DOEStandard Number



2.G.2 Identify, describe, draw, and compare two-dimensional shapes, including both polygonal (up to six sides) and curved figures such as circles.

Identify, describe, draw, and compare two-dimensional shapes including polygons (up to four sides) and circles.

Identify, describe, draw, and compare two-dimensional shapes including both polygons (up to six sides) and curved figures, such as circles

Grade 1Mathematical Thinking at Grade 1Investigation 1, 2-23Quilt Squares and Block TownsInvestigation 1, 2-61Investigation 2, 62-97Investigation 3, 98-126Every Day CountsOct., Nov., Jan.,

Grade 2Mathematical Thinking at Grade 2Investigation 3, 52-75Shapes, Halves, and SymmetryInvestigation 1, 2-43Investigation 2, 36-57Investigation 3, 72-93Every Day CountsOct., Jan., March, April, May/June

2.G.3 Recognize congruentshapes

Recognize congruent shapes (see above).

Use the term “congruent” correctly

Recognize congruent shapes (see above).

Use the term “congruent” correctly

Grade 1Every Day CountsJanuary

Grade 2Shapes, Halves, and SymmetryInvestigation 1, 2-43Investigation 3, 72-93Every Day CountsJan., March, April, May/June


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STRAND: GEOMETRY

DOEStandard Number



2.G.4 Identify shapes that have been rotated (turned), reflected (flipped), translated (slid), and enlarged. Describe direction of translations (e.g., left, right, up, down).

Demonstrate flips, slides, and turns with their bodies.

Identify shapes that have been turned, flipped, slid, and enlarged.

Demonstrate flips, slides, and turns with manipulatives.

Identify shapes that have been turned, flipped, slid, and enlarged. Describe the direction (e.g., left, right, up, down).

Grade 1Quilt Squares and Block TownsInvestigation 1, 2-61Every Day CountsJanuary

Grade 2See Grade 1Quilt Squares and Block Towns2-61Every Day CountsNone

2.G.5 Identify symmetry in two-dimensional shapes.

Identify horizontal and vertical lines of symmetry in two-dimensional shapes.

Identify various forms of symmetry in two-dimensional shapes (e.g. Lines of symmetry, rotational symmetry).

Grade 1Readiness:Quilt Squares and Block TownsInvestigation 2-61 (Reading Only)Every Day CountsNone

Grade 2Shapes, Halves, and SymmetryInvestigation 4, 94-115Every Day CountsJan., March, April, May/June


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STRAND: GEOMETRY

DOEStandard Number



2.G.6 Predict the results of putting shapes together and taking them apart.

Predict and confirm the results of putting shapes together and taking them apart.

Predict and confirm the results of putting shapes together and taking them apart.

Grade 1Quilt Squares and Block TownsInvestigation 1, 2-61Investigation 2, 62-97Every Day CountsOct., Nov., Jan.

Grade 2Mathematical Thinking at Grade 2Investigation 3, 52-75Shapes, Halves, and SymmetryInvestigation 1, 2-43; Investigation 2, 36-57Every Day CountsNone

2.G.7 Relate geometric ideas to numbers (e.g., seeing rows in an array as a model of repeated addition).

Relate geometric ideas to numbers (e.g., seeing rows in an array as a model for addition and subtraction).

Relate geometric ideas to numbers (e.g., seeing rows in an array as a model of repeated addition).

Grade 1Every Day CountsNone

Grade 2Mathematical Thinking at Grade 2Investigation 1, 2-19Shapes, Halves, and SymmetryInvestigation 1, 2-43Investigation 2, 36-57Every Day Counts


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STRAND: GEOMETRY

DOEStandard Number



None


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STRAND: MEASUREMENT

DOEStandard Number



2.M.1 Identify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar.

Identify the use of a calendar and verbally identify the days of the week and months of the year.

Identify parts of the day (e.g., morning, afternoon, evening).

Identify the four seasons

Identify parts of the day (e.g., morning, afternoon, evening), days of the week, and months of the year. Identify dates using a calendar.

Relate specific months to the seasons

Grade 1Survey Questions and Secret RulesInvestigation 3, 54-73Every Day CountsAll months

Grade 2Timelines and Rhythm PatternsInvestigation 1, 2-33

Every Day CountsAll months

2.M.2 Tell time at quarter-hour intervals on analog and digital clocks using a.m. and p.m.

Tell and record time to the hour using an analog and digital clock, and using a.m. and p.m.

Tell and record time to the half hour, and quarter hour using an analog or digital clock, and using a.m. and p.m.

Grade 1Every Day CountsSept., Oct., Nov., Dec., Feb., March, May, June

Grade 2Timelines and Rhythm PatternsInvestigation 1, 2-33Every Day CountsMarch

Brockton Public Schools MEASUREMENT: GRADES 1 AND 2

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DOEStandard Number



2.M.3 Compare the length, weight, area, and volume of two or more objects by using direct comparison.

Compare length and weight of two or more objects by using direct comparison.

Identify capacity (which holds more) using direct comparison and containers.

Compare length, weight, area, and volume of two or more objects by using direct comparison.

Grade 1Bigger, Taller, Heavier, SmallerInvestigation 1, 2-31Investigation 2, 32-59Investigation 3, 60-86Building Number SenseInvestigation 3, 92,113Every Day CountsNov., May, June

Grade 2How Long? How Far? Investigation 1, 2-43, Investigation 2, 44-81Every Day CountsNov., Feb., March, May/June

2.M.4 Measure and compare common objects using metric and English units of length measurement (e.g., centimeter, and inch).

Measure and compare common objects using metric and English units of length measurement (e.g., centimeter, and inch).

Measure and compare common objects using metric and English units of length measurement (e.g., 36”, 1 m, 100 cm).

Measure to the nearest ½ inch and nearest centimeter.

Grade 1Readiness:Bigger, Taller, Heavier, SmallerInvestigation 1, 2-3Investigation 2, 32-59Investigation 3, 60-86Every Day CountsMay, JuneGrade 2Readiness:How Long? How Far?Investigation 1, 2-43, 34-63Every Day Counts


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STRAND: MEASUREMENT

DOEStandard Number



Feb., March, April, May/June2.M.5 Select and correctly use the

appropriate measurement tools (e.g., ruler, balance scale, thermometer).

Select and correctly use the appropriate measurement tools (e.g., ruler, balance scale).

Select and correctly use the appropriate measurement tools (e.g., ruler, balance scale, thermometer).

Grade 1Bigger, Taller, Heavier, SmallerInvestigation 1, 2-31Every Day CountsMay, June

Grade 2How Long? How Far?Investigation 1, 2-43Every Day CountsNov., Jan., Feb., Mar., Apr., May/June

2.M.6 Make and use estimates of measurement, including time, volume, weight, and area.

Make and use estimates of measurement, including time and weight.

Make and use estimates of measurement, including time, volume, weight, and area.

Grade 1Bigger, Taller, Heavier, SmallerInvestigation 1, 2-31Investigation 2, 32-59Every Day CountsSept., May, June

Grade 2How Long? How Far? Investigation 1, 2-43Every Day CountsFeb., March, May/June


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2.D.1 Use interviews, surveys, and observations to gather data about themselves and their surroundings.

Take a class survey and record information.

Use interviews, surveys, and observations to gather data about themselves and their surroundings.

Grade 1Mathematical Thinking at Grade 1 Investigation 5, 114-144Survey Questions and Secret RulesInvestigation 2, 32-53Investigation 4, 74-99Investigation 3, 54-73Every Day CountsDec., Feb., March

Grade 2Mathematical Thinking at Grade 2,100-123Does It Walk, Crawl, or Swim?Investigation 1, 2-35; Investigation 2, 36-57Investigation 3, 58-69Investigation 4, 70-85How Many Pockets? How Many Teeth?Investigation 1, 2-27Everyday CountsSept., Oct., Jan.

Brockton Public Schools DATA ANALYSIS, STATISTICS AND PROBABILITY: GRADE 1 & 2

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2.D.2 Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.

Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.

Organize, classify, represent, and interpret data using tallies, charts, tables, bar graphs, pictographs, and Venn diagrams; interpret the representations.

Grade 1Mathematical Thinking at Grade 1Investigation 5, 114-144Survey Questions and Secret RulesInvestigation 2, 32-53Investigation 4, 74-99InvestigationBigger, Taller, Heavier, SmallerInvestigation 2, 32-59Every Day CountsDec., Jan., Feb., March, April, May, June

Grade 2Mathematical Thinking at Grade 2100-123Does It Walk, Crawl, or Swim?Investigation 1, 2-35Investigation 2, 36-57Investigation 3, 58-69Investigation 4, 70-85How Many Pockets? How Many Teeth?Investigation 1, 2-27Investigation 2, 28-59Investigation 3, 60-73Every Day CountsSept., Oct., Jan. April, May/June


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2.D.3 Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.

Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.

Formulate inferences (draw conclusions) and make educated guesses (conjectures) about a situation based on information gained from data.

Grade 1Mathematical Thinking at Grade 1 Investigation 5, 114-144Survey Questions and Secret RulesInvestigation 2, 32-53Investigation 4, 74-99Investigation 3, 54-73

Every Day CountsDecember

Grade 2Does It Walk, Crawl, or Swim?Investigation 1, 2-35; Investigation 2, 36-57Investigation 3, 58-69, Investigation 4, 70-85How Many Pockets? How Many Teeth?Investigation 1, 2-27Investigation 2, 28-59Investigation 3, 60-73Every Day CountsFeb.


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2.D.4 Decide which outcomes of experiments are most likely.

Based on data gathered, decide which outcomes of experiments are most likely.

With guided discussion, decide which outcomes of experiments are most likely

Grade 1Every Day CountsDecember

Grade 2See Grade 3Things that Come in GroupsInvestigation 2, 58,Investigation 5, 76, 93-94Every Day CountsFeb., May/June


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Brockton Public Schools ADDITIONAL RESOURCES: GRADE 1 AND 2


CCC Lab ActivitiesQuestion of the Day, Lakeshore Publishing – K onlyEvery Day Counts Pattern Games – K-3 only – Great SourceGames for Number Sense – Great Source – K OnlyPlaying Math Games – Teacher Resource Center – K OnlyDeveloping Number Concepts: Counting, Comparing and Patterns – Dale Seymour Publications – K OnlySuper Source K-8 – All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes TangramsHundred Chart – ETA CuisenaireAnalog Clocks – ETA CuisenaireEqua Beam – ETA CuisenaireHands-On Equations – ETA CuisenaireFraction Strips – ETA Cuisenaire


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State Standard Grade 3Progress Indicators Resources

3.N.1 Exhibit an understanding of the values of the digits in the base-ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999.

Exhibit an understanding of the values of the digits in the base-ten number system by reading, modeling, writing, comparing, and ordering whole numbers through 9,999.

Mathematical Thinking at Grade 3Investigation 1, 2-13; Investigation 4, 68-86Landmarks in the HundredsInvestigation 1, 2-29: Combining and ComparingInvestigation 4, 40-57Exploring Solids and BoxesInvestigation 5, 52-62Every Day Counts, AllDigi-Blocks

3.N.2 Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three.

Represent, order, and compare numbers through 9,999. Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three.

Mathematical Thinking at Grade 3Investigation 3, 46-67; Everyday Counts, NovemberDigi-Blocks

Every Day Counts- None

3.N.3 Identify and represent fractions between 0 and 1 with denominators through 10 as parts of unit wholes and parts of groups.

Demonstrate an understanding of fractions with denominators through 10 as parts of unit wholes and parts of a group. Measure to the nearest ¼ inch

Mathematical Thinking at Grade 3Investigation 4, 68-86Fair SharesInvestigation 1, 2-21Investigation 2, 22-45Investigation 3, 46-59Every Day Counts, March

Brockton Public Schools NUMBER SENSE AND OPERATIONS: GRADE 3

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DOEStandard Number


3.N.4 Locate on the number line and compare fractions (between 0 and 1) with denominators 2, 3, and 4, e.g., 2/3: and the mixed numbers 1 ¼, 1 ½, and 1 ¾.

Locate on the number line and compare fractions (between 0 and 1) with denominators 2, 3, and 4, e.g., 2/3: and the mixed numbers 1 ¼, 1 ½, and 1 ¾. Show which fractions are

equivalent (using manipulatives)

Mathematical Thinking at Grade 3Investigation 4, 68-86Fair SharesInvestigation 1, 2-2Investigation 2, 22-45Investigation 3, 46-59Every Day Counts, None

3.N.5 Recognize classes (odd numbers, even numbers; and multiples of numbers through 10) to which a number may belong, and identify the numbers in those classes, e.g., the class of multiples of 7 between 1 and 29 consist of 7, 14, 21, 28.

Recognize classes (in particular, odds, evens; and multiples of a given number) to which a number may belong, and identify the numbers in those classes.

Use these in the solution of problems.

Predict whether an addition or subtraction problem will have an even or odd answer.

Mathematical Thinking at Grade 3Investigation 4, 68-86Things That Come in GroupsInvestigation 2, 20-39Landmarks in the HundredsInvestigation 1, 2-29; Investigation 2, 30-51; Investigation 3, 52-60Combining and ComparingInvestigation 1, 2-12Every Day CountsAllDigi-Blocks

3.N.6 Select, use, and explain various meanings and models of multiplication (through 10 x 10). Relate a multiplication problem to a corresponding division problem, e.g., draw a model to represent 5 x 6 and 30 ÷ 6.

Select, use, and explain various meanings and models of multiplication (up to 10 x 10) and division of whole numbers. Understand and use the inverse

Mathematical Thinking at Grade 3Investigation 2, 14-45Things That Come in GroupsInvestigation 1, 4-16Investigation 3, 40-53Investigation 4, 56-70


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relationship between the two operations.

Model and describe multiplication as repeated addition.

Model and describe division as repeated subtraction.

Investigation 5, 74-87Landmarks in the HundredsInvestigation 1, 2-30Every Day Counts December, February April-JuneDigi-Blocks

3.N.7 Use the commutative and identify properties of addition and multiplication on whole numbers in computations and problem situations, e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4

Select, use, and explain the commutative, and identity properties of operations on whole numbers, e.g., 3 + 4 + 7 = 3 + 7 + 4 = 10 + 4

Additional Resources Needed

3.N.8 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

Mathematical Thinking at Grade 3Investigation 2, 14-45; Things That Come in GroupsInvestigation 1, 2-19Investigation 4, 56-73Investigation 5, 74-90Landmarks in the HundredsInvestigation 2, 30-51Combining and comparingInvestigation 1, 2-12Investigation 3, 26-35Investigation 4, 40-53Up and Down the Number LineInvestigation 1, 2-31Every Day Counts September, October, December-May/JuneDigi-Blocks


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3.N.9 Know multiplication facts through 10 x 10 and related division facts, e.g., 9 x 8 = 72 and 72 ÷ 9 = 8. Use these facts to solve related problems e.g., 3 x 5 is related to 30 x 50.

Know multiplication facts through 10 x 10 and related division facts.

Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500).

Things That Come in GroupsInvestigation 1, 2-19Investigation 4, 56-73Investigation 5, 74-90Landmarks in the HundredsInvestigation 2, 30-51Every Day Counts, February, April-JuneDigi-Blocks

3.N.10 Add and subtract (up to four-digit numbers) and multiply (up to two digit numbers by one digit numbers) accurately and efficiently.

Add and subtract (up to four-digit numbers) and multiply one- and two-digit numbers by another one-digit number accurately and efficiently.

Mathematical Thinking at Grade 3Investigation 2, 14-45Landmarks in the HundredsInvestigation 2, 30-51Every Day Counts, January, AprilDigi-Blocks

3.N.11 Round whole numbers through 1,000 to the nearest 10, 100, and 1000.

Round whole numbers through 1,000 to the nearest 10 and 100, and 1,000.

Landmarks in the HundredsInvestigation 2, 30-51Investigation 3, 52-60Every Day Counts, February-JuneDigi-Blocks

3.N.12 Understand and use the strategies of rounding, and regrouping to estimate quantities, measures, and the results of whole-number computations (addition, subtraction, and multiplication) up to two-digit whole numbers and amounts of money to $100, and to judge the reasonableness of the answer.

Select and use a variety of strategies (e.g., rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to two-digit whole numbers and amounts of money to $100, and to

Readiness:Fair SharesInvestigation 1, 2-29Investigation 2, 30-51Investigation 3, 52-57Every Day CountsFebruary


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judge the reasonableness of the answer.

3.N.13 Use concrete objects and visual models to add and subtract (only when the answer is greater than or equal to zero) common fractions (halves, thirds, fourths, sixths, and eighths) with like denominators.

Use concrete objects and visual models to add and subtract common fractions, halves, thirds, fourths, sixths, and eighths (with like denominators)

Landmarks in the HundredsInvestigation 2, 30-51Combining and ComparingInvestigation 3, 26-35Every Day Counts MarchDigi-Blocks


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3.P.1 Create, describe, extend, and explain symbolic (geometric) patterns and addition and subtraction patterns, e.g., 2, 6, 10, ...; and 50, 45, 40...

Create, describe, extend, and explain symbolic (geometric) and addition and subtraction patterns, e.g., 2, 6, 10, ...; and 50, 45, 40...

Mathematical Thinking at Grade 3Investigation 1,2-13Investigation 2, 14-45Things That Come in GroupsInvestigation 2, 20-39Investigation 5, 74-90Flips, Turns, and AreaInvestigation 1, 2-31Landmarks in the HundredsInvestigation 1, 2-29Exploring Solids and Boxes, Investigation 4, 38-51Every Day Counts, September-December, February, April-JuneDigi-Blocks

3.P.2 Determine which symbol (<, >, or =) is appropriate for a given number sentence, e.g., 7 x 8 __ 49 + 6.

Determine which symbol (<, >, or =) is appropriate for a given number sentence, e.g., 7 x 8 __ 49 + 6.

Write number sentences using <, >, or =.

Mathematical Thinking at Grade 3Investigation 1,2-13Investigation 2, 14-45Things That Come in Investigation 2, 20-39; Investigation 5, 74-90; Flips, Turns, and AreaInvestigation 1, 2-31Landmarks in the HundredsInvestigation 1, 2-29Exploring Solids and Boxes, Investigation 4, 38-51Every Day Counts, NoneDigi-Blocks

Brockton Public Schools PATTERNS, RELATIONS, AND ALGEBRA: GRADE 3

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3.P.3 Determine value of a variable (through 10) in simple equations involving addition, subtraction, or multiplication, e.g., 2 + = 9: 5 x = 35

Determine values of variables in simple equations (e.g., 106 - = 37; 5 = + 3 and - = 3)(up to 1,000).

Readiness:Combining and ComparingInvestigation 3, 26-39Investigation 4, 40-57Investigation 5, 58-70Every Day Counts, None

3.P.4 Write number sentences using + , -, x, ÷, <, =, and/or > to represent mathematical relationships in everyday situations.

Write number sentences using + , -, x, ÷, <, =, and/or > to represent mathematical relationships in everyday situations.

Mathematical Thinking at Grade 3Investigation 1, 2-13Things That Come in GroupsInvestigation 2, 20-39Exploring Solids and BoxesInvestigation 4, 38-51Every Day Counts, MarchDigi-Blocks


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STRAND: GEOMETRYDOE Standard Number

State Standard Grade 3Progress Indicator Resources

3.G.1 Compare and analyze attributes and other features (e.g., number of sides, corners, diagonals, and lines of symmetry) of two-dimensional geometric shapes.

Compare and analyze attributes and other features (e.g., number of sides, corners, diagonals and lines of symmetry) of two- dimensional geometric shapes.

Mathematical Thinking at Grade 3Investigation 2, 14-45Turtle Paths, Investigation 2, 28-61Exploring Solids and BoxesInvestigation 1, 2-13Investigation 2, 14-25Investigation 3, 26-37Everyday Counts November, April-JuneDigi-BlocksGeometry Packet

3.G.2 Describe, model, draw, compare, and classify two- dimensional shapes, e.g., circles, triangles and quadrilaterals. Identify and describe simple three-dimensional shapes, e.g., cubes, spheres, and pyramids

Describe, model, draw, compare, and classify two- dimensional shapes, e.g., circles, triangles, squares,.

Identify and describe simple three-dimensional shapes, e.g., cubes, spheres, and pyramids

Turtle Paths, Investigation 2, 28-61Exploring Solids and BoxesInvestigation 1, 2-13Investigation 2, 14-25Investigation 3, 26-37Every Day CountsApril-May

Brockton Public Schools GEOMETRY: GRADE 3

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3.G.3 Identify angles as right angles, less than a right angle, and greater than a right angle.

Identify angles as right angles.

Identify angles less than or greater than right angles.

Additional Resources NeededEvery Day CountsNoneGeometry Packet

3.G.4 Identify and draw parallel lines, perpendicular lines, and other intersecting lines.

Describe and draw parallel, perpendicular, and intersecting lines.

Additional Resources NeededEvery Day Counts NoneGeometry Packet

3.G.5 Using ordered pairs of whole numbers and/or letters, locate, and identify points on a grid.

Using ordered pairs of numbers and/or letters, graph, locate, and identify points on a grid.

Turtle Paths, Investigation 1, 2-27; Investigation 2, 28-61Investigation 3, 62-81Every Day Counts NoneGeometry Packet

3.G.6 Identify and draw lines symmetry in two-dimensional shapes.

Identify and describe line symmetry in two-dimensional shapes.

Additional Resources NeededEvery Day Counts-April

3.G.7 Predict and explain the results of taking apart and combining two-dimensional shapes.

Predict and validate the results of partitioning, folding, and combining two-dimensional shapes.

Flips, Turns, and AreaInvestigation 2, 32-52Every Day Counts None


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STRAND: MEASUREMENTDOEStandard Number


3.M.1 Demonstrate an understanding of the attributes length, area, and weight, and select the appropriate type of unit for measuring each attribute using both the U. S. Customary (English) and metric systems.

Demonstrate an understanding of such attributes as length, area, and weight and select the appropriate type of unit for measuring each attribute.

Use metric system for determining above attributes.

Things That Come in GroupsInvestigation 3, 40-55Flips, Turns, and AreaInvestigation 1, 2-31Investigation 2, 32-52From Paces to FeetInvestigation 1, 2-25Investigation 2, 26-59Investigation 3, 6-67Investigation 4, 68-74Combining and ComparingInvestigation 2, 18-25Turtle Paths, Investigation 1, 2-27Investigation 3, 62-81Every Day CountsNovember, February-JuneDigi-Blocks

3.M.2 Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).

Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).

Combining and ComparingInvestigation 3, 74-92Every Day Counts-Nov., Feb., June

Brockton Public Schools MEASUREMENT: GRADE 3

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3.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time less than one hour using a clock (e.g., minutes since …) and using a calendar (e.g., days since …).

Identify time to the minute on analog and digital clocks using a.m. and p.m.

Compute elapsed time less than one hour using a clock (e.g., minutes since …) and using a calendar (e.g., days since …).

Combining and ComparingInvestigation 4, 40-57Investigation 5, 58-70Every Day Counts October, November, April-June

3.M.4 Estimate and find area and perimeter of a rectangle using diagrams, models, and grids or by measuring.

Estimate and find area and perimeter of a rectangle, using diagrams, models, and grids or by measuring.

Things That Come in GroupsInvestigation 3, 40-55; Flips, Turns, and AreaInvestigation 2, 32-52From Paces to FeetInvestigation 4, 68-74Turtle Paths, Investigation 1, 2-27Every Day Counts, NoneDigi-Blocks

3.M.5 Identify and use appropriate metric and U. S. Customary (English) units and tools (e.g., ruler, scale, thermometer, clock) to estimate, measure, and solve problems involving length, area, weight, temperature, and time.

Identify and use appropriate metric and English units and tools (e.g., ruler, grids, scales, thermometer, clock) to estimate, measure, and solve problems involving length, area, weight, time, and temperature.

Flips, Turns, and AreaInvestigation 2, 32-52From Paces to FeetInvestigation 2, 26-59Investigation 3, 60-67Investigation 4, 68-74Every Day Counts March-June


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DATA ANALYSIS, STATISTICS, AND PROBABILITYDOEStandard Number


3.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

Collect data to draw simple bar graphs, line graphs, and pictographs, and to compare and explain what is recorded.

Mathematical Thinking at Grade 3Investigation 3, 46-67Digi-BlocksFrom Paces to FeetInvestigation 3, 60-67Combining and ComparingInvestigation 4, 40-57Every Day Counts October, December-January, April

3.D.2 Match representations of a data set in the form of tables, line plots, pictographs, tallies, or bar graphs with the actual data set.

Match representations of a data set such as tables, line plots, or graphs with the actual set of data.

Combining and ComparingInvestigation 4, 40-57Every Day CountsDecember, January, March

3.D.3 Construct and draw conclusions from representations of data sets, in the form of tables, line plots, pictographs, tallies, and bar graphs.

Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, and tallies.

Combining and ComparingInvestigation 4, 40-57Every Day Counts, October, December, January, March-June

3.D.4 List and count the number of possible combinations of objects from two sets (e.g., how many different outfits can one make from a set of two sweaters, and a set of three skirts?).

List and count the number of possible combinations of objects from two sets.

Additional Resources NeededEvery Day Counts-None

Brockton Public Schools DATA ANALYSIS, STATISTICS AND PROBABILITY: GRADE 3

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CCC Lab Activities Question of the Day, Lakeshore Publishing – K onlyEvery Day Counts Pattern Games – K-3 only – Great SourceGames for Number Sense – Great Source – K OnlyPlaying Math Games – Teacher Resource Center – K OnlyDeveloping Number Concepts: Counting, Comparing and Patterns – Dale Seymour Publications – K OnlySuper Source K-8 – All Grades - ETA Cuisenaire Base Ten Blocks Color Tiles Geoboards Pattern Blocks Snap Cubes TangramsHundred Chart – ETA CuisenaireAnalog Clocks – ETA CuisenaireEqua Beam – ETA CuisenaireHands-On Equations – ETA CuisenaireFraction Strips – ETA Cuisenaire


Brockton Public Schools ADDITIONAL RESOURCES: GRADE 3

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NUMBER SENSE AND OPERATIONSDOEStandard Number


4.N.1 Exhibit an understanding of the base-ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers.

Exhibit an understanding of the base-ten number system by reading, modeling, writing, and interpreting whole numbers to at least 100,000; demonstrating an understanding of the values of the digits; and comparing and ordering the numbers.

Mathematical Thinking at Grade 4Investigation 1, 2-31Investigation 2, 32-45Investigation 3, 46-63Landmarks in the ThousandsInvestigation 2, 18-35Investigation 3, 36-51;Investigation 4, 52-58Every Day Counts-Sept., Oct., May, June

4.N.2 Represent, order, and compare large numbers (to at least 100,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3.

Represent, order, and compare large numbers (to at least 1,000,000) using various forms, including expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3.

Landmarks in the ThousandsInvestigation 3, 36-51Investigation 4, 52-58Every Day Counts- None

4.N.3 Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line.

Demonstrate an understanding of fractions as parts of unit wholes, as parts of a collection, and as locations on the number line.

Measure on a ruler to the nearest 1/8 inch

Different Shapes, Equal PiecesInvestigation 1, 2-21;Investigation 2, 22-37Investigation 3, 38-54Three out of Four Like SpaghettiInvestigation 1, 2-25Everyday Counts-None


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4.N.4 Select, use, and explain models to relate common fractions and mixed numbers (½, ⅓, ¼, 1/6, 1/8, 1/12, and 1½), find equivalent fractions, mixed numbers, and decimals, and order fractions.

Select, use, and explain models to relate common fractions and mixed numbers to twelfths, find equivalent fractions, mixed numbers, and decimals, and order fractions.

Compare and order fractions and mixed numbers with like denominators up to twelfths.

Represent mixed numbers as improper fractions and vice versa

Different Shapes, Equal PiecesInvestigation 1, 2-21Investigation 2, 22-37Investigation 3, 38-54Money, Miles, and Large NumbersInvestigation 2, 30-45Three out of Four Like SpaghettiInvestigation 1, 2-25Every Day Counts- Nov., Jan., Feb., March, April

4.N.5 Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths).

Identify and generate equivalent forms of common decimals and fractions less than one whole (halves, quarters, fifths, and tenths).

Different Shapes, Equal PiecesInvestigation 2, 22-37Investigation 3, 38-54Money, Miles, and Large NumbersInvestigation 2, 30-45Combining and ComparingInvestigation 1, 2-12LandmarksInvestigation 1, 2, 3Every Day Counts- None

4.N.6 Exhibit an understanding of the base-ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths.

Exhibit an understanding of the base-ten number system by reading, naming, and writing decimals between 0 and 1 up to the hundredths.

Money, Miles, and Large NumbersInvestigation 1, 2-29Every Day CountsOct.


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4.N.7 Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems.

Recognize classes (in particular, odds, evens; factors or multiples of a given number; and squares) to which a number may belong, and identify the numbers in those classes. Use these in the solution of problems.

Find common multiples and common factors for sets of numbers.

Make predictions about the solutions to problems using an understanding of the classes of numbers (i.e. even x even)

Arrays and SharesInvestigation 1, 2-11Landmarks in the ThousandsInvestigation 1, 2-17Investigation 2, 18-35Investigation 3, 36-51Packages and GroupsInvestigation 1, 2-1Investigation 3, 28 62Every Day Counts- Sept., Nov., Dec., Jan., Feb. March, April, May, June

4.N.8 Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.

Select, use, and explain various meanings and models of multiplication and division of whole numbers. Understand and use the inverse relationship between the two operations.

Model and describe multiplication as repeated addition.

Model and describe division as repeated subtraction.

Arrays and SharesInvestigation 2, 12-41Investigation 3, 42-59Landmarks in the ThousandsInvestigation 2, 18-35Packages and GroupsInvestigation 1, 2-15Investigation 2, 16-23Investigation 3, 28-62Every Day Counts-None


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4.N.9 Select, use, and explain the commutative, associative, and identify properties of operations on whole numbers in problem situations (e.g., 37 x 46 = 46 x 37, [5 x 7] x 2 = 5 x [7 x 2]).

Select, use, and explain the commutative, associative, and identity properties of operations on whole numbers in problem situations (e.g., 37 x 46 = 46 x 37, [5 x 7] x 2 = 5 x [7 x 2]).

Arrays and SharesInvestigation 2, 12-4Investigation 3, 42-59Every Day Counts- None

4.N.10 Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

Select and use appropriate operations (addition, subtraction, multiplication, and division) to solve problems, including those involving money.

Arrays and SharesInvestigation 1, 2-11Investigation 3, 42-59Landmarks in the ThousandsInvestigation 1, 2-17Investigation 2, 18-35Investigation 3, 36-51Investigation 4, 52-58Money, Miles, and Large NumbersInvestigation 1, 2-29Investigation 2, 30-45Packages and GroupsInvestigation 2, 16-23Investigation 3, 28-62Every Day Counts-All months

4.N.11 Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, and 30 x 500).

Know multiplication facts through 12 x 12 and related division facts. Use these facts to solve related multiplication problems and compute related problems (e.g., 3 x 5 is related to 30 x 50, 300 x 5, 30 x 500).

Arrays and SharesInvestigation 1, 2-11Packages and GroupsInvestigation 2, 16-23Investigation 3, 28-62Every Day Counts-None


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4.N.12 Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.

Add and subtract (up to five-digit numbers) and multiply (up to three digits by two digits) accurately and efficiently.

Landmarks in the ThousandsInvestigation 1, 2-17Investigation 2, 18-35Investigation 3, 36-51Investigation 4, 52-58Money, Miles, and Large NumbersInvestigation 1, 2-29Packages and GroupsInvestigation 2, 16-23Every Day Counts- None

4.N.13 Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders.

Divide up to a three-digit whole number with a single-digit divisor (with or without remainders) accurately and efficiently. Interpret any remainders as fractions.

Arrays and SharesInvestigation 2, 12-41Investigation 3, 42-59Everyday Counts- None

4.N.14 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).

Demonstrate in the classroom an understanding of and the ability to use the conventional algorithms for addition and subtraction (up to five-digit numbers), and multiplication (up to three digits by two digits).

Landmarks in the ThousandsInvestigation 1, 2-17;Investigation 2, 18-3Investigation 3, 36-51Investigation 4, 52-58Packages and GroupsInvestigation 2, 16-23Every Day Counts-None


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4.N.15 Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).

Demonstrate in the classroom an understanding of and the ability to use the conventional algorithm for division of up to a three-digit whole number with a single-digit divisor (with or without remainders).

Arrays and SharesInvestigation 2, 12-41Investigation 3, 42-59Every Day Counts-None

4.N.16 Round whole numbers through 100,000 to the nearest 10, 100, 1000, 10,000, and 100,000.

Round whole numbers through 100,000 to the nearest 10, 100, 1,000, 10,000, and 100,000.

Mathematical Thinking at Grade 4Investigation 1, 2-31Landmarks in the ThousandsInvestigation 1, 2-17Investigation 3, 36-51Money, Miles, and Large NumbersInvestigation 1, 2-29Every Day Counts-None

4.N.17 Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer.

Select and use a variety of strategies (e.g., front-end, rounding, and regrouping) to estimate quantities, measures, and the results of whole-number computations up to three-digit whole numbers and amounts of money to $1000, and to judge the reasonableness of the answer.

Readiness:Different Shapes, Equal PiecesInvestigation 1, 2-19Investigation 2, 22-37Investigation 3, 38-54Every Day Counts

4.N.18 Use concrete objects and visual models to add and subtract common fractions.

Use concrete objects and visual models to add and subtract common fractions, represent answers in

Mathematical Thinking at Grade 4 Investigation 1, 2-31Every Day Counts- None


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lowest terms.


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PATTERNS, RELATIONS, AND ALGEBRA

DOEStandard Number


4.P.1 Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, ….

Create, describe, extend, and explain symbolic (geometric) and numeric patterns, including multiplication patterns like 3, 30, 300, 3000, ….or 1, 4, 9, 16, 25, ___, ___

Mathematical Thinking at Grade 4Investigation 4, 64-90Arrays and SharesInvestigation 1, 2-11Investigation 3, 42-59Packages and GroupsInvestigation 1, 2-15Sunken Ships and Grid PatternsInvestigation 1, 2-41Every Day Counts- All months

4.P.2 Use symbol and letter variables (e.g., , x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >).

Use symbol and letter variables (e.g., , x) to represent unknowns or quantities that vary in expressions and in equations or inequalities (mathematical sentences that use =, <, >).

Mathematical Thinking at Grade 4Investigation 4, 64-90Arrays and SharesInvestigation 1, 2-11Investigation 3, 42-59Packages and GroupsInvestigation 1, 2-15Sunken Ships and Grid PatternsInvestigation 1, 2-41Every Day Counts- All months

4.P.3 Determine values of variables in simple equations (e.g., 4106 - = 37; 5 = + 3 and - = 3).

Determine values of variables in simple equations (e.g., 4106 - = 37; 5 = + 3 and - = 3) (up to 100,000).

Readiness:Money, Miles, and Large NumbersInvestigation 1, 2-29Every Day Counts- None


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PATTERNS, RELATIONS, AND ALGEBRA

DOEStandard Number


4.P.4 Use pictures, models, tables, charts, graphs, words, number sentences, and mathematical notations to interpret mathematical relationships.

Use pictures, models, tables, charts, graphs, bar line, circle, words, number sentences, and mathematical notations to interpret mathematical relationships.

Mathematical Thinking at Grade 4Investigation 4, 64-90The Shape of the DataInvestigation 1, 2-19Investigation 2, 20-49Investigation 3, 50-64Money, Miles, and Large NumbersInvestigation 2, 30-45Investigation 3, 46-57Three out of Four Like SpaghettiInvestigation 1, 2-25Investigation 2, 26-50Every Day Counts-All months

4.P.5 Solve problems involving proportional relationships, including unit pricing (e.g., four apples cost 80¢, so one apple costs 20¢) and map interpretation (e.g., one inch represents five miles, so two inches represent ten miles).

Solve problems involving proportional relationships, including unit pricing (e.g., five apples cost 0.80, so one apple costs 0.16) and map interpretation (e.g., one inch represents five miles, so ½ inch represent 2 ½ miles).

Money, Miles, and Large NumbersInvestigation 2, 30-45Investigation 3, 46-57Every Day Counts-None

4.P.6 Determine how change in one variable relates to a change in a second variable (e.g., input-output tables).

Determine how change in one variable relates to a change in a second variable (e.g., input-output tables). (i.e. in 7 10 12 (n) out 3 6 8 (n-4)

Landmarks in the Thousands, Ten Minute Math 61-62Every Day Counts- None


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4.G.1 Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional geometric shapes.

Compare and analyze attributes and other features (e.g., number of sides, faces, corners, right angles, diagonals, and symmetry) of two- and three-dimensional shapes.

Seeing Solids and SilhouettesInvestigation 1, 2-13Investigation 2, 14-41Investigation 3, 42-49Investigation 4, 50-62Every Day Counts-None

4.G.2 Describe, model, draw, compare, and classify two- and three-dimensional shapes, e.g., circles, polygons—especially triangles and quadrilaterals—cubes, spheres, and pyramids.

Describe, model, draw, compare, and classify two- and three-dimensional shapes (e.g., circles, polygons—especially triangles and quadrilaterals—cubes, spheres, and pyramids).

Seeing Solids and SilhouettesInvestigation 1, 2-13Investigation 2, 14-41Investigation 3, 42-49Investigation 4, 50-62Every Day Counts- April, May, June

4.G.3 Recognize similar figures. Recognize similar figures. Describe what makes them similar.

See Grade 3Turtle Paths, Investigation 3, 62-81Every Day Counts-None

4.G.4 Identify angles as acute, right, or obtuse.

Identify angles as acute, right, or obtuse.


4.G.5 Describe and draw intersecting, parallel, and perpendicular lines.

Describe and draw intersecting, parallel, and perpendicular lines.



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4.G.6 Using ordered pairs of numbers and/or letters, graph, locate, and identify points, and describe paths (first quadrant).

Using ordered pairs of numbers and/or letters, graph, locate, and identify points, and describe paths (first quadrant). See Math Frameworks, Nov. 2000, p. 41.

Sunken Ships and Grid PatternsInvestigation 1, 2-41Investigation 2, 42-86Every Day Counts-None

4.G.7 Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent.

Describe and apply techniques such as reflections (flips), rotations (turns), and translations (slides) for determining if two shapes are congruent. Use these terms correctly.

Mathematical Thinking at Grade 4Investigation 4, 64-90Every Day Counts-None

4.G.8 Identify and describe line symmetry in two-dimensional shapes.

Identify and describe line symmetry in two-dimensional shapes.

Mathematical Thinking at Grade 4Investigation 4, 64-90Sunken Ships and Grid PatternsInvestigation 2, 42-86Every Day Counts- None

4.G.9 Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.

Predict and validate the results of partitioning, folding, and combining two- and three-dimensional shapes.

Sunken Ships and Grid PatternsInvestigation 2, 42-86Every Day Counts- None


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4.M.1 Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.

Demonstrate an understanding of such attributes as length, area, weight, and volume, and select the appropriate type of unit for measuring each attribute.

Seeing Solids and SilhouettesInvestigation 1, 2-13Different Shapes, Equal PiecesInvestigation 1, 2-21Every Day Counts- Nov., Jan., Feb., March, April

4.M.2 Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).

Carry out simple unit conversions within a system of measurement (e.g., hours to minutes, cents to dollars, yards to feet or inches, etc.).

Additional Resources NeededSee Grade 5, Measurement Benchmarks, Investigation 3, 74-92

4.M.3 Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since …) and using a calendar (e.g., days since …).

Identify time to the minute on analog and digital clocks using a.m. and p.m. Compute elapsed time using a clock (e.g., hours and minutes since …) and using a calendar (e.g., days since …) correctly use a.m. and p.m.

Additional Resources NeededEvery Day Counts-Oct., Nov., Dec., Feb., March, April, May

4.M.4 Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.

Estimate and find area and perimeter of a rectangle, triangle, or irregular shape using diagrams, models, and grids or by measuring.

Different Shapes, Equal PiecesInvestigation 1, 2-21Every Day Counts-None


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4.M.5 Identify and use appropriate metric and English units and tools (e.g., ruler, angle, ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.

Identify and use appropriate metric and English units and tools (e.g., ruler, scales, compass, ruler, graduated cylinder, thermometer) to estimate, measure, and solve problems involving length, area, volume, weight, time, angle size, and temperature.

Seeing Solids and SilhouettesInvestigation 1, 2-13Every Day Counts-Jan., March, April


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DATA, STATISTICS, AND PROBABILITYDOEStandard Number


4.D.1 Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

Collect and organize data using observations, measurements, surveys, or experiments, and identify appropriate ways to display the data.

The Shape of the DataInvestigation 1, 2-19Investigation 2, 20-49Investigation 3, 50-64Changes Over TimeInvestigation 1, 10-29Investigation 2, 30-45Investigation 3, 46-57Three out of Four Like SpaghettiInvestigation 1, 2-25Investigation 2, 26-50Every Day Counts- Oct., March, May, June

4.D.2 Match representations of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.

Match representations of a data set such as lists, tables, or graphs (including circle graphs) with the actual set of data.

The Shape of the DataInvestigation 1, 2-19Investigation 2, 20-49Investigation 3, 50-64Changes Over TimeInvestigation 1, 10-29Investigation 2, 30-45Investigation 3, 46-57Three out of Four Like Spaghetti Investigation 1, 2-25Investigation 2, 26-50Every Day Counts-None

Brockton Public Schools DATA ANALYSIS, STATISTICS, AND PROBABILITY: GRADE 4

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4.D.3 Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

Construct, draw conclusions, and make predictions from various representations of data sets, including tables, bar graphs, pictographs, line graphs, line plots, and tallies.

The Shape of the DataInvestigation 1, 2-19Investigation 2, 20-4Investigation 3, 50-64Changes Over TimeInvestigation 1, 10-29Investigation 2, 30-45Investigation 3, 46-57Three out of Four Like SpaghettiInvestigation 2, 26-50Every Day Counts-Oct., March, May, June

4.D.4 Represent the possible outcomes for a simple probability situation (e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles).

Represent the possible outcomes for a simple probability situation (e.g., the probability of drawing a red marble from a bag containing three red marbles and four green marbles). See Math Frameworks, Nov.2000, p.57. Represent the outcome as a ratio, i.e. ¾)

Landmarks in the ThousandsInvestigation 2, 20Investigation 5, 59-60Three out of Four Like SpaghettiInvestigation 1, 51-52Every Day Counts-None

4.D.5 List and count the number of possible combinations of objects from three sets (e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?).

List and count the number of possible combinations of objects from three sets (e.g., how many different outfits can one make from a set of three shirts, a set of two skirts, and a set of two hats?).

Grade 4Landmarks in the ThousandsInvestigation 5, 59-60Every Day Counts-None


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4.D.6 Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.

Classify outcomes as certain, likely, unlikely, or impossible by designing and conducting experiments using concrete objects such as counters, number cubes, spinners, or coins.

Landmarks in the ThousandsInvestigation 2Investigation 5, 34, 59-60Money, Miles, and Large NumbersInvestigations 1, 13Investigation 3, 48, 58-59Three out of Four Like SpaghettiInvestigation 1, 17, 51-52Every Day Counts-None


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STRAND: NUMBER SENSE AND OEPRATIONSDOEStandard Number


5.N.1. Demonstrate an understanding of (positive integer) powers of ten, e.g., 102, 105.

Identify powers of ten up to 106. Mathematical Thinking at Grade 5Investigation 3, 48-54Every Day CountsNone

5.N.2 Demonstrate an understanding of place value through millions and thousandths.

Demonstrate an understanding of place value through millions and thousandths.

Mathematical Thinking at Grade 5Investigation 2, 26-47Name That PortionInvestigation 3, 64-82Building on Numbers You KnowInvestigation 4, 106-119Every Day CountsAll months

5.N.3 Represent and compare large (millions) and small (thousandths) positive numbers in various forms, such as expanded notation without exponents, e.g., 9724= 9 x 1000 + 7 x 100 +2 x 10 + 4.

Compare and order decimals to the 1,000ths.

Represent and compare millions. Represent whole numbers without

exponents in expanded notation.

Mathematical Thinking at Grade 5Investigation 4Every Day CountsJanuary

5.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, as parts of unit wholes, as parts of a collection, and as locations on a number line. This standard is intentionally the same as standard 6.N.4.

Demonstrate fractions as parts of unit wholes, parts of a collection, and as locations on a number line.

Demonstrate fractions as ratios.

Name That PortionInvestigation 1, 2-3Investigation 2, 32-63Every Day CountsAll months


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5.N.5 Identify and determine common equivalent fractions and mixed numbers with denominators 2, 4, 5, 10 only, decimals, and percents (through 100%), e.g., ¾=0.75=75%.

Recognize commonly used fractions and their decimal equivalents.

Recognize the relationship between percents and fractions with denominators of 2, 4, 5, and 10.

Name That PortionInvestigation 1, 2-31Investigation 2, 32-63Every Day CountsAll months

5.N.6 Find and position whole numbers, and positive fractions, positive mixed numbers, and positive decimals on a number line.

Find and position whole numbers, positive fractions, mixed numbers, and decimals on a number line.

Name That PortionInvestigation 1, 2-31Investigation 2, 32-63Investigation 3, 64-99Every Day Counts – All Months

5.N.7 Compare and order whole numbers, positive fractions, positive mixed numbers, positive decimals, and percents.

Compare and order whole numbers, and positive fractions, mixed numbers, decimals, and percents.

Mathematical Thinking at Grade 5Investigation 4, 72-95Name That Portion Investigation 1, 2-31Investigation 2, 32-63Investigation 3, 64-99Every Day Counts – All months

5.N.8 Apply the number theory concepts of common factor, common multiple, and divisibility rules for 2, 3, 5 and 10 to the solution of problems. Demonstrate an understanding of the concepts of prime and composite numbers.

Demonstrate understanding that a number can be prime or composite and that numbers can be divided into factors.

Recognize when one number is a multiple of another.

Find the greatest common factor and least common multiple for sets

Mathematical Thinking at Grade 5Investigation 1, 2-25Investigation 2, 26-47Investigation 3, 48-71Investigation 4, 72-95Building on Numbers You KnowInvestigation 1, 2-39Investigation 4, 106-119


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of numbers. Apply divisibility rules for 2, 3, 5,and 10

Every Day CountsDecember, January, February

5.N.9 Solve problems involving multiplication and division of whole numbers, and multiplication of a positive fraction with a whole number.

Select the appropriate operations to solve problems.

Determine if there is too little or too much information when solving problems.

Model real-world problems using numbers other than whole numbers.

Mathematical Thinking at Grade 5Investigation 3, 48-71Investigation 4, 72-95Picturing PolygonsInvestigation 2, 28-79Name That PortionInvestigation 3, 64-99Building on Numbers You KnowInvestigation 1, 2-39Investigation 2, 40-7Investigation 5, 120-146Every Day CountsNone

5.N.10 Demonstrate an understanding of how parentheses affect expressions involving addition, subtraction, and multiplication, and use to solve problems, e.g., 3 x (4+2) = 3 x 6

Recognize and demonstrate that addition, subtraction, multiplication and division follow an Order of Operations and that parentheses can affect the order.

Building on Numbers You Know - may be used as a springboard for meeting this standard. See Grade 3

Every Day CountsNone

5.N.11 Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve

Explain how addition and subtraction, and multiplication and division are related.

Building on Numbers You KnowInvestigation 1, 2-39Every Day CountsNone


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problems.This standard is intentionally the same as standard 6.N.12.

5.N.12 Accurately and efficiently add and subtract whole numbers and positive decimals; multiply and divide (with double-digit divisors) whole numbers; multiply positive decimals with whole numbers

Use algorithms to perform division with two-digit divisors.

Use algorithms to add and subtract decimal numbers.

Demonstrate understanding of multiplication and division of decimals using diagrams and manipulatives.

Mathematical Thinking at Grade 5Investigation 4, 72-95Building on Numbers You KnowInvestigation 1, 2-39Investigation 2, 40-71Investigation 3, 72-105; Investigation 5, 120-146Every Day CountsNone

5.N.13 Accurately and efficiently add and subtract positive fractions and mixed numbers with like denominators and with unlike denominators (2, 4, 5, 10 only); multiply positive fractions with whole numbers. Simplify fractions in cases when both the numerator and the denominator have 2, 3, 4, 5, and 10 as a common factor.

Use algorithms to perform division with two-digit divisors.

Use algorithms to add and subtract decimal numbers.

Demonstrate understanding of multiplication and division of decimals using diagrams and manipulatives.

Mathematical Thinking at Grade 5Investigation 4, 72-95Building on Numbers You KnowInvestigation 1, 2-39Investigation 2, 40-71Investigation 3, 72-105; Investigation 5, 120-146Every Day CountsNone

5.N.14 Estimate sums and differences of whole numbers, and positive fractions and decimals. Estimate

Add and subtract common fractions with like and unlike denominators.

Add and subtract mixed numerals

Readiness:Name That PortionInvestigation 1, 2-31


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products of whole numbers, and positive decimals with whole numbers. Use a variety of strategies and judge the reasonableness of the answer.

with like denominators. Simplify fractions

Every Day CountsNone


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STRAND: PATTERNS, RELATIONS, AND ALGEBRADOE StandardNumber


5.P.1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions, e.g., ABBCCC, 1, 5, 9,13….;3,9,27….

Recognize, describe, and extend whole number sequences (e.g., square numbers 1, 4, 9, 16 and Fibonacci Numbers 1, 1, 2, 3, 5).

Recognize and extend patterns involving various two-dimensional geometric shapes.

Represent patterns with manipulatives by building towers, pyramids, or other patterns.

Mathematical Thinking at Grade 5Investigation 2, 26-47Building on Numbers You KnowInvestigation 1, 2-39Patterns of ChangeInvestigation 1, 2-25Investigation 3, 54-92Every Day CountsAll months

5.P.2 Replace variables with given values and evaluate/simplify [e.g., 2() + 3 when = 4].

This standard is essentially the same as standard 6.P.2.

Find the “missing number” in a number sentence.

Recognize and describe the concept of variable as the “missing number” in a number sentence.

Additional Resources NeededEvery Day CountsNone

5.P.3 Use the properties of equality to solve problems (e.g., if + 7 = 13, then = 13 - 7, therefore = 6; if 3 x = 15, then =15/3, therefore = 5.

Identify properties of equality with whole numbers in four operations.

Mathematical Thinking at Grade 5Investigation 3, 55-59, 63Every Day CountsNone

5.P.4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols (e.g., input-output tables).This standard is intentionally the same as standard 6.P.4.

Analyze and describe the data orally and in writing, commenting on patterns and trends.

Organize data logically with a table, chart or other model.

Patterns of ChangeInvestigation 1, 2-25Investigation 3, 54-92Every Day CountsNone


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5.P.5 Solve problems involving proportional relationships using concrete models, tables, graphs, and paper-pencil methods.

Find the value of an expression given the replacement value for the variables (e.g., what is 7 - C if C = 3.5?).

Solve equations in one variable using concrete objects and “guess and check.”

Patterns of ChangeInvestigation 3, 54-92Every Day CountsNone

5.P.6 Interpret graphs that represent the relationship between two variables in everyday situations.

Determine and express simple ratios.

Create graphs using data from table of values (examples in Frameworks, Nov. 2000, page 35).

Patterns of ChangeInvestigation 1, 2-25Investigation 3, 54-92Every Day CountsNone


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STRAND: GEOEMTRYDOEStandard Number

STATE STANDARD GRADE 5Progress Indicators RESOURCES

5.G.1 Identify, describe, and compare special types of triangles (isosceles, equilateral, right) and quadrilaterals (square, rectangle, parallelogram, rhombus, trapezoid), e.g., Recognize that all equilateral triangles are isosceles, but not all isosceles triangles are equilateral.

Compare and classify acute, right, and obtuse angles.

Identify and compare types of triangles (acute, obtuse, right, scalene, isosceles, and equilateral) and quadrilaterals.

Identify pentagons, hexagons, and octagons.

Draw all acute, right, and obtuse triangles and draw quadrilaterals.

Picturing PolygonsInvestigation 1, 2-27Investigation 2, 28-79Investigation 3, 80-111Every Day CountsNovember, December, April

5.G.2 Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.

Identify three-dimensional shapes based on their properties.

Containers and CubesInvestigation 1, 2-23Every Day CountsMay, June

5.G.3 Identify relationships among points, lines, and planes (e.g. intersecting, perpendicular).

Identify and describe points, lines, angles, and circles.

Draw illustrations of points, lines, angles, and segments.

Describe the properties of points and lines.

Identify segments of lines. Describe the length of a segment.

Picturing PolygonsInvestigation 2, 28-79Every Day CountsNovember, April,

5.G.4 Using ordered pairs of whole numbers (including zero), graph, locate, and identify points, and describe paths on the Cartesian coordinate plane.

Graph points and identify coordinates of points on the Cartesian coordinate plane on the first quadrant.

Picturing PolygonsInvestigation 1, 2-27Investigation 1, 5-10Every Day CountsNone


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STRAND: GEOEMTRYDOEStandard Number


5.G.5 Describe and perform transformations on two-dimensional shapes, e.g., translations, rotations, and reflections.

Using manipulatives, perform and record simple transformations.

Picturing PolygonsInvestigation 2, 28-79Investigation 3, 80-111Every Day CountsNone

January

5.G.6 Identify and describe line symmetry in two-dimensional shapes, including shapes that have multiple lines of symmetry.

Using manipulatives, illustrate and record examples/patterns that represent rotational symmetry and line of symmetry.


5.G.7 Determine if two triangles or two quadrilaterals are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions, e.g., translations, rotations, and reflections.

Describe properties of congruence. Determine congruence through

measurement and transformations.

Patterns of ChangeInvestigation 3, 54-92Every Day CountsMay, June


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5.M.1 Apply the concepts of perimeter and area to the solution of problems involving triangles and rectangles. Apply formulas where appropriate.

Find the area of squares and rectangles.

Describe how to find the perimeter of a polygon.

Calculate perimeter of a polygon.

Picturing PolygonsInvestigation 3, 80-111Every Day CountsOctober, November, December

5.M.2 Identify, measure, describe, classify, and draw various angles. Draw triangles given two sides and the angle between them, or two angles and the side between them, e.g., Draw a triangle with one right angle and two sides congruent.

Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals. (e.g. acute, right, obtuse, equilateral, square, rectangle)

Picturing PolygonsInvestigation 3, 80-111Every Day CountsFebruary, April, May, June

5.M.3 Solve problems involving simple unit conversions within a system of measurement.

Use a ratio such as 2:1 to create a simple scale drawing or map.

Measurement BenchmarksInvestigation 1, 2-43Picturing PolygonsInvestigation 3, 93-111Patterns of ChangeInvestigation 2, 26-53 Investigation 3, 54-92Every Day CountsNone

5.M.4 Find volumes and surface areas of rectangular prisms.

This standard is intentionally the same as standard 6.M.6.

Find areas of triangles and parallelograms.

Recognize that shapes with the same number of sides but different appearances can have the same areas.

Picturing PolygonsInvestigation 3, 80-111Every Day CountsNone


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5.M.5 Find the sum of the measures of the interior angles in triangles with and without measuring the angles.

Using sum of angles in a triangle = 180°, find sum of simple polygons without measuring.

Estimate various angles in simple polygons.

Picturing PolygonsInvestigation 3, 80-111Every Day CountsNone


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STRAND: DATA ANALYSIS, STATISTICS, AND PROBABILITYDOEStandard Number


5.D.1 Give a set of data, find the median, mean, mode maximum, minimum, and range, and apply to solutions of problems.

Using given data, apply the concepts of median, mean, mode, maximum and minimum, and range.

Data: Kids, Cats, and AdsInvestigation 1, 2-34Every Day CountsNovember

5.D.2 Construct and interpret line plots, line graphs and bar graphs. Interpret and label circle graphs.

Construct line plots, line and bar graphs.

Interpret line and bar graphs, and interpret and label circle graphs.

Data: Kids, Cats, and AdsInvestigation 1, 2-34Every Day CountsNovember, April

5.D.3 Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions.

Demonstrate a basic understanding of the probability of an event occurring as the likelihood that an event will happen.

Conduct an experiment that produces experimental data and compute a ratio to represent the probability.

Between Never and AlwaysInvestigation 1, 2-45Investigation 2, 46-70Data: Kids, Cats, and AdsInvestigation 3, 44-67; Investigation 4, 68-81Every Day CountsNone


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STRAND: NUMBER SENSE AND OPERATIONSDOEStandard Number


6.N.1 Demonstrate an understanding of positive integer exponents.

Identify powers of ten up to 106.

Identify and evaluate 2nd and 3rd power of small positive integers (e.g. 0,1,2).

Prime TimeSE: 49Every Day CountsJan., Feb., Mar., Apr.

6.N.2 Demonstrate an understanding of place value to billions and thousandths.

Demonstrate an understanding of place value to billions and hundred thousandths.

Bits and Pieces ISE: 43-45, 48-49, 51-52, 55, 63-64TE: 52c-h, 92, 95TR: Transparencies: 151, 153 Every Day CountsAll months

6.N.3 Represent and compare billions and thousandths positive numbers in various forms (e.g., expanded notation).

Compare and order decimals to hundred thousandths

Represent whole numbers and decimals in expanded notation.

(8x102)+(5x101)=3x100)=853

Bits and Pieces ISE: 43-45, 48-49, 51-52, 55, 63-64TE: 52c-h, 92, 95TR: Transparencies: 151, 153Every Day CountsAll months

6.N.4 Demonstrate an understanding of fractions as a ratio of whole numbers, parts of a collection.

Demonstrate an understanding of fractions as ratios of whole numbers, parts of a collection.

Bits and Pieces ISE: 5-18, 19-30, 31-38, 39-52, 53-66, 67-83, 84-86TE: 18a-j, 30a-i, 38a-d, 52a-h, 66a-g,

83a-g, 86-87, 88-89, 90-92, 94-95,96-97, 98

TR: Labsheets: 125-126


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Transparencies: 137-139, 146-151, 153,156, 158, 159, 160-163;

Additional Practice: 175, 177-179

How Likely Is It?SE: 5-13, 14-21, 22-28, 29-41, 42-48, 49-

56, 57-64, 65-67TE: 13a, 13b, 13c, 13d, 21a, 21b, 21c, 28a,

28b, 41a, 41b, 41c, 41d, 48a, 48b, 48c, 56a, 56b, 64a, 64b, 64c, 67-68, 69-70, 71-72, 73, 74-77

TR: Labsheets: 90, 91Transparencies: 95-106Additional Practice: 112Bits and Pieces IISE: 11, 13-16, 31-42, 43-53, 54-63TE: 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f,

53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 88-90, 91

TR: Labsheets: 108Transparencies: 118, 119, 120, 121, 122, 123,

124, 125, 127; Additional Practice: 146, 147, 148, 149

Every Day Counts: All Months6.N.5 Identify and determine common

equivalent fractions, mixed numbers, decimals, and percents.

Express common fractions as equivalent fractions, decimals and percents.

Investigate and describe the

Bits and Pieces ISE: 40-43, 54-55, 57, 67-78TE: 52a, 52b, 66a, 66b, 83a, 83b, 83c, 83d,

83e, 83f, 83g, 93Brockton Public Schools NUMBER SENSE AND OPERATIONS: GRADE 6

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relationship among fractions, decimals, and percents.

TR: Labsheets: 125-126Transparencies: 145-151, 155, 157-163Additional Practice: 176-179Bits and Pieces IISE: 31-42, 43-53, 54-63TE: 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f,

53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 87-90, 91

TR:Transparencies: 122-125, 127Additional Practice: 146-149Every Day CountsAll months

6.N.6 Find and position integers, fractions, mixed numbers, and decimals.

Find and position both positive and negative integers, fractions, mixed numbers, and decimals on a number line, in an ordered list, or in relation to zero.

Bits and Pieces ISE: 22-24, 27-28, 63-64, 82TE: 30d, 92TR:Transparencies: 141Every Day CountsAll months

6.N.7 Compare and order integers (including negative integers), and positive fractions, mixed numbers, decimals, and percents.

Compare whole numbers, fractions, integers (including negative), and decimals using the “<” and “>” symbols.

Demonstrate knowledge of the structure of sets of numbers including whole numbers, fractions, and integers using Venn Diagrams.

Bits and Pieces ISE: 5-18, 19-30, 39-52, 53-66, 67-83, 84-86TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 18h,

18i, 18j, 30i, 38a, 38b, 38c, 38d, 52a, 52b, 52c, 52d, 52e, 52f, 52g, 52h, 66a, 66b, 66c, 66d, 66e, 66f, 66g, 83a, 83b, 83c, 83d, 83e, 83f, 83g, 86-87, 88-89, 90-92, 94-95, 96-97, 98

TR: Labsheets: 126


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Compare fractions, decimals, and percents.

Transparencies: 128-141, 152-156, 159-163Additional Practice: 174-179

Bits and Pieces IISE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c,

30d, 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d,76e, 76f, 79, 80-81, 82-83, 84-86, 87-90, 91-92

TR: Labsheets: 106-109Transparencies: 110-132Additional Practice: 144-149Every Day CountsAll months

6.N.8 Apply number theory concepts—including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10—to the solution of problems.

Apply number theory concepts—including prime and composite numbers, prime factorization, greatest common factor, least common multiple, and divisibility rules for 2, 3, 4, 5, 6, 9, and 10—to the solution of problems.

Prime TimeSE: 6-16, 17-25, 26-35, 36-45, 46-57, 58-

64, 65-67TE: 16a, 16b, 16c, 16d,16e, 25a, 25b, 25c,

25d, 25e, 35a, 35b, 35c, 35d,45a, 45b, 45c, 57a, 57b,57c, 57d, 57e, 57f, 64a, 64b, 68, 69, 70, 71, 72-73, 74-75

TR: Labsheets: 96, 97, 98, 99Transparencies: 100-115Additional Practice: 122-127Bits and Pieces ISE: 5-18, 19-30, 31-38, 39-52, 53-66, 67-


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83, 84-86

TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 18h, 18i, 18j, 30a, 31b, 30c, 30d, 30e, 30f,30g, 30h, 30i, 38a, 38b, 38c, 38d, 52a, 52b, 52c, 52d, 52e, 52f, 52g, 52h, 66a, 66b, 66c, 66d, 66e, 66f, 66g,83a, 83b, 83c, 83d, 83e, 83f, 83g, 86-87, 88-89, 90-92, 94-95, 96-97, 98

TR: Labsheets: 118, 124Transparencies: 137-139, 152-154, 156Additional Practice: 174-175, 178-179Bits and Pieces IISE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c,

30d, 42a, 42b, 53a, 53b, 53c,53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d, 76e, 76f, 79, 80-81, 82-83, 84-86, 8790, 91-92

TR:Transparencies: 127, 129- 131Additional Practice: 146-147Every Day CountsSept., Oct., Nov., Dec., Jan.

6.N.9 Select and use appropriate operations to solve problems involving addition,

Select the appropriate operations to solve problems.

Data About UsSE: 54-66, 70


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subtraction, multiplication, division, and positive integer exponents with whole numbers, and with positive fractions, mixed numbers, decimals, and percents.

Determine if there is too little or too much information when solving problems.

Model real-world problems using numbers other than whole numbers.

TE: 67j, 75, 76TR:Transparencies: 111, 114, 116Covering and SurroundingSE: 46, 49-52, 59-61, 74, 76-78TE: 45b, 45c, 55e, 55f, 68d, 68e, 68f, 81c,

81g, 90, 91-92, 93, 96-97, 98-99TR:Transparencies; 123, 127, 136Additional Practice: 150, 152-156How Likely Is It?SE: 36TE: 71, 75-77Bits and Pieces IISE: 5-17, 18-30, 31-42, 43-53, 54-63, 64-76TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c,

30d, 42a, 42b, 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a, 63b, 63c, 63d, 63e, 63f, 63g, 76a, 76b, 76c, 76d, 76e, 76f, 79, 80-81, 82-83, 84-86, 87-90, 91-92

TR: Labsheets: 106, 107, 109; Transparencies: 110-117, 122-128, 130-132Additional Practice: 144-149Every Day Counts: Sept.-Feb.

6.N.10 Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers.

Use the number line to model addition and subtraction of

subtracting negative integers).


6.N.11 Apply the Order of Operations for Apply Order of Operations for Covering and Surrounding


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expressions involving addition, subtraction, multiplication, and division with grouping symbols (+, -, x, ).

all four operations. SE: 30, 46, 49-52, 59-61, 74, 76-78TE: 34b, 34c, 45b, 45c, 55e, 55f, 68d, 68e,

68f, 81c, 81g, 90, 91-92, 93, 96-97, 98-99

TR: Transparencies; 123, 127, 136;Additional Practice: 150-156Every Day CountsAll months

6.N.12 Demonstrate an understanding of the inverse relationship of addition and subtraction, and use that understanding to simplify computation and solve problems.

Demonstrate knowledge of identities and inverses for all four operations.


6.N.13 Accurately and efficiently add, subtract, multiply, and divide (with double-digit divisors) whole numbers and positive decimals.

Add, subtract, multiply, and divide decimals.

Bits and Pieces IISE: 5-17, 18-30, 64-76TE: 17a, 17b, 17c, 17d, 17e, 30a, 30b, 30c,

30d,76a, 76b, 76c, 76d, 76e,76f, 87, 89-90, 91

TR: Labsheets: 106-107,109Transparencies: 110-113, 116, 128-132Additional Practice: 144-146, 149Every Day CountsNone

6.N.14 Use the number line to model addition and subtraction of integers, with the exception of subtracting negative integers.

Add and subtract mixed numerals with unlike denominators.

Multiply and divide fractions

How Likely Is It?SE: 36TE: 71, 75-77Bits and Pieces II


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and mixed numerals. Simplify fractions

SE: 43-53, 54-63TE: 53a, 53b, 53c, 53d, 53e, 53f, 53g, 63a,

63b, 63c, 63d, 63e, 63f, 63g, 80-81, 82-83, 84-86, 88-90, 91

TR: Transparencies: 120-127, 132Additional Practice: 146-149Every Day CountsAll months

6.N.15 Add and subtract integers, with the exception of subtracting negative integers.

Add and subtract integers without number line, with the exception of subtracting negative integers.

Data About UsSE: 54-66, 70TE: 67j, 75, 76TR: Transparencies: 111, 114, 116Every Day CountsNone

6.N.16 Estimate results of computations with whole numbers, and with positive fractions, mixed numbers, decimals, and percents. Describe reasonableness of estimates.

Estimate sums, differences, products, and quotients with whole numbers, fractions, and decimals with reasoned strategies.

Bits and Pieces IISE: 4, 31-41, 64-66, 72-73TE: 42a, 42b, 76a, 76bTR: Labsheets: 106-107Transparencies: 111, 118-119Additional Practice: 146Every Day CountsNone


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6.P.1 Analyze and determine the rules for extending symbolic, arithmetic, and geometric patterns and progressions.

Recognize and extend sequences of numbers involving whole numbers, fractions, and decimals.

Recognize and extend patterns of various two- and three-dimensional shapes.

Extend patterns, organize information, and make tables to solve problems.

Prime TimeSE: 58-60, 64TE: 64a, 64bTR:Transparencies: 102, 103, 107Additional Practice: 127Data About UsSE: 42-45, 48-49TE: 52a, 52d, 77, 78TR:Transparencies: 96-99, 108-110Additional Practice: 125How Likely Is It?SE: 43-45TE: 48a, 48b, 48cEvery Day CountsAll months

6.P.2 Replace variables with given values and evaluate/simplify [e.g., 2() + 3 when = 4].

Recognize the term “variable” as used in an equation.

Determine the numerical value of an algebraic expression given the value of the variable in the expression.

Shapes and DesignsSE: 47TE: 50d, 81TR:Additional Practice: 135, 137, 138Covering and SurroundingSE: 49-52, 59-61, 74, 76-78TE: 55e, 55f, 68d, 68e, 68f, 81c, 81g, 90,

91-92, 93, 96-97, 98-99TR: Labsheets: 117- 119Transparencies; 120-141Additional Practice: 150-156Every Day CountsAll months


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6.P.3 Use the properties of equality to solve problems (e.g., if + 7 = 13, then = 13 - 7, therefore = 6; if 3 x = 15, then ⅓ x 3 x = ⅓ x 15, therefore = 5).

Identify and use the properties of equality to solve problems with whole numbers, fractions and decimals.


6.P.4 Represent real situations and mathematical relationships with concrete models, tables, graphs, and rules in words and with symbols (e.g., input-output tables).

Construct expressions, equations, and inequalities that describe real-world problems using a symbol to represent the “missing number.”

Collect data from an experiment and express the data in a table of values.

Data About UsSE: 42-45, 48-49TE: 52a, 52d, 77, 78TR:Transparencies: 108-110Additional Practice: 125How Likely Is It?SE: 43-45TE: 48a, 48b, 48cEvery Day CountsAll months


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6.P.5 Solve linear equations using concrete models, tables, graphs, and paper-pencil methods.

Solve first-degree equations in one variable using manipulatives and “guess and check.”

Solve equations using manipulatives.

Recognize variables and solve basic equations with one variable by using properties of equality.

Additional Resources NeededEvery Day CountsAll months

6.P.6 Produce and interpret graphs that represent the relationship between two variables in everyday situations.

Analyze and describe data in tables and graphs orally and in writing, commenting on patterns and trends.

Create a graph using data from a table of values.

How Likely Is It?SE: 43-45TE: 48a, 48b, 48cEvery Day CountsFeb., May, Jun.

6.P.7 Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.

Identify and describe relationships between two variables with a constant rate of change. Contrast these with relationships where the rate of change is not constant.

Solve problems on speed as a ratio using formula S = D / T or



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D = R x T.


120

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STRAND: GEOMETRYDOEStandard Number

STATE STANDARD Grade 6Progress Indicators Resources

6.G.1 Identify polygons based on their properties, including types of interior angles, perpendicular or parallel sides, and congruence of sides (e.g., squares, rectangles, rhombuses, parallelograms, trapezoids, and isosceles, equilateral and right triangles).

Describe the distinction between similar and congruent figures.

Recognize vertical angles and adjacent angles formed by intersecting lines.

Describe the sum of angles of a quadrilateral.

Use the correct terminology to describe parts of angles.

Use the correct terminology to describe parts of triangles and quadrilaterals.

Draw all types of triangles, including scalene, isosceles, and equilateral triangles.

Shapes and DesignsSE: 8-14, 15-21, 22-41, 42-50, 51-63, 76-78TE: 14a, 14b, 21a, 21b, 21c, 21d, 21e, 21f, 21g,

41a, 41b, 41c, 41d, 41e, 41f, 41g, 41h, 41i, 50a, 50b, 50c, 50d, 50e, 50f, 50g, 63a, 63b, 63c, 63d, 78-79, 80-81, 82-85, 86-87, 88-89

TR:Transparencies: 106, 107, 108, 109, 117, 118, 119, 121

Additional Practice: 135, 136, 137, 138Covering and SurroundingSE: 30, 46, 49-52, 59-61, 74, 76-78TE: 34b, 34c, 45b, 45c, 55e, 55f, 68d, 68e, 68f,

81c, 81g, 90, 91-92, 93, 96-97, 98-99TR:Transparencies; 130, 132, 133, 134, 135,

136, 138, 139, 140Additional Practice: 153, 154, 156Every Day CountsNone

6.G.2 Identify three-dimensional shapes (e.g., cubes, prisms, spheres, cones, and pyramids) based on their properties, such as edges and faces.

Describe and discuss three-dimensional figures.

Identify the relationship among vertices, faces, and edges of three-dimensional figures.

Ruins of MontarekSE: 7-25,26-39,40-51,52-61,62-71, 72-81,82-84TE: 25a, 25b, 25c, 25d, 25e, 25f, 25g, 25h, 39a, 39b,

39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61g, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 92-96, 97-98

TR: Labsheets: 114-120Transparencies: 121-136, 138-146;Additional Practice: 154-159;Every Day Counts


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Apr., May, June6.G.3 Identify relationships among

points, lines, and planes (e.g. intersecting, perpendicular).

Identify and describe rays. Identify real-world examples

that portray points, lines, segments, rays, and planes.

Describe planes and identify points, lines, rays, and segments that lie in the plane and those that do not.

Draw rays and planes. Describe intersecting lines. Describe parallel lines and

perpendicular lines.

Shapes and DesignsSE: 18, 52-56TE: 63a, 63b, 63c, 63dTR: Transparencies: 105-106Ruins of MontarekSE: 10-12, 23-24TE: 25b, 25c, 25d, 93TR: Labsheets: 114,116Transparencies: 123Every Day CountsNone

6.G.4 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants)

Graph points and identify coordinates of points on the Cartesian coordinate plane on all four quadrants.

Bits and Pieces IISE: 47Data About UsSE: 42-52TE: 52c, 52d, 52e, 73, 77TR: Labsheets: 94-95Transparencies: 108-110Additional Practice: 125Every Day CountsNone

6.G.5 Find the distance between two points on horizontal or vertical number lines.

Find the distance between two points on horizontal or vertical number lines.

Bits and Pieces ISE: 22-24, 27-28, 63-64, 82TE: 30d, 92TR:Transparencies: 141Every Day Counts


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None

6.G.6 Predict, describe, and perform transformations on two-dimensional shapes (e.g., translations, rotations, and reflections).

Predict, describe, and perform transformations on two-dimensional shapes (e.g., translations, rotations, and reflections).

Shapes and DesignsSE: 52-56 TE: 63a, 63b, 63c, 63dTR:Transparencies: 105, 106Ruins of MontarekSE: 10-12, 23-24TE: 25b, 25c, 25d, 93TR: Labsheets: 114, 116Transparencies: 123Every Day CountsNone

6.G.7 Identify types of symmetry, including line and rotational.

Identify and describe various types of symmetry.

Shapes and DesignsSE: 52-56 TE: 63a, 63b, 63c, 63dTR:Transparencies: 105, 106Ruins of MontarekSE: 10-12, 23-24TE: 25b, 25c, 25d, 93TR: Labsheets: 114, 116Transparencies: 123Every Day CountsJan., Feb.


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6.G.8 Determine if two shapes are congruent by measuring sides or a combination of sides and angles, as necessary; or by motions or series of motions (e.g., translations, rotations, and reflections).

Recognize reflections, slides, and rotations.

Determine congruence through measurement and transformations.

Shapes and DesignsSE: 52-56 TE: 63a, 63b, 63c, 63dTR:Transparencies: 105, 106Ruins of MontarekSE: 10-12, 23-24TE: 25b, 25c, 25d, 93TR: Labsheets: 114, 116Transparencies: 123Every Day CountsNone

6.G.9 Match three-dimensional objects and their two-dimensional representations (e.g., nets, projections, and perspective drawings).

Identify and draw shapes and figures from different views/perspectives (e.g., nets, projections, orthogonal and isometric perspectives).

Ruins of MontarekSE: 7-25,26-39,40-51,62-71, 72-81,82-84TE: 25a, 25b, 25c, 25d, 25e, 25d, 25e, 25h, 39a,

39b, 39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 992-96, 97-98

TR: Labsheets: 114-120Transparencies: 121-125,127-146Additional Practice: 154-159Every Day CountsMay, Jun.


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STATE STANDARD GRADE 6PROGRESS INDICATORS

RESOURCES

6.M.1 Apply the concepts of perimeter and area to the solution of problems. Apply formulas where appropriate.

Explain how changes in one or more dimensions of a figure result in a change in the area or perimeter of the figure.

Define the size of a region as area.

Apply correct formulas to find area and perimeter of basic shapes (e.g., 3 or 4 sided).

Covering and SurroundingSE: 6-18, 19-28, 29-34, 35-45, 46-55, 56-68, 69-81;TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 28a, 28b,

34a, 34b, 34c, 34d, 34e, 45a, 45b, 45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 86, 87-88, 89-90, 91-92, 93-97, 98-99

TR: Labsheets: 116-119Transparencies: 120-136Additional Practice: 150-156Bits and Pieces IISE: 54-59TE: 63a, 63b, 63c, 63d, 63e, 63fTR: Labsheets: 108Transparencies: 117, 120-121;Additional Practice: 147- 149Every Day CountsSept., Oct., Nov. Dec., Jan., Feb., Mar., May, June


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RESOURCES

6.M.2 Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals.

Identify, measure, describe, classify, and construct various angles, triangles, and quadrilaterals (e.g. acute, right, obtuse, straight, regular, trapezoid, parallelogram).

Shapes and DesignsSE: 8-14, 15-21, 22-41, 42-50, 51-63, 76-78TE: 14a, 14b, 21a, 21b, 21c, 21d, 21e, 21f,

21g, 41a, 41b, 41c, 41d, 41e, 41f, 41g, 41h, 41i, 50a, 50b, 50c, 50d, 50e, 50f, 50g, 63a, 63b, 63c, 63d, 78-79, 80-81, 82-85, 86-87, 88-89;

TR: Transparencies: 106-109, 117-119, 121Covering and SurroundingSE: 6-18, 35-4 5, 46-55, 56-68TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 45a, 45b,

45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 86, 88, 89-90, 91- 92, 93-97, 98-99

TR: Labsheets: 116-118,Transparencies: 120-127, 129-137Additional Practice: 150, 152- 155Ruins of MontarekSE: 7-25, 26-39, 40-51, 52-61, 62-71, 72-81, 82-

84TE: 25a, 25b, 25c, 25d, 25e, 25f, 25g, 25h, 39a,

39b, 39c, 39d, 51a, 51b, 51c, 51d, 61a, 61b, 61c, 61d, 61e, 61f, 61g, 61h, 61i, 71a, 71b, 71c, 81a, 81b, 81c, 81d, 81e, 84-85, 87-89, 90-91, 92-96, 97-98

TR: Labsheets: 114-120Transparencies: 121-146Additional Practice: 154-159Every Day CountsAll months


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RESOURCES

6.M.3 Solve problems involving proportional relationships and units of measurement (e.g., same system unit conversions, scale models, maps, and speed).

Use a ratio to create a simple scale drawing or map.

Recognize unit conversions as ratios and proportions.

Bits and Pieces ISE: 61-62, 74TE: 83b, 83c, 83dTR: Additional Practice: 178Every Day CountsNone

6.M.4 Find areas of triangles and parallelograms. Recognize that shapes with the same number of sides but different appearances can have the same areas. Develop strategies to find the area of more complex shapes.

Develop strategies to find the area of more complex shapes.

Recognize that complex regions can be divided into simpler shaped regions.

Covering and SurroundingSE: 6-18, 19-28, 29-34, 35-45, 46-55, 56-68, 69-

81TE: 18a, 18b, 18c, 18d, 18e, 18f, 18g, 28a, 28b,

34a, 34b, 34c, 34d, 34e, 45a, 45b, 45c, 45d, 45e, 55a, 55b, 55c, 55d, 55e, 55f, 68a, 68b, 68c, 68d, 68e, 68f, 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 86, 87-88, 89-90, 91-92, 93-97, 98-99

TR: Labsheets: 116- 119Transparencies; 120-141Additional Practice: 150-156Every Day CountsSept., Oct., Nov., Feb.

6.M.5 Identify, measure, and describe circles and relationships of the radius, diameter, circumference, and area (e.g., d = 2r, p = C/d), and use the concepts to solve problems.

Recognize the ratio between the circumference of a circle and its diameter as a little more than 3.

Use 3.14 in formulas to find area and circumference.

Covering and SurroundingSE: 69-81TE: 81a, 81b, 81c, 81d, 81e, 81f, 81g, 81h, 89-

90, 91-92, 94, 96, 98-99TR: Labsheets: 119Transparencies; 137-141Additional Practice: 156Every Day Counts


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RESOURCES

Sept., Oct., Nov., Dec., Jan., Feb., Mar.

6.M.6 Find volumes and surface areas of rectangular prisms.

Find volumes and surface areas of rectangular prisms.


6.M.7 Find the sum of the angles in simple polygons (up to eight sides) with and without measuring the angles.

Using protractor, measure with accuracy to find sums of angles in simple polygons.

Without a protractor find the sum of the angles in a polygon (3 to 8 sides).

Shapes and DesignsSE: 42-45, 47, 49-50, 59, 62-63, 77-78TE: 50a, 50b, 50c, 50d, 50e, 80TR:Transparencies: 117- 119Every Day CountsNone


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RESOURCES

6.D.1 Describe and compare data sets using the concepts of median, mean, mode, maximum and minimum, and range.

Collect, organize, and record data using the concepts of median, mean, mode, maximum and minimum, and range.

Data About UsSE: 9-18, 21, 24-27, 29, 38-39, 53-67, 69-70TE: 21c, 21d, 21e, 21f, 21g, 21h, 21i, 29b,

29c, 41d, 67a, 67b, 67c, 67d, 67e, 67f, 67g, 67h, 67i, 67j, 67k, 67l, 71, 72-73, 74-75, 76, 78

TR:Transparencies: 100-101, 103-105, 112,114-116

Additional Practice: 122-126Every Day CountsDec., Jan., Feb., Mar., May, June

6.D.2 Construct and interpret stem-and-leaf plots, line plots, and circle graphs.

Construct circle graphs. Describe and interpret circle

graphs. Construct and interpret stem-

and-leaf plots.

Data About UsSE: 6-11, 30-41, 56, 58, 60, 62TE: 21c, 21d, 21e, 41a, 41b, 41c, 41d, 41e,

41f, 67c, 67d, 67e, 67g, 70, 74-75, 76, 78TR:Transparencies: 97-99, 105-107, 114Additional Practice: 122-126Shapes and DesignsTE: 41iEvery Day CountsSept., Oct., Nov., Jan., Feb.

6.D.3 Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes.

Use tree diagrams and other models (e.g., lists and tables) to represent possible or actual outcomes of trials. Analyze the outcomes.

How Likely Is It?SE: 12, 33, 43-48, 49, 59-64, 65TE: 21c, 41b, 41c, 48a, 48b, 48c, 56a, 56b, 75TR:Transparencies: 102, 104, 106Additional Practice: 114-116Every Day CountsAll months


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RESOURCES

6.D.4 Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions. Use appropriate ratios between 0 and 1 to represent the probability of the outcome and associate the probability with the likelihood of the event.

Compare the theoretical probability of an event occurring with experimental results.

Predict the probability of outcomes of simple experiments (e.g., tossing a coin, rolling a die) and test the predictions.

How Likely Is It?SE: 5-13, 14-21, 22-28, 29-32, 35-38TE: 13a, 13b, 13c, 13d, 21a, 21b, 21c, 28a,

28b, 41a, 41b, 48a, 67-68, 71-72, 76-77TR: Labsheets: 92, 93Transparencies: 95-97, 99-101Additional Practice: 110-113Every Day CountsMay, June


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131

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7.N.1 Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e. rational numbers), decimals, and percents.

Compare, order, estimate, and translate among integers, fractions and mixed numbers, decimals and percents.

Comparing and ScalingSE: 5-15, 16-25, 26-36, 37-51, 52-64, 65-81, 82-86TE: 15a-d, 25a-c, 36a-f, 51a-f, 64a-h, 81a-c, 86-87,

88, 89-90, 91-95, 96-97, 98-99TR: Labsheets: 118, 119, 120;Transparencies: 124-146Additional Practice: 152-159Data Around UsSE: 5-11, 12-22, 23-37, 38-50, 51-60, 61-69, 70-72TE: 11a-d, 22a-e, 37a-g, 50a-f, 60a-f, 69a-d, 73, 74,

75-77, 78-79TR: Transparencies: 106, 112, 116; Additional Practice: 130, 131, 133, 134

7.N.2 Use ratios and proportions in the solution of problems, involving unit rates, scale drawings, and reading of maps.

Use ratios and proportions in the solution of problems involving unit rates and scale factors.

Comparing and ScalingSE: 16-25, 26-33, 37-51, 52-64, 65-81, 82-86TE: 25a-c, 36a-f, 51a-f, 64a-h, 81a-c, 86-87, 88,

89-90, 91-95, 96-97, 98-99TR: Transparencies: 124-138Additional Practice: 155-159Data Around UsSE: 5-11, 12-22, 58-60, 61-69TE: 11a-d, 22a-e, 60a-f, 69a-d, 76TR: Transparencies: 108-113, 117, 120-123Additional Practice: 128-134


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7.N.3 Represent numbers in scientific notation, (positive powers of ten only) and use in problem situations.

Represent numbers in scientific notation with positive exponents.

Data Around UsSE: 40-49TE: 37j, 50e-f, 78TR: Transparencies: 116Additional Practice: 131

7.N.4 Demonstrate an understanding of absolute value (e.g., | -3 | = | 3 | = 3)This standard is intentionally the same as standard 8.N.6.

Define and demonstrate an understanding of absolute value.

Accentuate the NegativeSE: 39TE: 33g, 52h

7.N.5 Apply the rules of positive integer exponents to the solution of problems. Extend the Order of Operations to include positive integer exponents.

Extend the Order of Operations to include positive integer exponents.

Data Around UsSE: 40-49TE: 37j, 50e-f, 78TR: Transparencies: 116Additional Practice: 131

7.N.6 Use the inverse relationships of addition and subtraction, multiplication and division, to simplify computations and solve problems (e.g. multiplying by ½ or 0.5 is the same as dividing by 2).

Use the inverse relationships of addition and subtraction, multiplication and division, to simplify computations and solve problems.

Accentuate the NegativeSE: 18-33, 34-52, 53-66TE: 33a-g, 52a-l, 66a-I, 84-85, 86, 87-89, 90-92TR: Labsheets: 102Transparencies: 104-119Additional Practice: 144-149

7.N.7 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).

This standard is intentionally the same as

Estimate and compute with fractions (including simplification of fractions), decimals, and percents.

Comparing and ScalingSE: 16-25, 28-33, 48, 52-64, 65-81TE: 25a-b, 36c-f, 51d, 51f, 64a-h, 81a-c, 86-87, 88,

89-90, 91-95, 96-97TR: Transparencies: 130-131, 140-142, 144-146Additional Practice: 155-159


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standard 8.N.10.Accentuate the NegativeSE: 18-33, 34-52, 54-55, 59, 61-62, 64TE: 33a-g, 52a-l, 66a-e, 84-85, 86, 87-89, 90-92TR: Labsheets: 102Transparencies: 104-119Additional Practice: 144-147, 149

Data Around UsSE: 38-47, 61-69, 70-72TE: 50d-f, 73, 74, 75-77, 78-79TR: Transparencies: 101-102, 118, 120-121Additional Practice: 130-134

7.N.8 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.

This standard is intentionally the same as standard 8.N.11.

Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.

Comparing and ScalingSE: 16, 20-21, 52-64TE: 25a, 64a-hTR: Transparencies: 124-125, 128, 137-138Data Around UsSE: 16-21, 51-59, 63-68TE: 11f, 22d-e, 60a-f, 69c-d, 73, 75-77, 78TR: Transparencies: 100-102, 111, 118-119, 121Additional Practice: 128-130


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7.N.9 Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives).

This standard is intentionally the same as standard 8.N.12.

Select and use appropriate operations to solve problems with rational numbers (excluding negative integers).

Comparing and ScalingSE: 16-25, 26-36, 48, 65-81TE: 25a-b, 36c-f, 51d, 51f, 81a-c, 86-87, 88, 89-90,

91-95, 96-97TR: Transparencies: 130-131, 140-142, 144-146Additional Practice: 155-159

Accentuate the NegativeSE: 18-33, 34-52, 53-66TE: 33a-g, 52a-l, 66a-I, 84-85, 86, 87-89, 90-92TR: Labsheets: 102Transparencies: 104-119;Additional Practice: 144-147, 149Data Around UsSE: 6-10,41-50,61-69, 71-72TE: 50d-f, 60a-f, 69a-d, 73, 74, 75-77TR: Transparencies: 101-102, 118, 120-121Additional Practice: 130-134


135

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DOEStandard Number


7.P.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions (e.g., compounding).

This standard is intentionally the same as standard 8.P.1.

Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and symbolic expressions. Include arithmetic and geometric progressions.

Variables and PatternsSE: 6-7, 12-16, 19-21, 25, 33-34, 36-48, 49-60, 61-68, 69-70TE: 35j-k, 48a-f, 60a-e, 68a-d, 74, 76-78, 79-82TR: Transparencies: 102-126Additional Practice: 134-136, 138-139Comparing and ScalingSE: 26-36, 37-51, 68-69, 73TE: 36a-f, 51a-f, 81b-cTR: Transparencies: 128, 134-136, 144Additional Practice: 156Moving Straight AheadSE: 5-14, 15-34, 35-52, 53-63, 64-79, 80-91, 92-94TE: 14a-c, 34a-l, 52a-k, 63a-g, 79a-j, 91a-g, 95-96, 97-99,

100-101, 102-104, 105-108TR: Transparencies: 128-154Additional Practice: 160-169

7.P.2 Evaluate simple algebraic expressions for given variable values (e.g., 3a2 - b for a = 3 and b = 7).


Evaluate simple algebraic expressions for given variable values.

Stretching and ShrinkingSE: 11-13, 22-25, 28-40, 41-58, 59-74, 79-84, 85-87TE: 27c-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92, 93-95, 96-98,

99-102, 103-105, 106, 107-108TR: Transparencies: 150-156Additional Practice: 178-179

Filling and WrappingSE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72, 73-76TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77, 78-79,

80-82, 83-84, 85-86, 87TR: Labsheets: 108- 110Transparencies: 111-131


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DOEStandard Number


Additional Practice: 140-1497.P.3 Create and use symbolic

expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

Variables and PatternsSE: 38-47, 49-60, 61-68, 69-70TE: 48a-f, 60a-e, 68a-d, 74, 76-78, 79-82TR: Transparencies: 101-126Additional Practice: 134-139Comparing and ScalingSE: 42-51, 68-69, 73TE: 51d-fTR: Transparencies: 134-136, 144Moving Straight AheadSE: 5-14, 15-34, 35-52, 53-63, 64-79, 80-91, 92-94TE: 14a-c, 34a-l, 52a-k, 63a-g, 79a-j, 91a-g, 95-96, 97-99,

100-101, 102-104, 105-108TR: Transparencies: 128-154Additional Practice: 160-169

7.P.4 Solve linear equations, using tables, graphs, models and algebraic methods.

Set up and solve linear equations with one variable, using algebraic methods, models, and/or graphs.

Variables and PatternsSE: 49-60, 62-65, 67TE: 60a-eTR: Additional Practice: 138 Comparing and ScalingSE: 33-34TR: Transparencies: 144Additional Practice: 156Moving Straight AheadSE: 53-63, 85-86, 88, 93-94TE: 63a-g, 98, 101, 104, 107-108TR: Transparencies: 135, 137, 141-149, 152, 154Additional Practice: 161, 163, 165, 167-169


137

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DOEStandard Number


7.P.5 Identify, describe, and analyze linear relationships between two variables. Compare positive rate of change, e.g., y = 3x + 1, to negative rate of change, e.g., y = -3x + 1

Explain and analyze how a change in one variable results in a change in another variable in functional relationships.

Variables and PatternsSE: 49-60, 69-70TE: 60a-e, 76, 81TR: Transparencies: 101-126Additional Practice: 134-139Comparing and ScalingSE: 44TE: 51dTR: Transparencies: 134-136Additional Practice: 156Moving Straight AheadSE: 15-34, 42-43, 53-63, 80-83, 85-91, 92-94TE: 34a-l, 52g-h, 63a-g, 91a-g, 98, 101, 104, 107-108TR: Transparencies: 128-154Additional Practice: 160-163, 165, 167-169

7.P.6 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.


Variables and PatternsSE: 49-60, 62-65, 67TE: 60a-eTR: Additional Practice: 138Comparing and ScalingSE: 33-34TR: Transparencies: 144Additional Practice: 156Moving Straight AheadSE: 55-56, 68, 70-73, 76-77


138

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STRAND: GEOMETRY

DOEStandard Number


7.G.1 Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons.

Analyze, apply, and explain the relationship between the number of sides and the sums of the interior angle measures of polygons.


7.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.

This standard is intentionally the same as standard 8.G.2.

Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.

Stretching and ShrinkingSE: 5-13, 14-27, 28-40, 41-58, 59-74, 75-84, 85-87TE: 13a-d, 27a-j, 40a-g, 58a-f, 74a-h, 84a-g, 90-92,

93-95, 96-98, 99-102, 103-105, 106, 107-108TR: Labsheets: 124-134Transparencies: 135-161Additional Practice: 172-180

7.G.3 Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.


Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.

Stretching and ShrinkingSE: 59-74TE: 74a-h, 100TR: Transparencies: 154-156;Additional Practice: 174, 178-179

7.G.4 Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants) *


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DOEStandard Number


7.G.5 Use a ruler, protractor, and compass to draw polygons and circles.

Use a ruler, protractor, and compass to draw polygons and circles.

Stretching and ShrinkingSE: 6-13, 28-40, 75-84TE: 13a-d, 40a-g, 84a-g TR: Labsheets: 124-130, 134;

Transparencies: 157- 161Filling and WrappingSE: 9-10, 13, 27-28, 39-40, 44, 48-49, 58-59TE: 14a-h, 36d-e, 45b, 45d-f, 56a-e, 67a-bTR: Labsheets: 108-110Transparencies: 111-117, 122-126,

128-1307.G.6 Predict the results of translations

and reflections of figures on unmarked or coordinate planes and draw the transformed figure.

Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure.


93-95, 96-98, 99-102, 103-105, 106, 107-108TR: Labsheets: 124-134Transparencies: 135- 161Additional Practice: 172-180

7.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.


Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.

Filling and WrappingSE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-

72,73-76TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a, 77,

78-79, 80-82, 83-84, 85-86, 87TR: Transparencies: 114-131Additional Practice: 140-149


140

5/16/06

STRAND: MEASUREMENT

DOEStandard Number


7.M.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.


Select, convert, and use appropriate units of measurement or scale.


93-95, 96-98, 99-102, 103-105, 106, 107-108TR: Labsheets: 130, 131Transparencies: 135-142, 154-156Additional Practice: 172-179Filling and WrappingSE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72,

73-76TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a,

77, 78-79, 80-82, 83-84, 85-86, 87TR: Labsheets: 108- 110Transparencies: 111-131Additional Practice: 140- 149

7.M.2 Given the formulas, convert from one system of measurement to another. Use technology as appropriate.


Given the formulas, convert from one system of measurement to another.

Stretching and ShrinkingSE:36, 49, 65Filling and WrappingSE: 54TR: Additional Practice: 146Data Around UsSE: 14-15TE: 22a-d


141

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STRAND: MEASUREMENT

DOEStandard Number


7.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.

This standard is intentionally the same as standard 6.G.4., which is currently not being assessed at grade 6. This standard will be assessed at grade 7.

Understand concepts and the application of formulas for area and perimeter of parallelograms, trapezoids, and circles.

Stretching and ShrinkingSE: 10-13, 19-20, 24, 36-37, 39TE: 27e-g, 100TR: Transparencies: 136, 142Additional Practice: 172-177Filling and WrappingSE: 5-14, 15-23, 24-36, 37-45, 46-56, 57-67, 68-72,

73-76TE: 14a-h, 23a-e, 36a-e, 45a-g, 56a-e, 67a-f, 72a,

77, 78-79, 80-82, 83-84, 85-86, 87TR: Transparencies: 111-131Additional Practice: 140-149


142

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7.D.1 Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts).

Select, create, interpret, and utilize the following tabular and graphical representations of data: circle graphs, Venn diagrams, stem-and-leaf plots, tables, and charts).

What Do You Expect?SE: 8-9, 22-23, 30, 38-39, 42, 51-52TE: 31a-b, 31e-f, 49a-b, 58a-b, 68bTR: Labsheets: 124-130

Transparencies: 134, 153Additional Practice: 166Comparing and ScalingSE: 48-49, 77-78TE: 86, 91, 94-95TR: Labsheets: 118-120Transparencies: 124-130, 134, 138, 145-146Additional Practice: 152- 154, 157

7.D.2 Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data.This standard is intentionally the same as standard 8.D.3.

Find, describe, and interpret appropriate measures of central tendency and spread that represent a set of data.

What Do You Expect?SE: 52-54TE: 58a-58b

7.D.3 Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).

Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).

What Do You Expect?SE: 10-18, 24-25, 28-29, 42-44, 66, 69-78 TE: 21e -i, 31c-g, 49c-e, 49g, 68c-d, 68g, 78a-e, 83,

85-86, 91-92, 93-94, 95-96TR:Labsheets: 126-127Transparencies: 132, 135-137, 145, 152Additional Practice: 165, 170


143

5/16/06


144

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145

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8.N.1 Compare, order, estimate, and translate among integers, fractions and mixed numbers (e.g., rational numbers), decimals, and percents.

Compare, order, estimate, and translate among integers, rational numbers, decimals, and percents.

Looking For PythagorasSE: 19-26, 27-40TE: 26a-h, 40a-j, 74, 80, 84,85-86TR: Transparencies: 119, 121-123, 128-129; Additional Practice: 139, 141, 143, 145-146Clever CountingSE: 20-26, 30-31, 41-46, 50-56TE: 26d-g, 46d-f, 56a, 61, 65-66TR: Transparencies: 86-89, 97;Additional Practice: 102-109

8.N.2 Define, compare, order, and apply frequently used irrational numbers, such as √2 and π.

Compare, order, and apply frequently used irrational numbers such as √2 and π.

Looking For PythagorasSE: 53-63,64-72TE: 63a-f, 72a-f, 82, 85-86TR: Labsheets: 108, 109; Transparencies: 127, 131, 132; Additional Practice: 140-143,146,147

8.N.3 Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change.

Use ratios and proportions in the solution of problems involving rate of change.

Growing. Growing. GrowingSE: 33-37, 49-52 TE: 30h, 44a-g, 60c-iTR: Transparencies: 103-107Additional Practice: 124

8.N.4 Represent numbers in scientific notation, and use them in calculations and problem situations.

Represent numbers in scientific notation, and use them in calculations and problem solving (including negative exponents).

Growing, Growing, GrowingSE: 26


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8.N.5 Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems.

Looking For PythagorasSE: 19-26, 28-40, 53-63TE: 26a-h, 40a-j, 63a-f, 80, 82, 86TR: Labsheets: 108;Transparencies: 119, 122, 123, 127-129Additional Practice: 140, 146-147

8.N.6 Demonstrate an understanding of absolute value (e.g., | -3 | = | 3 | = 3).

Define and demonstrate an understanding of absolute value.


8.N.7 Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots.

Use the rules of powers and roots to the solution of problems, including positive integer exponents, and square roots in the Order of Operations.

Looking For PythagorasSE: 19-26, 28-40, 53-63TE: 26a-h, 40a-j, 63a-f, 78-79, 80-82, 86TR: Transparencies: 118, 119, 127-129Additional Practice: 140, 143, 147

Growing, Growing, GrowingSE: 17-30TE: 30a-f, 65-66, 70-73TR: Transparencies: 99- 101, 113; Additional Practice: 122-126


147

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8.N.8 Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 =1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition).

Use the properties of the identity and inverse elements and the notion of closure of a subset of the rational numbers under an operation.

Looking For PythagorasSE: 19-26, 27-40TE: 26a-h, 40a-j, 74, 80, 84-86TR: Transparencies: 119, 121-123,128,129Additional Practice: 139, 141, 143, 145, 146

Say It With SymbolsSE: 34-52, 53-64, 65-70, 71-75TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85TR: Transparencies: 103-104, 107-116, 121,

124- 127Additional Practice: 134-135, 138, 140,141-143

8.N.9 Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems (e.g. multiplying by ½ or 0.5 is the same as dividing by 2).

Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems.

Looking For PythagorasSE: 19-26, 28-40, 53-63 TE: 26a-h, 40a-j, 63a-f, 78-79, 80-82, 86 TR: Transparencies: 118-119, 127-129;Additional Practice: 140, 143, 147


148

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8.N.10 Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).

Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1).

Looking For PythagorasSE: 19-26, 27-40, 41-52, 53-63TE: 26a-h, 40a-j, 52a-h, 63a-f, 77, 78-79,

80-84, 85-86TR: Labsheets: 108Transparencies: 119, 121-124, 126, 128-129Additional Practice: 139-146Clever CountingSE: 8-13,15-26, 28-36, 41-46, 50-56, 59-61TE: 14c-e, 26d-g, 36a-f, 46a-f, 56a, 61, 65-66 TR: Transparencies: 86-89, 97Additional Practice: 102-109

8.N.11 Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.

Determine when an estimate rather than an exact answer is appropriate and apply in problem situations.

Looking For PythagorasSE: 56-60TE: 63bTR: Transparencies: 127

8.N.12 Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives).

Select and use appropriate operations to solve problems with rational numbers (including negative integers).

Looking For PythagorasSE: 19-26, 27-40TE: 26a-h, 40a-j, 74, 80, 84, 85-86TR: Transparencies: 119, 121-123,128-129Additional Practice: 139, 141, 143, 145-146Say It With SymbolsSE: 34-52, 53-64, 65-70, 71-75TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81,

82-85TR: Transparencies: 103, 104, 107-116, 118-

121, 124-127Additional Practice:134-135, 138, 140-143


149

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8.P.1 Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions (e.g., compounding).

Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and symbolic expressions. Include arithmetic and geometric progressions.

Thinking With Mathematical ModelsSE: 5-25, 26-36, 37-46, 47-59, 60-62TE: 25a-j, 36a-g, 46a-e, 59a-f, 63-64, 65-66,

67-68, 69-71Labsheets: 92, 93Transparencies: 94-109Additional Practice: 116-125Looking For PythagorasSE: 44-52TE: 52a-b, 52f-hTR: Labsheets: 108Transparencies: 119, 122-123Growing. Growing. GrowingSE: 5-16, 17-30, 31-44, 45-60, 61-64TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68,

69-73, 74-77Labsheets: 96Transparencies: 97-113Additional Practice: 120-127Frogs. Fleas, and Painted CubesSE: 5-18, 19-40, 41-51, 52-70, 71-84, 85-87TE: 18a-k, 40a-r, 51a-i, 70a-i, 84a-g, 87-88,

89, 90-92, 93-95, 96-98TR: Labsheets: 112-114 Transparencies: 115-122, 127-140Additional Practice: 146-154


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Say It With SymbolsSE: 22-23, 25-27, 48-49,53-64, 65-70, 71-75TE: 33d-g, 52e-h, 64a-m, 70a-f, 76-77, 78,

79-81, 82-85TR: Transparencies: 103-104, 107-121

124-127Additional Practice: 134-135, 138, 140-143

8.P.2 Evaluate simple algebraic expressions for given variable values (e.g., 3a2 - b for a = 3 and b = 7).

Evaluate simple algebraic expressions for given variable values.

Looking For PythagorasSE: 17-26, 27-40, 41-52, 53-57, 60-63, 64-72TE: 26a-h, 40a-j, 52a-h, 63a-f, 72a-f, 76-77,

78-79, 80-84, 85-86TR: Labsheets: 99-102, 107-108Transparencies: 116-120, 126Additional Practice: 138-141, 143-146 Say It With Symbols SE: 5-19, 51, 53-64, 65-70, 71-75 TE: 19a-h, 52g, 76-77, 81, 83-84 TR: Transparencies: 104, 106-108, 116

118-119;Additional Practice: 134- 137

8.P.3 Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions (e.g., -2[-x+2] = 2x – 4).

Demonstrate an understanding of the identity (-x)(-y) = xy and use this identity to simplify algebraic expressions.

Say It With SymbolsSE: 38-39


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8.P.4 Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.

Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations.


67-68, 69-71TR: Labsheets: 92, 93;Transparencies: 94-101, 103-109Additional Practice: 116-125Looking For PythagorasSE: 44-52TE: 52a-b, 52f-hTR: Transparencies: 119, 122-123Growing, Growing. GrowingSE: 5-16,17-30, 31-44, 45-60, 61-64TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68,

69-73, 74-77TR: Labsheets: 96 Transparencies: 97-113Additional Practice: 120-127.Frogs. Fleas, and Painted CubesSE: 5-18, 19-40, 41-51, 52-70, 71-84, 85-87TE: 18a-k, 40a-r, 51a-i, 70a-i, 84a-g, 87-88, 89, 90-92, 93-95, 96-98TR: Labsheets: 112-114; Transparencies: 115, 117-122, 127-140Additional Practice: 146-154 Say It With SymbolsSE: 34-52, 53-64, 65-70, 71-75TE: 52a-m, 64a-m, 70a-f, 76-77, 78, 79-81, 82-85TR: Transparencies: 103-104, 107-116,


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118-121, 124-127Additional Practice:134-135, 138, 140-143

8.P.5 Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems.

Thinking With Mathematical ModelsSE: 8-25, 60-61TE: 25a-j, 63-64, 65-66, 68TR: Transparencies: 97-100; Additional Practice: 116-119, 121,123,125 Looking For PythagorasSE: 64-72 TE: 83-84,85TR: Labsheets: 109Transparencies: 131, 132;Additional Practice: 148

8.P.6 Identify the roles of variables within an equation (e.g., y = mx + b, expressing y as a function of x with parameters m and b).

Identify the roles of variables within an equation. Identify coefficients


67- 68, 69TR: Transparencies: 106, 107, 108, 109;Additional Practice 125Growing, Growing. GrowingSE: 17-30, 31-44, 45-60, 61-64TE: 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73,

74-77TR: Transparencies: 97-113Additional Practice: 120-127 Frogs. Fleas, and Painted CubesSE: 6-18,19-40, 52-53, 56-70, 71-84, 85-87TE: 18b-k, 40a-r, 70a-i, 84a-g, 87-88, 89,

90-92, 93-95, 96-98TR: Labsheets: 113-114


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Transparencies: 115-122, 131-134, 136- 140Additional Practice:146-147, 150-152

Say It With Symbols SE: 38-41, 57-58, 60-63, 71-75 TE: 64a-c, 76-77, 78, 79-81, 82-83, 85TR: Transparencies: 103-104, 106-107, 113,

115, 118-120, 124, 127; Additional Practice: 135, 140-143

8.P.7 Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.

Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs.

Add like terms

Thinking With Mathematical ModelsSE: 9, 12-14, 16, 18-25, 29-36, 37-38, 44-45,

56, 60-62TE: 36b-g, 46a-b, 63-64, 65-66, 67-68, 69-71TR: Additional Practice: 124Looking For PythagorasSE: 44-52 TE: 52a-b, 52f-hSay It With SymbolsSE: 53-64, 65-70, 71-75TE: 64a-m, 70a-f, 76-77, 78, 79-81, 82-85 TR: Transparencies: 121-123,125-12Additional Practice: 141, 142

8.P.8 Explain and analyze—both quantitatively and qualitatively, using pictures, graphs, charts, or equations—how a change in one variable results in a change in another variable in functional relationships (e.g., C = πd, A = πr2 [A as a function of r], Arectangle = lw [Arectangle as a function of l and

Explain and analyze how a change in one variable results in a change in another variable in functional relationships.


67-68,69TR: Transparencies: 106-109Additional Practice:125Growing. Growing. GrowingSE: 17-30, 31-44, 45-60, 61-64


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w]). TE: 30a-f, 44a-g, 60a-i, 65-66, 67-68, 69-73, 74-77

TR: Transparencies: 97- 113Additional Practice: 120-127 Frogs. Fleas, and Painted CubesSE: 6-18,19-40, 52-53, 56-70, 71-84, 85-87TE: 18b-k, 40a-r, 70a-i, 84a-g, 87-88, 89,

90-92, 93-95, 96-98TR: Labsheets: 113-114Transparencies: 115-122, 131-134, 136-140; Additional Practice: 146-147, 150-152Say It With SymbolsSE: 38-41, 57-58, 60-63, 71-75TE: 64a-c, 76-77, 78, 79-81, 82-83, 85TR: Transparencies: 103-104, 106-107, 113,

115, 118-120, 124, 127Additional Practice: 135, 140-143

8.P.9 Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate.

Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. (i.e. computer programs, graphing calculators, etc.)

Thinking With Mathematical ModelsSE: 5-13, 15-15,18-25, 26-36, 37-46, 47-59,

60-62 25a-e, 25g-j, 36a-g, 46a-e, 59a-f, 64, 65-66, 67-68, 69-71

TE: Transparencies: 94-108Additional Practice: 119, 122, 124, 125Looking For PythagorasSE: 46-52TE: 52a-bGrowing. Growing. GrowingSE: 5-16,17-30, 31-44, 45-60, 61-64TE: 16a-g, 30a-f, 44a-g, 60a-i, 65-66, 67-68,

69-73, 74, 76-77


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TR: Labsheets: 96Transparencies: 97-109, 111-113Additional Practice: 120, 122, 124, 126, 127

Frogs. Fleas, and Fainted CubesSE: 5-7,19-21, 36-37, 41-42, 45-46, 49, 52-57,

60-63, 65, 67-69, 85-86TE: 18a-c, 51a-d, 70a-g, 92, 95, 96, 98 TR: Transparencies: 116, 120, 129, 130,

132-135Additional Practice: 149, 152 Say It With SymbolsSE: 36-39, 41-42, 48-49, 53-64, 65-70, 71-75TE: 52e-h, 64a-m, 70a-f, 76-77, 79-81, 82, 84TR: Transparencies: 103-106, 108-116,

118-120Additional Practice: 134-135, 140-142

8.P.10 Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns.

Use tables and graphs to represent and compare linear growth patterns. Compare rates of change and x- and y-intercepts of different linear patterns.

Thinking With Mathematical ModelsSE: 5-13,14-15, 18-25, 26-36, 37-46, 47-59,

60-62 TE: 25a-e, 25g-j, 36a-g, 46a-e, 59a-f, 64,

65-66, 67-68, 69-71 TR: Transparencies: 94-108Additional Practice: 119, 122, 124, 125


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8.G.1 Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.

Analyze, apply, and explain the relationship between the number of sides and the sums of the interior and exterior angle measures of polygons.


8.G.2 Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.

Classify figures in terms of congruence and similarity, and apply these relationships to the solution of problems.

Kaleidoscopes. Hubcaps, and MirrorsSE: 5-23, 24-41, 42-58, 59-70, 71-77TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83,

84-85, 86-89, 90-93TR: Labsheets: 116-146Transparencies 147-173Additional Practice: 184-195

8.G.3 Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal.

Kaleidoscopes. Hubcaps, and MirrorsSE: 27TE: 23h, 41d, 41i

8.G.4 Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems

Demonstrate an understanding of the Pythagorean theorem. Apply the theorem to the solution of problems.

Looking For PythagorasSE: 27-40, 41-52, 53-63TE: 40a-j, 52a-h, 63a-f, 77, 78-79, 80-84, 85-86 TR: Labsheets: 108; Transparencies: 119, 121-124, 126, 128-129;Additional Practice: 139-146

8.G.5 Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.

Use a straightedge, compass, or other tools to formulate and test conjectures, and to draw geometric figures.

Looking For PythagorasSE: 17-26TE: 26a-h, 83-84, 85-86TR: Labsheets: 100, 101, 106, 111;Transparencies: 117-118;Additional Practice: 146


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8.G.6 Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure (e.g., predict how tessellations transform under translations, reflections, and rotations).

Predict the results of transformations on unmarked or coordinate planes and draw the transformed figure.

Kaleidoscopes. Hubcaps, and MirrorsSE: 5-23, 24-41, 42-58, 59-70, 71-77TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83,

84-85, 86-89, 90-93TR: Labsheets: 116-146;Transparencies: 147-173;Additional Practice: 184-195;

8.G.7 Identify three-dimensional figures (e.g., prisms, pyramids) by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.

Identify three-dimensional figures by their physical appearance, distinguishing attributes, and spatial relationships such as parallel faces.

Say It With SymbolsSE: 16-17, 67-69TE: 70c-eTR: Transparencies: 127;Additional Practice: 136

8.G.8 Recognize and draw two-dimensional representations of three-dimensional objects (e.g., nets, projections, and perspective drawings).

Recognize and draw two-dimensional representations of three-dimensional objects.

Say It With SymbolsSE: 16-17, 67-69TE: 70c-eTR: Transparencies: 127;Additional Practice: 136


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8.M.1 Select, convert (within the same system of measurement), and use appropriate units of measurement or scale.

Select, convert, and use appropriate units of measurement or scale.

Looking For PythagorasSE: 17-26, 27-40, 41-52, 53-57, 60-63, 64-72TE: 26a-h, 40a-j, 52a-h, 63a-f, 72a-f, 76-77, 78-79, 80-84, 85-86 TR: Labsheets: 99-102, 107-108;Transparencies: 116-120,126Additional Practice: 138-141, 143-146

8.M.2 Given the formulas, convert from one system of measurement to another. Use technology as appropriate.

Given the formulas, convert from one system of measurement to another.


8.M.3 Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/ circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms, cylinders, and spheres. Use technology as appropriate.

Determine formulas and understand surface area and volume of rectangular prisms, cylinders, and spheres.

Looking For PythagorasSE: 17-26,45TE: 26a-e, 52f-h, 76-77, 78-79, 85-86 Labsheets: 99-102, 107-108; Transparencies: 116-120, 126Additional Practice: 138-141, 143-146:


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8.M.4 Use ratio and proportion (including scale factors) in the solution of problems, including problems involving similar plane figures and indirect measurement.

Looking For PythagorasSE: 64-72TE: 72a-f, 83-84, 85TR: Transparencies: 122Kaleidoscopes. Hubcaps, and MirrorsSE: 5-23, 24-41, 42-58, 59-70, 71-77TE: 23a-k, 41a-o, 58a-j, 70a-k, 79, 80-83,

84-85, 86-89, 90-93TR: Labsheets: 116-146Transparencies: 147-173Additional Practice: 184-95

8.M.5 Use models, graphs, and formulas to solve simple problems involving rates (e.g., velocity and density).

Use models, graphs, and formulas to solve simple problems involving velocity and density rate of change.

Looking For PythagorasSE: 64-72TE: 72a-f, 83-84, 85TR: Labsheets: 109Transparencies: 131, 132


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8.D.1 Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample (e.g., convenience sampling, responses to a survey, random sampling).

Describe the characteristics and limitations of a data sample. Identify different ways of selecting a sample.

Samples and PopulationsSE: 24-28, 32, 34-35, 37-47,148TE: 36b-d, 48a-h, 75, 76-78TR: Transparencies: 112-15, 117-21Additional Practice: 134-38

8.D.2 Select, create, interpret, and utilize various tabular and graphical representations of data (e.g., circle graphs, Venn diagrams, scatterplots, stem-and-leaf plots, box-and-whisker plots, histograms, tables, and charts). Differentiate between continuous and discrete data and ways to represent them.

Differentiate between continuous and discrete data and ways to represent them.

Samples and PopulationsSE: 5-23, 24-36, 37-48, 49-62, 63-69TE: 23a-o, 36a-e, 48a-h, 62a-f, 69-70, 71, 72-75, 76-78TR: Labsheets: 96-102Transparencies: 103-122Additional Practice: 130-140

8.D.3 Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data.

Use measures of central tendency and spread to compare different sets of data.

Samples and PopulationsSE: 7-11, 21, 23, 33, 41-44, 63-69 23e-n, 48d-h,

70, 72, 74-75, 76 Labsheets: 100Transparencies: 104, 105, 106, 107, 108, 118,

119, 120;Additional Practice: 131, 132,137,138,139,140

8.D.4 Use tree diagrams, tables, organized lists, basic combinatorics (“fundamental counting principle”), and area models to compute probabilities for simple compound events (e.g., multiple coin tosses or rolls of dice).

Use tree diagrams, tables, organized lists, basic combinatorics and area models to compute probabilities for simple compound events.

Clever CountingSE: 5-14,15-26, 27-36, 7-46, 47-56, 57-61 TE: 14a-e, 26a-g, 36a-f, 46a-f, 56a, 60-67-69Transparencies: 85-98;Additional Practice: 102-109


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Documents

LEARNING GUIDELINE · Web view2006/05/16 · Represent numbers using expanded notation, e.g., 853 = 8 x 100 + 5 x 10 + 3, and written out in words, e.g., eight hundred fifty-three