7th Grade Math Curriculum Map Maps/Math gr 7... · 7th Grade Math Curriculum Map ... an intense focus on the most critical material at each grade allows depth in learning, ... Quarter

2013-2014

7th Grade Math Curriculum Map

This document was intended to be used “digitally”. This means that many of

the supporting resources can only be accessed through the internet and/or

through the hyper-links created within the document itself. In order to

“activate” the link properties hold down the control (Ctrl) key and mouse over

the linked information. A hand should appear and you should be able to “left-

click” the link to access the resource. Contained within the curriculum map

you will find dually-aligned 7th grade NM and CCS standards, as well as, the

remaining 7th grade NM standards not able to be paired with grade level

CCSS. Each learning target is supported by resources for student practice

activities and application of math practices, as well as, additional clarification

of mathematical concepts and problems for assessment purposes linked on

the envisioning pages.

Directions for Optimal use of this Document:

on the depth of the ideas, the time that they take to master, and/or their

importance to future mathematics or the demands of college and career

readiness. In addition, an intense focus on the most critical material at

each grade allows depth in learning, which is carried out through the

Standards for Mathematical Practice.

To say that some things have greater emphasis is not to say that

anything in the standards can safely be neglected in instruction.

Neglecting material will leave gaps in student skill and understanding and

may leave students unprepared for the challenges of a later grade. All

standards figure in a mathematical education and will therefore be eligible

for inclusion on the PARCC assessment. However, the assessments will

strongly focus where the standards strongly focus.

Key: Major Clusters; Supporting Clusters; Additional Clusters

Roswell Independent School District Math Curriculum Map 2013- 7th Grade

1

Target # Table of Contents

Description

Approximate # of Days in

Learning Cycle

Target 1 Operations with Decimals 5 days

Target 2 Operations with Fractions 5 days

Target 3 Adding and Subtracting Integers 5 days

Target 4 Multiply and Divide Integers 5 days

Target 5 Exponents, Square Roots, and Expressions 7 days

Target 6 Number Properties 5 days

Target 7 Conversions and Equivalents of Percents, Fractions, and Decimals 5 days

Target 8 Percent Equations (Simple interest, commissions, sales tax, tips, etc..) 5 days

Target 9 Percent with Proportions (Discounts, Mark-up, Percent of Change) 5 days

Target 10 Algebraic Expressions from Word Phrases 5 days

Target 11 One-step equations and inequalities 5 days

Target 12 Two-step equations and inequalities 5 days

Target 13 Graphing Linear Equations and Slope 8 days

Target 14 Transformations (8th

grade Common Core) 5 days

Target 15 Properties of plane figures and angles 5 days

Target 16 Congruent and Similar Polygons, Ratio and Proportions, Indirect Measurement 8 days

Target 17 Angle Relationships and Triangular Sum Theorem 5 days

Target 18 Perimeter and Area of Polygons 5 days

Target 19 Circles 5 days

Target 20 Pythagorean Theorem (8 grade Common Core) 5 days

Target 21 Probabilities 5 days

Target 22 Central Tendencies and Analyzing Data 5 days


2

Domain: The Number System Pacing Guide: Quarter 1

Cluster: Apply and Extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Essential Questions: How does a negative sign compare to a subtraction symbol?

For additional probing questions: http://www.keyschool.org/documents/Concepts%20of%20Elementary%20Mathematics.pdf

CCSS Standards Criteria for Success

(Plan)

Vocabulary Activity/Assessment/Resources Math Practice/s Focus

7.NS.A.1d Apply properties of

operations as strategies To add and

subtract rational numbers.

7.NS.A.2d Convert a rational number to

a decimal using long division; know that

the decimal form of a rational number

terminates in 0s eventually repeats.

7.NS.A.3 Solve real-world and

mathematical problems involving the

four operations with rational numbers.

7.NS.A.2c Apply properties of

operations as strategies to multiply and

divide rational numbers.








7.NS.A.1a

Describe situations in which opposite

quantities combine to make 0.

7.NS.A.1b

Understand p+q as the number located a

distance │q│from p, in the positive or

negative direction depending on whether

q is positive or negative. Show that a

number and its opposite have a sum of 0

(are additive inverses). Interpret sums of

rational numbers by describing real-

world contexts.

7.NS.A.1c

Understand subtraction of rational

numbers as adding the additive inverse,

p-q = p+(-q). Show that the distance

between the two rational numbers on the

number line is the absolute value of their

differences, and apply this principal in

real-world contexts.


operations as strategies To add and

subtract rational numbers..

7.NS.A.2b Understand that integers can

be divided, provided that the divisor is

not zero, and every quotient of integers

Target 1-

Demonstrate and

apply addition, subtraction,

multiplication, and

division of decimals in problem situations.

Additional Activity

Target 2- Demonstrate and

apply addition,

subtraction, multiplication, and

division of fractions

and mixed numbers in problem situations.

Additional Activity

Target 3- Construct the extended

number line to include

all rational numbers, including negative

integers. Illustrate the

concept of absolute value using a number

line. Demonstrate and

apply addition and subtraction of integers

in problem situations.

Additional Activity

Target 4- Demonstrate and

apply multiplication

and division of integers in problem

situations.

Additional Activity

Rational

Irrational

Place Value Unit Price

Mixed Numbers,

Improper Fractions,

Reciprocal

Rational Irrational

Factor

Precision

Integers Absolute Value,

Demonstrate

Opposites, Additive Inverse

Product

Calculate

Equivalent Quotient

Estimate

Activities

Operations with Decimals

Add and subtract decimals using personal checkbook register

Write and solve application problems involving money, unit price,

and gas mileage Operations with Fractions

Use colored number cubes to represent numerators and

denominators to perform operations with fractions

Operations with Integers

Use colored number cubes to represent positive and negative integers to perform basic operations

Assessments

Prentice Hall Course 2

Activity lab 4-16 Pg. 173 Using Spreadsheets

Resources:

http://www.khanacademy.org/#arithmetic

Supportive video tutorials and practice problems: “Fractions” 7.NS.A.1d

“Applying mathematical reasoning” 7.NS.A.3

“Negative numbers and absolute value” 7.NS.A.1a,b,c

http://www.illustrativemathematics.org/standards/k8

A task bank organized by grade level domains “Distance between houses” 7.NS.A.1

“Repeating decimal as approximation” 7.NS.A.2d

Materials

Checkbook register

Number cubes or wooden blocks Expression keeper template

Check Register Activity:

MP #2-

Contextualize/Decontextualize

MP #4- Real World

MP #5- Appropriate tools MP #6- Precision

Colored Number Cubes

Activity:

MP #2- Contextualize/ Decontextualize

MP #4- Modeling

MP #6- Precision MP #8- look for repeated

reasoning

http://www.keyschool.org/documents/Concepts%20of%20Elementary%20Mathematics.pdf




3

(with non-zero divisor) is a rational

number. If p and q are integers, then –

(p/q) = p/(-q). Interpret quotients of

rational numbers by describing real-

world contexts.





4



Essential Questions: What would happen if there were no set rules for solving problems with multiple mathematical operations?



(Plan)



operations as strategies to add and


7.NS.A.2c Apply properties of

operations as strategies to multiply and

divide rational numbers.

7.EE.A.1 Apply properties of operations

as strategies to add, subtract, factor, and

expand linear expressions with rational

coefficients.

7.EE.A.2 Understand that rewriting and

expression in different forms in a

problem context can shed light on the

problem and how the quantities in it are

related. Example: a+0.05a = 1.05a

means that “increase by 5%” is the same

as “multiplied by 1.05”.

Target 5

Using Order of

Operations to evaluate expressions which

include exponents and

square roots.

Additional Activity

Evaluate

Expression

Exponent Square Root

Activities

Students will explore the need for order of operations, and learn how to use it

through small group discussion and presentation by solving the same multi-step problem without any teacher direction as to process and NO discussion

between groups until each group has achieved their own solution. Students

should then present their process for solving and their finite solution. (Increase level of difficulty over the cycle by adding exponents and square

roots)

http://illuminations.nctm.org/ActivityDetail.aspx?ID=216

Assessment Small group presentation of accurate demonstration of order of operations via

student group created posters.

Resources

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations

%20Web%20Page/Order_of_Operations_Lesson.html Lesson plan that addresses order of operations where students create games

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations

%20Web%20Page/Game_Rubric.html

Rubric for the above listed activity


Video tutorials and practice problems “Arithmetic properties” 7.NS.A.1d and 7.NS.A.2c

http://www.illustrativemathematics.org/standards/k8 A task bank organized by grade level domains

“Rounding and subtraction” 7.NS.A.1

MP #1- Make sense and

persevere

MP #3- Construct viable arguments

MP #5- Appropriate tools

MP #6- Attend to precision


http://illuminations.nctm.org/ActivityDetail.aspx?ID=216

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Order_of_Operations_Lesson.html

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Order_of_Operations_Lesson.html

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Game_Rubric.html

http://www.gips.org/Technology/T.I.E./Alberts/Order%20of%20Operations%20Web%20Page/Game_Rubric.html




5



Essential Questions: How can number properties assist in solving mathematical problems?



(Plan)



operations as strategies to add and


7.NS.A.2a Understand that multiplication is extended from

fractions to rational numbers by

requiring that operations continue

to satisfy the properties of

operations, particularly the

distributive property, leading to products such as (-1)(-1) and rules

for multiplying signed numbers. Interpret products of rational

number by describing real-world

contexts. 7.NS.A.3 Solve real-world and

mathematical problems involving

the four operations with rational numbers.

Target 6

Select the appropriate

number property and apply the property to

simplify operations.

Additional Activity

Identify

Associative

Commutative Distributive

Activity 1

“Spoons” or “Books” style card game involving matching cards for each

property (1 property name card and 1 property example card)

Materials

Plastic spoons (or something to represent spoons) Paper to create cards

One deck of cards per group (student created)

Assessment

Students create Foldable and/or a group poster to summarize the Number

Properties, including algebraic and numeric examples, pictures to aid memory, and/or pneumonic devices

http://www.khanacademy.org/#arithmetic Video tutorials and practice problems

“Distributive Property” there are 5 supportive videos/examples 7.NS.A.1d

Activity1


persevere MP #3- Construct viable

arguments

Assessment

MP #2- Abstract to concrete

MP #5- Use appropriate tools




6

Domain: The Number System/Expressions and Equations Pacing Guide: Quarter 1

Cluster: Apply and Extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. AND Solve real life and mathematical problems using numerical and algebraic expressions and equation. AND

To analyze proportional relationships and use them to solve real-life and mathematical problems.

Essential Questions: Explain the relationship between the quantities in a given problem (teacher chooses problem) i.e. ½, 0.50, 50/100 etc. For additional probing questions: http://www.keyschool.org/documents/Concepts%20of%20Elementary%20Mathematics.pdf


(Plan)






7.EE.B.3 Solve multi-step real-life and

mathematical problems posed with

positive and negative rational numbers in

any form (whole numbers, fractions, and

decimals), using tools strategically.

Apply properties of operations to

calculate with numbers in any form;

convert between forms as appropriate;

and assess the reasonableness of answers

using mental computation and estimation

strategies. For example: If a woman

making $25 an hour gets a 10% raise,

she will make an additional 1/10 of her

salary on hour, or $2.50, for a new salary

of $27.50. If you want to place a towel

bar 9 ¾ in. long in the center of a door

that is 21 ½ in. wide, you will need to

place the bar about 9 in. from each edge;

this estimate can be used as a check.

7.RP.A.3 Use proportional

relationships to solve multi-step ratio and percent problems.

Examples: simple interest, tax,

mark ups & mark downs, gratuities & commissions, fees, percent

increase and decrease, and percent

error.

Target 7

Convert fractions to

decimals and percent’s

and use these representations in

estimations,

computations, and applications.

Additional Activity

Target 8

Calculate given percentages of

quantities using

equations and use them to solve

problems, including

simple interest, sales

tax, and commission.

Additional Activity

Target 9

Calculate given

percentages of quantities using

proportions and use

them to solve problems, and

including discounts

and percent of change.

Conversion, Prime Numbers,

Composite

Numbers, Numerator

Denominator

Simplify (Simplest Form)

Formula Function

Principle

Commission, Percent of change

Proportion

Unit rate

Unit cost Mark-up

Discount

Activity 1 Using current newspaper ads and/or store flyers have students calculate

discounts/sales tax/etc. and compile a table to compare better prices per unit

between similar items, as well as, the total cost of their shopping list and/or expense.

Assessment Completed poster comparison chart presented in a table by student groups.

Activity 2 Use 10 x 10 grids or geo-board to explore the relationship of fractions with

percents. Then calculate decimal equivalency.

Assessment

illustrativemathematics.org (task bank organized by grade level domains)

Katie and Margarita have $20 to spend at the bookstore, where all students

receive a 20% discount. They both want to purchase a copy of the same book

which normally sells for $22.50 plus 10% sales tax.

To check of she has enough money, Katie takes 20% of $22.50

and subtracts the amount from the original price. She takes 10% of the discounted selling price and adds it back to find the

purchase amount.

Margarita takes 80% of the normal price and then computes 110% of the reduced price.

Which student is correct? Do either of the girls have enough money?

Additional Supportive Activity/Extension

Prentice Hall Course 2 2-6a Activity Lab

Pg. 95

Comparing Fractions & Decimals Suggestion: Teachers might want to have students add an additional column

for %.

Resources


Video tutorials and practice problems “Intro to percentages” supportive video for 7.EE.B.3


A task bank organized by grade level domains

Activity 1 MP #1- Analyze and ask

“Does this make sense?”

MP #2- Contextualize/Decontextualize

MP #4- Model with real world

MP #5- Logical reasoning

Activity 2

MP #2- Contextualize/Decontextualize

MP #4- Model with

manipulatives MP #5- Appropriate tools





7

Domain: Expressions and Equations Pacing Guide: Quarter 1

Cluster: Solve real life and mathematical problems using numerical and algebraic expressions and equation. AND Use properties of operations to generate equivalent expressions.

Essential Questions: How do you decide what to solve for in an algebraic equation (determine the unknown)?



(Plan)


7.EE.A.1 Apply properties of operations

as strategies to add, subtract, factor, and

expand linear expressions with rational

coefficients.

7.EE.A.2 Understand that rewriting an

expression in different forms in a

problem context can shed light on the

problem and how the quantities in it are

related. Example: a+0.05a = 1.05a

means that “increase by 5%” is the same

as “multiplied by 1.05”.

7.EE.B.3 Solve multi-step real-life and

mathematical problems posed with

positive and negative rational numbers in

any form (whole numbers, fractions, and

decimals), using tools strategically.

Apply properties of operations to

calculate with numbers in any form;

convert between forms as appropriate;

and assess the reasonableness of answers

using mental computation and estimation

strategies. For example: If a woman

making $25 an hour gets a 10% raise,

she will make an additional 1/10 of her

salary on hour, or $2.50, for a new salary

of $27.50. If you want to place a towel

bar 9 ¾ in. long in the center of a door

that is 21 ½ in. wide, you will need to

place the bar about 9 in. from each edge;

this estimate can be used as a check.

7.EE.B.4a Solve word problems leading

two equations of the form px+q=r and

p(x+q)=r, where p, q, and r are specific

rational numbers. Solve equations of

these forms fluently. Compare an

algebraic solution to an arithmetic

solution, identifying the sequence of the

operations used in each approach. For

example: the perimeter of a rectangle is

54 cm, it’s length is 6 cm. What is its

width?

7.EE.B.4b Solve word problems leading

to inequalities of the form px+q>r or

px+q < r where p, q, and r are specific

rational numbers. Graph the solution set

of the inequality and interpret it in the

context of the problem. For example: as

a salesperson, you are paid $50 per week

plus $3 per sale. This week you want

your pay to be at least $100. Write an

Target 10

Compose algebraic expressions for word

phrases and problem

situations. Apply substitution to

evaluate expressions.

Target 11

Compose one-step

equations and inequalities to

illustrate problem

situations. Select and apply inverse

operations to solve.

Target 12 Compose two-step

equations and inequalities to

illustrate problem

situations. Select and apply inverse

operations to solve.

Additional Activity

Variable

Expression Equations

Addition property

of inequality, Subtraction

property of

inequality, Multiplication

property of

equality, Division property of

equality,

Reciprocal

Inequalities

Solution,

Compound Inequality

Brain Teasers

Activity

Have the students read "Sideways Arithmetic from Wayside School." (The

book is full of middle school brain teasers and word problems.) For example, students must solve cryptograms where numbers are replaced by letters in

arithmetic equations and they must determine the numbers the letters

represent. Either assign the students to go through the book and read the stories and complete the math teasers or assign the students to devise their

very own seemingly impossible math teasers.

Assessment:

using the distance formula… d = rt, solve for t if the distance is 103 miles

and the rate is 25mph

Resources

http://www.ixl.com/math/grade-7 Supportive interactive (on-line) practice

“Graph solutions to two-step inequalities) 7.EE.B.4b


Video tutorials and practice problems “Thinking algebraically about inequalities” 7.EE.B.4b

“Percent word problems” 7.EE.A.2 & 7.EE.B.3


A task bank organized by grade level domains

Hands on algebra kit- a balanced scale/ manipulatives kit with two step

equations

Singapore Math+ Algebra (RISD Web-site)

Day 1 Presentation Problems Day 1 Answer Key



Day 4 Presentation Problems Day 4 Answer Key Day 5 Presentation Problems Day 5 Answer Key

Quiz Quiz Answer Key

Activity

MP #1- Analyze & persevere MP #2-

Contextualize/Decontextualize

MP #3- Break down complexity

MP #4- Modeling

MP #5- Appropriate tools MP #6- Precision (labeling

model)

MP #7- Make use of structure


http://www.ehow.com/info_7847322_math-projects-middle-school-students.html#ixzz1RSMAO1z8



http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/Presentaiton%20Problems/Algebra%20Day%201%20(Final).doc

http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/AnswerKeys/Algebra%20Day%201%20Answer%20Key%20(Final).doc









http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/Final%20Quizzes/Algebra%20Quiz%20(Final).doc

http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/AnswerKeys/Algebra%20Quiz%20Answer%20Key%20(Final).doc


8

inequality for the number of sales you

need to make, and describe the solutions.




7.RP.A.3 Use proportional relationships

to solve multi-step ratio and percent

problems. Examples: simple interest, tax,

mark ups & mark downs, gratuities &

commissions, fees, percent increase and

decrease, and percent error.


9

Domain: Ratios and Proportional Relationships Pacing Guide: Quarter 1

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Essential Questions: How can you prove proportional relationships?



(Plan)


7.RP.A.2a

Decide whether two quantities are

in a proportional relationship, eg, by testing for equivalent ratios in a

table or graphing on a coordinate

plane and observing whether the graph is a straight line through the

origin. 7.RP.A.2b

Identify the constant of proportionality

(unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of

proportional relationships. 7.RP.A.2c

Represent proportional relationships by equations. For

example, if total cost t is

proportional to the number n of items purchased at a constant price

p, the relationship between the total

cost and the number of items can be expressed as t= pn.

7.RP.A.2d

Explain what a point (x,y) on the graph of a proportional relationship

means in terms of the situation,

with special attention to the points (0,0) and (1,r) where r is the unit

rate.

Target 13

Plot points in

coordinate space, graph ordered pairs to

satisfy an equation,

then calculate and interpret the slope.

Additional Activity

Patterns

(arithmetic &

geometric), x-coordinate

y-coordinate

Coordinate plane Ordered pairs

Run

Rise Slope

Quadrant Construction Activity:

Constructing the four quadrants on a desk presents a visual enhancement of

coordinates and negative numbers. The center of the desk can be designated as point (0,0) and given objects can be described as being in various

quadrants in relation to the point of origin. Plot points in coordinate space,

graph the ordered pairs, and calculate and interpret the slope.

Assessment:

From the given data table… Cat food

# of cans 0 5 10 15

Cost ($) 0 1.25 2.50 3.75

Find the unit rate and label the corresponding coordinate pair on a graph.

Describe the proportional relationship.

Resources

http://www.ixl.com/math/grade-7

Real-world proportion application word problems


Video tutorial and practice problems

“Finding unit rates” & “Mixture problems” 7.RP.A.2b

“Age problems” 7.RP.A.2c


A task bank organized by grade level domains “Buying Bananas” & “Buying Coffee” 7.RP.A.2c

Activity

MP #2-

Contextualize/Decontextualize MP #4- Modeling


MP #6 Attend to precision (labeling)






10

Domain: Geometry Pacing Guide: Quarter 1

Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them.

Essential Questions: What are the similarities and differences between the images and pre-images generated by translations?



(Plan)


Not addressed in 7th grade CCSS-

Concept picked up in 8th grade

8.G.1a & 8.G.2,3,4 & 8.EE.1,2.

Target 14

Construct

transformations in coordinate space,

including translations,

reflections, and rotations. Recognize

linear and rotational

symmetry.

Line symmetry

Reflections

Rotations Translation

Transformations

Image Vertex

Equilateral

Activity (Intro to Translations & Reflections)

Prentice Hall Course 2

Pg. 518 Extension- Tessellations & Reflections

Assessment:

Prentice Hall Course 2 Pg. 512 #17, Pg. 516 #19 and #27, Pg. 522 #22

Resources:

http://www.ixl.com/math/grade-7 Math games and activities http://www.khanacademy.org/#arithmetic Video tutorials and practice problems

Activity

MP #2- Abstract idea of

transformations to a concrete model





11


Cluster: Draw, construct, and describe geometrical figures and describe the relationships between them. AND Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Essential Questions: How can plane and solid shapes be described?



(Plan)


7.G.A.2

Draw (free hand, with ruler and protractor, and technology)

geometric shapes with given

conditions. Focus on constructing triangles from three measures of

angles or sides, noticing when the

conditions determine a unique triangle, more than one triangle, or

no triangle.

7.G.A.3. Describe the two-dimensional

figures that result from slicing

three-dimensional figures, as in plane sections of right rectangular

prisms and right rectangular

pyramids

7.G.B.5

Use facts about supplementary,

complimentary, vertical, and

adjacent angles in a multi-step

problem to solve and write equations for an unknown angle in

a figure.

Target 15

Identify properties of plane figures, and

classify angles,

triangles, and quadrilaterals by their

angle measures and

side lengths.

Point

Acute angle Obtuse angle

Rhombus

Skew lines Isosceles triangle

Segment

Activity

Students will create individual graphic organizer/ foldable for identifying properties of plane figures, classifying angles, triangles, and quadrilaterals by

their angle measures and side lengths showing similarities and differences.

Assessment

Complete an accurate graphic organizer

Resources

Promethean Flipcharts

www.dr-mikes-math-games-for-kids.com

A web-site with a collection of other web links to supportive math activities.


Video tutorials and practice problems

“Supplementary and Complementary Angles” 7.G.B.5

Activity

MP #2- Reason abstractly MP #4- Modeling


MP #6- Attend to precision (labeling)

MP #7- Structure


http://www.dr-mikes-math-games-for-kids.com/



12

Domain: Ratio and Proportional Relationships Pacing Guide: Quarter 1

Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.

Essential Questions: How are geometric properties used to solve problems in everyday life?



(Targets)


7.RP.A.1

Compute unit rates associated with

ratios of fractions, including ratios of lengths, area and other quantities

measured in like or different units.

For example: if a person walks ½ mile in each ¼ hour, compute the

unit rate as the complex fraction ½ /

¼ mph, equivalently 2 mph.

Target 16

Distinguish between

congruence and similarity properties,

write proportions for

corresponding sides of a figure, and solve to

discover missing side

measures.

Additional Activity

Ratio

Proportions

Congruence Similarity

Corresponding

angles, Corresponding

sides

Activity

Students compile a list of objects/structures on school grounds that cannot be

directly measured due to height or inaccessibility. Outdoors, students measure their height and their shadow. Immediately following students

measure the shadows of the other objects and use similar triangles and

proportions to calculate their approximate height.

Materials needed:

Tape measure per group

Assessment

Teacher observation of project completion and accuracy of calculations Teacher created rubric

Resources

Zike, Dinah (Big Book of Math: For Middle School & High School)

ISBN: 1-882796-19-5 Foldable, activities, and templates



“Basic rate problem” 7.RP.A.1


A task bank organized by grade level domains “Molly’s run” and “Molly’s run assessment variation” 7.RP.A.1

Singapore Math + Ratios (RISD web-site) Day 1 Presentation Problems Day 1 Answer Key


Day 3 Presentation Problems Day 3 Answer Key Day 4 Presentation Problems Day 4 Answer Key

Quiz Quiz Answer Key

Activity

MP #1- Make sense &

persevere MP #2- Reason abstract to

concrete

MP #4- Real-world modeling MP #5- Use appropriate tools




http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/Presentaiton%20Problems/Ratios%20Day%201%20(Final).doc

http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/AnswerKeys/Ratios%20Day%201%20Answer%20Key%20(Final).doc







http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/Final%20Quizzes/Ratios%20Quiz%20(Final).doc

http://www.risd.k12.nm.us/assessment_evaluation/Math/Singmathmodelbk2010/AnswerKeys/Ratios%20Quiz%20Answer%20Key%20(Final).doc


13



Essential Questions: Explain the angle relationship/s for the given figure (teacher chooses figure).



(Targets)


7.G.A.2 Draw (free hand, with ruler and protractor, and technology)

geometric shapes with given

conditions. Focus on constructing triangles from three measures of

angles or sides, noticing when the

conditions determine a unique triangle, more than one triangle, or

no triangle.

7.G.B.5

Use facts about supplementary,

complimentary, vertical, and

adjacent angles in a multi-step problem to solve and write

equations for an unknown angle in

a figure.

Target 17

Apply the triangle sum theorem to discover

missing angle

measures. Recognize and construct special

angle relationships of

intersecting lines and calculate the measure

of missing angles.

Additional Activity

Complementary

Supplementary Vertical

Adjacent

Parallel Perpendicular

Activities:

Geometry Map Project Assign students the task of designing a map that includes several different

kinds of lines, angles and triangles. The map can be of a town, their

neighborhood or school, or even a made-up place. Instructors can feel free to be as specific or vague as to what the map includes, but is should contain

parallel and perpendicular streets; one obtuse angle and one acute angle

formed as the result of two streets intersecting; and buildings in the shape of equilateral triangle, a scalene triangle, and an isosceles triangle. Finally, the

map must also include a compass rose. Then, students should include at least

five directions from one to place to another on the map using the words parallel, perpendicular and intersect.

Activity 5.4 Triangle Constructions using side lengths and angle measures. http://www.cimt.plymouth.ac.uk/projects/mepres/book7/y7s5act.pdf

Assessment Completed map according to rubric

Resources

http://www.ixl.com/math/grade-7

Practice problems, games, and projects http://www.abcteach.com/free/g/geometry_maps.pdf A specific activity “Life in a geometrical town” Students will create a map

using a variety of geometrical concepts. http://www.khanacademy.org/#arithmetic

Video tutorials and practice problems “Congruency postulates” 7.G.A.2 “Exploring angle pairs” & “The angle game” 7.G.B.5

Geometry Map Project

MP #1- Make sense and persevere

MP #4- Model

MP #5- Appropriate modeling MP #6- Precision

MP #7- Structure/Pattern


http://www.cimt.plymouth.ac.uk/projects/mepres/book7/y7s5act.pdf


http://www.abcteach.com/free/g/geometry_maps.pdf



14



Essential Questions: What types of problems are solved with measurement?



(Targets)


7.G.B.6

Solve real-world and mathematical problems involving area, volume,

and surface area of two and three

dimensional objects composed of triangle, quadrilaterals, polygons,

cubes and right prisms.

7.G.B.4

Know the formulas for the area and

circumference of a circle and use

them to solve problems; give an informal derivation of the

relationship between the

circumference and area of a circle.

7.G.A.1

Solve problems involving scale

drawings of geometric figures,

including computing actual lengths and areas from a scale drawing and

reproducing a scale drawing at a

different scale.

Important Notes:

1.) Pythagorean theorem is not addressed in 7th grade common core

standards, it is specifically

introduced and applied in 8th grade common core standards (8.G.6,

8.G.7, 8.G.8).

2.) Exponents and square roots are introduced in the 5th and 6th grade

common core standards, however

the concepts are not explicitly listed in 7th grade standards but need to be

reinforced in order for students to

be prepared for 8th grade learning targets.

Target 18

Apply strategies and formulas to calculate

perimeter and area of

parallelograms, triangles, and

trapezoids. Manipulate

formulas to solve for unknown values.

Target 19

Apply strategies and formulas to calculate

circumference and

area of circles and complex figures.

Determine how area

and perimeter are

affected by changes of

scale.

Additional Activity

Target 20

Demonstrate a basic

proof of the

Pythagorean theorem. Apply the theorem to

find missing lengths of

a right triangle.

Linear

measurement -perimeter

-area

-height Precision

Circumference

Polygon Quadrilateral

Pi

Radius

Circumference Area

Chord

Central angle Arc

Semicircle

Activity

Create and solve for areas of regular and irregular polygons using geoboards to explore plane figure properties and dimensions.

Additional Supportive Activity/Extension Prentice Hall Course 2

Geometry in the Coordinate Plane

10-16 Activity Lab Suggestion for extension- Find the slope of the diagonal(s).

Assessment

Teacher observations Resources

Sir Cumference series by Cindy Neuschwander http://www.khanacademy.org/#arithmetic


“Solid geometry volume” 7.G.B.6


A task bank organized by grade level domain “Designs” & “Measuring the area of a circle” & “Stained glass” 7.G.B.4 Activity:

Students construct a basic proof of the Pythagorean Theorem by building a

right triangle with angles and constructing perfect squares on each side with square units

Assessment Teacher observation of completed and accurate constructions using angles

and/or Promethean Board.

Resources

What’s Your Angle, Pythagoras by Julie Ellis angles (plastic manipulative) Promethean Board

Prentice Hall Mathematics Course 2 textbook and materials http://www.khanacademy.org/#arithmetic

Video tutorial and practice problems


Under 8th grade CCSS additional student practice can be found.

Activity

MP #4- Modeling MP #5- Appropriate tools

MP #6- Structure

Activity

MP #1- Persevere

MP #2- Abstract to Concrete MP #3- Viable Arguments

MP #4- Modeling

MP #7- Structure







15

Domain: Statistics and Probability Pacing Guide: Quarter 1

Cluster: Investigate chance processes and develop, use, and evaluate probability models.

Essential Questions: How is the probability of an event determined and described?



(Targets)


7.SP.C.5

Understand that probability of a chance event is

a number between 0 and 1 that expressed the

likelihood of the event occurring. Larger

numbers indicate greater likelihood. A

probability near 0 indicated an unlikely event,

the probability around ½ indicates an event that

is neither likely nor unlikely, and the

probability near 1 indicated a likely event.

7.SP.C.6

Approximate the probability of a chance event

by collecting data on the chance process that

produces it and observing it’s long run relative

frequency, and predict the approximate relative

frequency given the probability. For example:

when rolling a number cube 600 times predict

that a 3 or 6 would be rolled likely 200 times,

but probably not exactly 200 times.

7.SP.C.7a

Develop a uniform probability model by

assigning equal probability to all outcomes, and

use the model to determine probabilities of

events. For example, if a student is selected at

random from a class, find the probability that

Jane will be selected and the probability that a

girl will be selected.

7.SP.C.7b

Develop a probability model (which may not be

uniform by observing frequencies in data

generated from a chance process. For example,

find the approximate probability that a spinning

penny will land heads up or that a tossed paper

cup will land open end down. Do the outcomes

for the spinning penny appear to be equally

likely based on the observed frequencies?

7.SP.C.8a

Understand that, just as with simple events, the

probability of a compound event is the fraction

of outcomes in the sample space for which the

compound event occurs.

7.SP.C.8b

Represent sample spaces for compound events

using methods such as organized lists, tables

and tree diagrams. For an event described in

everyday language (e.g., “rolling double

sixes”), identify the outcomes in the sample

space which compose the event.

7.SP.C.8c

Design and use a simulation to generate

frequencies for compound events. For example,

use random digits as a simulation tool to

approximate the answer to the question: If 40%

of donors have type A blood, what is the

probability that it will take at least 4 donors to

find one with type A blood?

Target 21

Differentiate

probability and odds, design basic

probability

simulations, and express probabilities

as ratios, decimals,

and percents.

Probability

Odds

Experimental Theoretical

Replacement

Real-World Probability

Activity Give the students the following probability problem to solve and illustrate.

In the real-world scenario, there are 350 parking spaces in the parking lot of

the school. On a normal Tuesday, 150 people drive and park in random parking spots. The students must determine the number of different ways the

cars can be parked in the lot. Determine the probability of two or more

specific cars parking side by side on any day, for two and three consecutive days, and for no consecutive days. Illustrate the four probability days.

Assessment: completed activity

Resources

RISD Media Library- Baseball math statistics & data analysis (PF-5795) & Activity card 2009.

Prentice Hall Course 2 12-2a activity lab pg. 585 Exploring Probability

12-4a activity lab pg. 597 Multiple Events

Vocabulary Builder pg. 603

http://www.ixl.com/math/grade-7 Supportive projects, games, and practice problems

http://www.khanacademy.org/#arithmetic Video tutorials and practice problems

“Probability” 7.SP.C.5

“Picking a non-blue marble” 7.SP.C.6


A task bank organized by grade level domain “Rolling dice” 7.SP.C.6 & 7.SP.C.7 “Rolling twice” 7.SP.C.8

Activity


persevere MP #2- Abstract to concrete

MP #3- Complex into plausible

arguments MP #5- Appropriate tools

MP #7- Structure/Patterning






16

Domain: Statistics and Probability Pacing Guide: Quarter 1

Cluster: Use random sampling to draw inferences about a population. AND Draw informal comparative inferences about two populations.

Essential Questions: What aspects of a graph help people understand and interpret data easily? How does the type of data influence the choice of display?



(Targets)


7.SP.A.1

Understand that statistics can be used to gain

information about a population by examining a

sample of the population; generalizations about

a population from a sample are valid only if the

sample is representative of that population.

Understand that random sampling tends to

produce representative samples and support

valid inferences.

7.SP.A.2

Use data from a random sample to draw

inferences about a population with an unknown

characteristic of interest. Generate multiple

samples (or simulated samples) of the same size

to gauge the variation in estimates or

predictions. For example, estimate the mean

word length in a book by randomly sampling

words; predict the winner of a school election

based on randomly sampled survey data. Gauge

how far off the estimate or prediction might be.

7.SP.B.3

Informally assess the degree of visual overlap

of two numerical data distributions with similar

variability measuring the difference between

the centers by expressing it as a multiple

measure of variability. For example: the mean

height of players on a basketball team is 10 cm

greater than the mean height of players on the

soccer team, about twice the variability (mean

absolute deviation) on either team; on a dot

(line) plot, the separation between the two

distribution of heights is noticeable.

7.SP.B.4 Use measures of center and measures of

variability for a numerical date from random

samples to draw informal comparative

inferences about two populations, for example:

decided whether the words in a chapter of a 7th

grade science book are generally longer than

the words in a chapter of a 4th grade science

book.

Target 22

Analyze data and calculate central

tendencies. Recognize

and explain the effects of outliers on the

mean. Create and

analyze stem and leaf, box and whisker, and

scatter plots. Analyze

charts and graphs for inconsistencies and

inaccuracies.

Note: Central

tendencies and

Measures of center are synonymous : Mean,

Median, Mode, and

Range

Trend

Mean Median

Mode

Range Outliers

Cafeteria Survey

Ask students to come up with five different questions to ask 50 people in the school about what foods they'd like to see in the cafeteria. The questions

should ideally suggest five different food suggestions, but the creative angle

is up to the students. The students then will decide the best way to graph and chart the results of their survey.

Assessment: completed activity

Resources

http://www.ixl.com/math/grade-7 Student practice problems and activities



“Finding mean, median, and mode” 7.SP.B.3 & 4 “Exploring mean & median” 7.SP.B.3 & 4


“Mr. Briggs class likes math” 7.SP.A.1

Cafeteria Survey

MP #4- Modeling MP #5- Appropriate tools

MP #6- Precision (labeling)






17

Math Practices:

CCSS MP 1

Make sense of

problems and

persevere in

solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.

They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a

solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and

simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change

course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the

viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain

correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships,

graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize

and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually

ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify

correspondences between different approaches.

CCSS MP 2

Reason

abstractly and

quantitatively

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary

abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and

represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to

their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents

for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering

the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different

properties of operations and objects

CCSS MP 3

Construct

viable

arguments and

critique the

reasoning of

others

Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing

arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to

analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate

them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into

account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two

plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain

what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such

arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to

determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they

make sense, and ask useful questions to clarify or improve the arguments.

CCSS MP 4

Model with

Mathematics

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the

workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student

might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use

geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically

proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated

situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their

relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships

mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on

whether the results make sense, possibly improving the model if it has not served its purpose


18

CCSS MP 5

Use appropriate

tools

Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil

and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic

geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions

about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example,

mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They

detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they

know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions

with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as

digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and

deepen their understanding of concepts

CCSS MP 6

Attend to

Precision

Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and

in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.

They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They

calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the

elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to

examine claims and make explicit use of definitions

CCSS MP 7

Look for and

make use of

structure

Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and

seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes

have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property.

In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing

line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an

overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being

composed of several objects. For example, they can see 5 – 3(x – y)2 as 5 minus a positive number times a square and use that to realize

that its value cannot be more than 5 for any real numbers x and y

CCSS MP 8

Look for and

express

regularity in

repeated

reasoning

Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper

elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude

they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line

through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms

cancel when expanding (x – 1)(x + 1), (x – 1)(x2 + x + 1), and (x – 1)(x

3 + x2 + x + 1) might lead them to the general formula for the sum

of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while

attending to the details. They continually evaluate the reasonableness of their intermediate results.


19

Envisioning: “CCSS Unpacked”

Ratios of Proportional Relationships 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems.

Major Cluster Explanations and Examples Mathematical Practices

7.RP.A.1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks ½ mile in each ¼ hour, compute the unit rate as

the complex fraction ½/¼ miles

per hour, equivalently 2 miles per hour.

Step 2: Explain the numbered standard in your own words: Calculate unit rate where the ratios are expressed as fractions and in quantities of like or different units. Example: 1. If two dozen cookies require 1 ¼ cups of sugar, how much sugar would be needed for a total of 3 dozen cookies? 2. A student reads 4/5 of a page in 1/12 of an hour. How many pages will they read in 1 hour? Example: A PARCC released question: “Spicy Vegetables” Note: the released question also assesses 7.EE.B.3 http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html

Step 3: Questions to develop mathematical thinking.

MP 1 What do you know that is not stated in

the problem?

MP 2 What is the relationship of the

quantities?

MP 3 Can you convince the rest of us that your

answer makes sense?

MP 4 What are some ways to represent the

quantities?

MP 5 In this situation, would it be helpful to

use a number line, diagram, manipulative,…?

MP 6 How could you test your solution to see if

it answers the problem?

MP 7 What ideas that we have learned before

were useful in solving this problem?

MP 8 What predictions or generalizations can

this pattern support?

http://www.ccsstoolbox.com/parcc/PARCCPrototype_main.html


20

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices.

Calculate unit rate using mathematical operations and ratios as fractions.

Step 5: What resource(s) will your team use to support student learning of the content and math practices?


21



7.RP.A.2. Recognize and represent proportional relationships between quantities. a. Decide whether two

quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

Step 2: Explain the numbered standard in your own words: Students will identify two quantities, decide on the proportionality, and justify their solution on a table and/or a coordinate plane. They will argue the solution as a line in relation to the origin (0,0). Example: Explain a situation where the relationship between quantities is proportional. Proportional relationship – line passes through the origin

# of dogs 0 1 2 3 4 n

# of dog legs 0 4 8 12 16 4n

Linear but not Proportional relationship – line does not pass through the origin a boat rental of $5 plus $3/h

# of hours 0 1 2 3 4 n

Cost ($) 5 8 11 14 17 5 + 3n

Step 3 Questions to develop mathematical thinking.

MP 1 How will you use that information?

MP 2 What is the relationship of the

quantities?

MP 3 What is the same and what is different

between the two scenarios given?

MP 4 How would it help to create a diagram, a

graph, an equation, or a table?

MP 5 What mathematical tools could we use to

visualize and represent the situation?



MP 7 What are other problems that are similar

to this one?

MP 8 What mathematical consistencies do you

notice?


22

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Students will represent a relationship between quantities on a graph. Is the relationship proportional? Does the line pass through the origin?



23



7.RP.A.2. Recognize and represent proportional relationships between quantities. b. Identify the constant of

proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Step 2: Explain the numbered standard in your own words: Calculate the unit rate from given tables, graphs, equations, and diagrams. In addition, students will identify and discuss the proportional relationships. Example: If 13 key chains cost $38.35, what is the cost of 20 key chains? Represent the quantities and unit rate in a table, graph the results, and write an equation. Draw a diagram and describe the situation in words. FYI…. Unit rate is just a calculation of slope. However, “slope” is not explicitly discussed until 8

th grade in CCSS.


MP 1 Could you try this with simpler numbers?

MP 2 What do the numbers used in the

problem represent?

MP 3 How did you test whether your approach

worked?

MP 4 What is an equation or expression that

matches the table and graph?

MP 5 What approach are you considering

trying first?

MP 6 How do you know your solution is

reasonable?

MP 7 In what ways does this problem connect

to other mathematical concepts?


24

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Identify the unit rate from a given set of data, graph, table, diagram, or equation.



25



7.RP.A.2. Recognize and represent proportional relationships between quantities. c. Represent proportional

relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

Step 2: Explain the numbered standard in your own words: Formulate an equation that represents a proportional relationship within a mathematical problem. Example: Fischer, Max “Go Figure: 102 Math Word Problems Based on Actual News Stories” An Australian man accidently fell 130ft out of a helicopter and landed without injury. If his fall took 3 seconds, how fast (in mph) was he traveling when he hit the ground?


MP 1 What is the problem asking?

MP 2 How do you know your answer is

reasonable?

MP 3 What mathematical evidence would

support your solution?

MP 4 How can you use a simpler problem to

help you find the answer?

MP 5 What could you use to help you solve the

problem?

MP 6 How can you use math vocabulary in

your explanation?


26

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Write an equation to model the situation.



27



7.RP.A.2. Recognize and represent proportional relationships between quantities. d. Explain what a point (x, y)

on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Step 2: Explain the numbered standard in your own words: Determine if a relationship is proportional by graphing the situation’s quantities and exploring the line’s relationship to the origin (0,0) and the unit rate (1,r) Example: From the given data table… Cat food

# of cans 0 5 10 15

Cost ($) 0 1.25 2.50 3.75

Find the unit rate and label the corresponding coordinate pair on a graph. Describe the proportional relationship.


MP 1 How would you describe the problem in

your own words?

MP 2 How is the cost of each can related to the

total cost?

MP 3 How did you decide to try that strategy?

MP 4 What number model could you construct

to represent the quantities?

MP 5 How would estimation help you solve the

problem?

MP 6 How are you showing the meaning of the

quantities?

MP 7 How did you discover that pattern?

MP 8 What might be a shortcut for finding unit

rate?


28

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Prove a proportional relationship between two quantities on a graph.



29



7.RP.A.3. Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

Step 2: Explain the numbered standard in your own words: Students will use quantitative relationships to solve real-world ratio and proportion problems. Example: The original cost of a pair of boots was $89. The tax rate in New Mexico is 7%. If the boots are discounted 25%, calculate the total cost, including tax. What would be the cost of the boots next week with an additional 15% discount?


MP 1 What information is given in the

problem?

MP 2 What do the numbers used in the

problem represent?

MP 3 How did you decide what the problem

was asking you to find?

MP 4 What are some ways to represent the

quantities?

MP 5 What estimate did you make for the

solution?

MP 6 How are you showing the meaning of the

quantities?


30

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Students will calculate simple interest, tax, tip, commission, and percent change.



31

The Number System 7.NS.A Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.


7.NS.A.1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. a. Describe situations in which

opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Step 2: Explain the numbered standard in your own words: Students will describe and illustrate siutations where addivie inverses combine to result in zero.

a + (-a) = 0 Example: Your rent payment of $525 is due on the first of each month. Unfortunately, you do not get paid until the 5

th and you are running low on

cash. You borrow $525 from your parents to pay your rent. On the 5th

, your check is exactly $525. After you repay your parents, how much cash do you have until your next pay check? Represent your solution at least three different ways.


MP 1 What are some other strategies you may

try?

MP 2 What properties might we use to find a

solution?

MP 3 How did you test whether your approach

worked?

MP 4 What number model could you construct

to represent the problem?

MP 5 What mathematical tools could we use to

visualize and represent the situation?



MP 7 What are other problems that are similar

to this one?

MP 8 What is happening in this situation?


32

Step 4: Describe (in student friendly language) how students will demonstrate understanding of the mathematical content and practices. Students will understand a number and its opposite combined equals zero.


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7th Grade Math Curriculum Map Maps/Math gr 7... · 7th Grade Math Curriculum Map ... an intense focus on the most critical material at each grade allows depth in learning, ... Quarter