G MAT H

S T R A N D - B Y- S T R A N D

ALGEBRA E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO C ON NEC TE D T O T H E C OM M ON C OR E STA N D AR D S

RALLY! EDUCATION 22 Railroad Avenue Glen Head, NY 11545 888-99-RALLY Fax: 1-516-671-7900 www.RALLYEDUCATION.com LESLIE@RALLYEDUCATION.com …………………………………………………………………………………………………………………………

Math Problem-Solving Skills & Strategies by Strand

………….. Math Strand-by-Strand Aligned to the Common Core State Standards Grade Levels 3–8

• Focuses on 5 specific math strands Number Sense & Operations, Measurement, Geometry, Statistics & Probability, Algebra

• Guided & independent practice with hints Each book provides math problem-solving practice. Hints offer strategies to help students solve the problem

Class Set: 10 Copies of each Strand Book – Total of 50 books Level C D E F G H

Grade 3 4 5 6 7 8

______ 6002-5 6003-2 6004-9 6005-6 6006-3 6007-0

----------------------------------------------

888-99-RALLY www.RALLYEDUCATION.com

LEVEL M AT H

G

S T R A N D - B Y- S T R A N D

ALGEBRA E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B N INO ATN H E MPLE CSSOIONN N ISECT A D S E C E D T S U I I D TH PERM REPRO C OM MON CO R E STA N D A R D S

To the Teacher Math Strand-by-Strand prepares students to succeed on the student expectations that appear on math tests. The program is organized into five books: • Number Sense and Operations • Algebra • Geometry • Measurement • Statistics and Probability Each student expectation has Guided Practice and Independent Practice math problems. The Guided Practice math problems have a hint for every problem. The hints offer strategies to help students solve the problem. Students are introduced to several different problem-solving strategies:

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Draw a Picture or Diagram Make a Chart or List, Graph, Sort Data Work Backwards Write a Number Sentence, Use Ratio or Proportion Use a Formula or Rule Guess and Check

STER. A M E IN In the Independent Practice section, students respond to four math for each ACKLproblems L B A T E O student expectation on their own. T IS N BOOK TO B I . D E T THIS YRIGH from R In each book, there are student expectations the particular grade level as well as, P O O F C N S E I . V Y I K A G O when appropriate, student T the previous NOfrom ANY W grade that are important LE BOexpectations S I P N I M N A D O I S E building blocks IStoS review.PRODUC THIS for students PERM RE The RALLY! Math Strands are connected to the Common Core State Standards: • Operations & Algebraic Thinking • Number & Operations in Base Ten • Number & Operations—Fractions • Measurement & Data • Geometry

ISBN 978-1-4204-6270-8 R 6270-8 Copyright ©2012 RALLY! EDUCATION. All rights reserved. No part of the material protected by this copyright may be reproduced in any form by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the copyright owner. Printed in the U.S.A. 0811.MAQ RALLY! EDUCATION • 22 Railroad Avenue, Glen Head, NY 11545 • (888) 99-RALLY

2 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Contents – Algebra Variables and Expressions . . . . . 4 Grade 7 Student Expectation

Guided Practice

Independent Practice

7.A.1 . . . . . . . . . . . . . 5 . . . . . . . . . 6 7.A.2 . . . . . . . . . . . . . 8 . . . . . . . . . 9 7.A.3 . . . . . . . . . . . . . 11 . . . . . . . . 12 Equations and Inequalities. . . . 13 Grade 7 Student Expectation

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Guided Practice

Independent Practice

7.A.4 . . . . . . . . . . . . . 14 . . . . . . . . 15 7.A.5 . . . . . . . . . . . . . 18 . . . . . . . . 19 7.A.6 . . . . . . . . . . . . . 21 . . . . . . . . 22

STER. A M E ACKLIN L B A S NOT OK TO BE I T I Grade 7 . GHTED OR THIS BO I R Student Guided Independent Y P F CO Expectation PracticeOOK IS Practice T GIVEN AY. W Y O B N N E A L IS 7.A.7 . . . . . . .IS . .S. A. M . .P26 . . . I.S.S.IO . .N28 ED IN C U H D M T O PER. . . . . . . . 33 7.A.8 . . . . . . . . . . . . . 32 REPR Patterns, Relations and Functions. . . . . . . . . . . . . . 25

Grade 7 Student Expectation

Guided Practice

Independent Practice

7.A.9 . . . . . . . . . . . . . 35 . . . . . . . . 36 7.A.10 . . . . . . . . . . . . 39 . . . . . . . . 40

3 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Variables and Expressions E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Student Expectation

7.A.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Translate two-step verbal expressions into algebraic expressions 7.A.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Add and subtract monomials with exponents of one

STER. A M E 7.A.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.L.A.C.K.L.IN . 11 A T O Identify a polynomial as an algebraic expression O BE S N containing I T T K I O . one or more terms GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

4 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.1 1

Variables and Expressions Translate two-step verbal expressions into algebraic expressions

This week, Daniel exercised nine hours less than twice the number of hours, h, he exercised last week. What expression represents the number of hours Daniel exercised this week?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT

Guess and Check. Look at each answer choice. Check the expression against the information given in the problem.

STER. A M E 2h ⫺ 2 ACKLIN L B A 9 ⫺ 2h S NOT OK TO BE I T I . GHTED OR THIS BO I 2h ⫺ 9 R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A 2 ⫺9h B C D

5 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Ms. Cannon is a tutor. She charges $25 for travel time and $35 for each hour, h, she tutors. What expression represents the total amount Ms. Cannon charges? A (35 ⫹ 25)h B 35 ⫹ 25h C 35h ⫹ 25

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

D 35 ⫹ (25 ⫹ h)

3

Jocelyn’s age is 6 years greater than three times the age of her niece, n. What expression represents Jocelyn’s age? A 3n ⫹ 6 B 6n ⫹ 3

STER. A M E ACKLIN L B A 3(n ⫹ 6) S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

C 18n ⫹ 3n D

6 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Alan has 5 less than 3 times as many CDs as Devon, d. What expression represents the number of CDs Alan has? A 5(d ⫺ 3) B 3d ⫺ 5 C 3d ⫹ 5 D 5d ⫺ 3

5

1ᎏ the cost of a basketball, b. The cost of a soccer ball is $3 more than ᎏ2 What expression represents the cost of the softball?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

1ᎏ(b ⫹ 3) A ᎏ2 1ᎏ)b B (3 ⫹ ᎏ2 1ᎏb ⫹ 3 C ᎏ2

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

1ᎏb D 3 ⫺ ᎏ2

7 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.2 1

Variables and Expressions Add and subtract monomials with exponents of one

Simplify the expression below. 4ab ⫺ 10b ⫹ 26ab

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT

Make It Simpler. Make the expression simpler by combining the like terms 4ab and 26ab.

A 30ab

STER. A M E ACKLIN L B A 20ab S NOT OK TO BE I T I . 30ab ⫺ 10b GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

B ⫺10b C D

8 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Simplify the expression below. 3mp ⫺ 4p ⫹ 6mp ⫹ 5p A 9mp ⫺ 9p B ⫺3mp ⫹ p C 9mp ⫹ p D 18mp

3

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Simplify the expression below.

5x ⫹ 8x

A 13

STER. A M E ACKLIN L B C 13x2 A S NOT OK TO BE I T I . D 13(x ⫹ x) GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B PLE Mexpression N IS N UCED IN AN A O I S Simplify the below. S S S I I D TH PERM REPRO B 13x

4

12c ⫺3c ⫹ 7c

A 16c B 2c C 16 D 2

9 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Simplify the expression below. 23x ⫹ 18xy ⫺ 6x A 18xy ⫺ 17x B 35xy C 35y D 17x ⫹ 18xy

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

10 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.3

1

Variables and Expressions Identify a polynomial as an algebraic expression containing one or more terms

Which polynomial has three terms?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT

Guess and Check. Remember that the terms of a polynomial are the parts separated by addition or subtraction signs. Look at each answer choice. Which one has 3 parts separated by addition or subtraction signs?

STER. A M E 3x ⫺ 3xy ⫹ 8 ACKLIN L B A 9xy S NOT OK TO BE I T I . GHTED OR THIS BO I 2x2 ⫹ 4xy ⫹ 3y2 ⫺ 8 R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A 4x ⫹ 6 B C D

11 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Which polynomial has two terms? A 3a ⫹ 3b B 5a – 8ab ⫹ 7 C 2ab D a2 ⫹ 6ab ⫹ 2b2 ⫹ 5

3

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Which polynomial has one term? A 2t ⫹ t2 – 3t ⫹ 5 B 4st ⫹ 7t C 3t2

STER. A M E ACKLIN L B A BE NOT O S I T T K I O . How many terms does the polynomial below GHTED have? HIS BO I T R Y R P O O 2 I–VxEN– 3F Y WAY. K IS C x3 ⫹O2x G O T O B PLE N IS N UCED IN AN O I A 1 HIS SAM S S I D T PERM REPRO B 2 D 5t2 – 6st ⫹ 2s2 ⫹ 2

4

C 3 D 4

5

How many terms does the polynomial below have? ab2 ⫹ 2bc2 A 1 B 2 C 3 D 4

12 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Equations and Inequalities E

L P M SA N O I T Student Expectation UCA D E ! Y L L Y L A L R A R . 9 9 . 888

7.A.4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Solve multi-step equations by combining like terms, using the STER. A M distributive property, or moving variables to one side of the E ACKLIN L B equation A T E

S NO I TO B T K I O . D O E B 7.A.5 . . . . . . . . . . . . . . . .Y.R.IG . .H.T. . . . . . R . . T. H . I.S. . . . . . . . . . 18 P O O F C Solve one-stepOinequalities (positive Y. K IS Aonly) GIVENcoefficients W T O Y O B N N E A L IS P N S SAM. . . .E.R.M. I.S.S.I.O.N. . . . R. .O.D.U. C.E.D. .I . . . . . . . . . . . . . . . . . 21 THI7.A.6 P REP input values Evaluate formulas for given (surface area, rate, and density problems)

13 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.4

1

Equations and Inequalities Solve multi-step equations by combining like terms, using the distributive property, or moving variables to one side of the equation

Solve for x in the equation below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 3(2x ⫹ 1) – 5 ⫽ 5x ⫹ 8 ⫺ x

HINT

Use a Formula or Rule. First, use the distributive property to clear the parentheses from the left side of the equation. Then combine like terms and solve for x.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH Answer PERM REPRO Show your work.

On the lines below, explain how to use the distributive property to help you solve this equation.

14 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

What value of x makes the equation below true? x –ᎏ 5 ᎏ 6 ⫽8 A 13 B 25 C 38 D 53

3

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Isabel must solve the equation 9x ⫹ 27 ⫽ 12x. If she subtracts 9x from the left side of the equation, what should Isabel write on the right side of the equation? A 3

STER. A M E 21 ACKLIN L B A S NOT OK TO BE 21x I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

B 3x C D

15 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Tyshawn compares the prices to rent movies from two different stores in town. Only Movies

Movies 4 Less

$6 sign-up fee $1.75 per movie

$10 sign-up fee $1.25 per movie

Tyshawn wrote the equation below to determine when the two plans will cost the same. He uses m to represent the number of movies. 1.75m ⫹ 6 ⫽ 1.25m ⫹ 10

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

What number of movies must be rented for both movie plans to cost the same? Show your work.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P Answer movies O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

16 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

In the figure ABCD shown below, the total length of the sides equals 36 centimeters. B

x+2

C

2x – 6

3x – 9

A x

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 D

—— Find the length of side CD . Show your work.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B LE N IS N UCED IN AN O AnswerIS SAMP centimeters I S S I D TH PERM REPRO

17 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.5 1

Equations and Inequalities Solve one-step inequalities (positive coefficients only) (See 7.G.10)

Which is the solution of the inequality below? 8 ⫹ x ≥ 12

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT

Draw a Picture or Diagram. Draw a number line from 0 to 12. Put a dot at 8. Then count how many units you have to move to get to 12. Write the solution using the same inequality sign that is used in the inequality.

STER. A M E ACKLIN L x≥4 B A S NOT OK TO BE I T I x< 4 . – GHTED OR THIS BO I R Y P O x< –8 IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A x≥8 B C D

18 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Which is the solution of the inequality below? m ⫺ 10 > 54 A m > 44 B m < 44 C m > 64 D m < 64

3

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Which is the solution of the inequality below? 5y < – 25

A y< –5 B y< – 125 C D

STER. A M E ACKLIN L B y≥5 A S NOT OK TO BE I T I . y ≥ 125 GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

19 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Which is the solution of the inequality below? c ⫺ 10 < 32 A c < 22 B c > 22 C c > 42 D c < 42

5

Which is the solution of the inequality below?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 ᎏ2tᎏ < –6

A t ≥ 12 B t< – 12 C t≥3 D t< –3

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

20 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.6

1

Equations and Inequalities Evaluate formulas for given input values (surface area, rate, and density problems)

What is the surface area, in square centimeters, of the cube shown below?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 5 cm

STER. A M E ACKLIN L B 5 cm A S NOT OK TO BE I T I . GHTED OR2THIS BO I R Y P CO SurfaceGIArea VEN ⫽F 6s Y WAY. K ISTotal O T O O B MPLE SSION IS N UCED IN AN A S S I D TH RMI E P REPRO HINT 5 cm

Use a Formula or Rule. Use the formula shown to find the surface area of the cube. Substitute the length of one side of the cube for s and then find the value.

A 30 B 125 C 150 D 900

21 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

What is the surface area, in square inches, of the cylinder shown below?

5 in. 10 in.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Total Surface Area ⫽ 2πrh ⫹ 2πr2

STER. A M E ACKLIN L B 150π A S NOT OK TO BE I T I . 200π GHTED OR THIS BO I R Y P O 250π IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A 100π B C D

3

What is the density, in grams per cubic centimeter, of an object if the mass is 15 grams and the volume is 5 cm3? mass Density ⫽ ᎏ voluᎏ me A 45 B 18 C 12 D 3

22 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

What is the surface area, in square centimeters, of the rectangular prism shown below?

3 cm 5 cm 6 cm

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 Total Surface Area ⫽ 2wl ⫹ 2lh ⫹ 2wh

A 126 B 90 C 63

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . D in 4.5Hhours. IS BO What was GHTEmiles Mr. Alba drove his car a distanceYof 243 I T R R P O F S CO in miles EN hour? Mr. Alba’s average rateOK ofIspeed IVper AY. G W T O Y O B N N E A L AMP ON IS DUCED IN THIS S PERMISSI Rate distan ce ᎏ REPRO⫽ ᎏ tim e D 14

5

A 238.5 B 60 C 54 D 44

23 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

24 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Patterns, Relations and Functions E

L P M SA N O I T Student Expectation UCA D E ! Y L L Y L A L R A R . 9 9 . 888

7.A.7 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Draw the graphic representation of a pattern from an STER. A M equation or from a table of data E LIN

BLACK E A T O 7.A.8 . . . . . . . . . . . . . . . . . . . . . . . . .IT. .I.S. N . . . . . . . . K. .T.O. .B32 . D E BOO S HTcharts/tables, I Create algebraic patterns Yusing graphs, G H I T R COP N FOR S E I equations, andOexpressions V I K AY. G W T O Y O B N N E A L IS P N S SAM. . . .E.R.M. I.S.S.I.O.N. . . . R. .O.D.U. C.E.D. .I . . . . . . . . . . . . . . . . . 35 THI7.A.9 P REP Build a pattern to develop a rule for determining the sum of the interior angles of polygons

7.A.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Write an equation to represent a function from a table of values

25 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.7

1

Patterns, Relations and Functions Draw the graphic representation of a pattern from an equation or from a table of data

Complete the table of values for the equation y – 2x ⫽ 3.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

HINT

Work Backwards. Replace x in the equation with ⫺2 to get the equation y ⫺ (⫺4) ⫽ 3. Then work backwards by adding ⫺4 to 3 to find the value of y. Repeat the process for each value of x.

STER. A M E ACKLIN L B A ⫺2 S NOT OK TO BE I T I . D ⫺1YRIGHTE HIS BO T R P O O F K IS C 0 OT GIVEN NY WAY. O O B MPLE SSION IS N UCED IN A A S S I I D 1 TH PERM REPRO x

y

26 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Using the table of values, graph the line of the equation on the coordinate plane below. y 5 4 3 2 1 25 24 23 22 21 0 21

1

2

3

4

5

x

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 22 23 24 25

27 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Complete the table of values for the equation y ⫹ 3x ⫽ 5. x

y

0 1

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 2 3

Using the table of values, graph the line of the equation on the coordinate plane below. y

STER. A M E ACKLIN L B 4 A S NOT OK TO BE I T I 3 . G2HTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C O 1G T O O B MPLE SSION IS N UCED IN AN A x S S I I TH PERM25 24 23RE22PR21OD0 1 2 3 4 5 5

21 22 23 24

25

28 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

Complete the table of values for the equation y – 3x ⫽ ⫺1. x

y

⫺1 0 1 2 Using the table of values, graph the line of the equation on the coordinate plane below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 y

5 4

3

STER. A M E 1 ACKLIN L B A NOT xTO BE S I T K I O . 1 2 3 4 5 25 24 23 22 21 0 TED GH HIS BO I T R 21 Y R P O O IVEN F Y WAY. K IS C G O T O 22 O B MPLE SSION IS N 23 UCED IN AN A S S I I D TH PERM REPRO 2

24 25

29 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Complete the table of values for the equation y – 2x ⫽ ⫺1. x

y

⫺1 0 1 2 Using the table of values, graph the line of the equation on the coordinate plane below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 y

5 4

3

STER. A M E 1 ACKLIN L B A NOT xTO BE S I T K I O . 1 2 3 4 5 25 24 23 22 21 0 TED GH HIS BO I T R 21 Y R P O O IVEN F Y WAY. K IS C G O T O 22 O B MPLE SSION IS N 23 UCED IN AN A S S I I D TH PERM REPRO 2

24 25

30 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Complete the table of values for the equation y ⫹ x ⫽ 2. x

y

⫺2 0 2 4 Using the table of values, graph the line of the equation on the coordinate plane below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 y

5 4

3

STER. A M E 1 ACKLIN L B A NOT xTO BE S I T K I O . 1 2 3 4 5 25 24 23 22 21 0 TED GH HIS BO I T R 21 Y R P O O IVEN F Y WAY. K IS C G O T O 22 O B MPLE SSION IS N 23 UCED IN AN A S S I I D TH PERM REPRO 2

24 25

31 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.8

1

Patterns, Relations and Functions Create algebraic patterns using charts/tables, graphs, equations, and expressions

An amoeba is a one-celled organism that reproduces by splitting into 2 amoebas. After one amoeba splits 5 times, there are 32 amoebas as shown in the table below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 AMOEBA SPLITTING

Split

Number of Amoebas

1

2

2

4

STER. A M E ACKLIN 4 16 L B A S NOT OK TO BE I T I 5 32 . GHTED OR THIS BO I R Y P NF IS CO IVEsplits? K there AY. G O W T O Y O B How many amoebas will be after 10 N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R HINT 3

8

Look for a Pattern. Look at the Number of Amoebas column in the table. What pattern do you see in the numbers? Use the pattern to find the number of amoebas after 10 splits.

A 64 B 256 C 512 D 1,024

32 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

Which expression can be used to find the nth term in the pattern below? Number of Term

Term

1

4

2

8

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 3

12

4

16

5

20

n

A n⫹4

STER. A M E ACKLIN L B C 4n A S NOT OK TO BE I T I . D 8n GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B AN N IStoNfind Uthe thIN AMPLE can Ibe D O I S E WhichHIexpression used n term in the pattern below? S C S S D T PERM REPRO B n⫹8

3

2, 5, 10, 17, 26, 37, . . .

A 2n ⫹ 1 B n2 ⫹ 1 C 2n ⫹ n D n2 ⫹ n

33 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

Carmen used blocks to build cubes. The table below shows the number of blocks Carmen used for each cube. Cube

Number of Blocks

1

1

2

8

3

27

4

64

5

125

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

If she continues the pattern, how many blocks will Carmen use to build the 7th cube? A 343 B 512 C 729

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . TEDnth termTinHIthe Which expression can be used to find S BOpattern below? GHthe I R Y R P O O IVEN20,F . . .Y WAY. K IS5, C8, 11,O14, G O 17, T O B MPLE SSION IS N UCED IN AN A S S I I A 2n TH ⫹ 3 PROD PERM E R 2

D 1,000

5

B n ⫹3

C 3n ⫹ 2 D n3 ⫹ 2

34 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.A.9

1

Patterns, Relations and Functions Build a pattern to develop a rule for determining the sum of the interior angles of polygons

What is the sum of the measures of the interior angles of the hexagon shown below?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. A M E Sum of measures of interior angles = (n ⫺ 2) ⫻ 180°, ACKLIN L B A where n is the number of sides of the O BE S NOTpolygon I T T K I O . GHTED OR THIS BO I R Y P IS CO IVEN F Y WAY. G T HINT LE BOOK O N N P IN Arule MFormula N ISYou A D O I S E Use a or Rule. can use the shown below the hexagon to S C S S U I I D M TH PERof REPROof the interior angles. find the sum the measures

A 540° B 720° C 900° D 1,080°

35 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

What is the sum of the measures of the interior angles of the pentagon shown below?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Sum of measures of interior angles = (n ⫺ 2) ⫻ 180°, where n is the number of sides of the polygon

A 180° B C D

TER. S A M E 270° ACKLIN L B A 360° S NOT OK TO BE I T I . 540° GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

36 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

What is the sum of the measures of the interior angles of the octagon shown below?

Sum of measures of interior angles = (n ⫺ 2) ⫻ 180°, where n is the number of sides of the polygon

A 1,080° B 1,260° C 1,440° D 1,620°

4

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

STER. A M E KLIN ACquadrilateral L What is the sum of the measures of the interior angles of the B A S NOT OK TO BE I shown below? T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

Sum of measures of interior angles = (n ⫺ 2) ⫻ 180°, where n is the number of sides of the polygon A 180° B 360° C 540° D 720°

37 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

What is the sum of the measures of the interior angles of the decagon shown below?

Sum of measures of interior angles = (n ⫺ 2) ⫻ 180°, where n is the number of sides of the polygon

A 1,080° B 1,260° C 1,440° D 1,620°

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

38 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Guided Practice Directions: Use the hint to help you solve the problem.

Band: Patterns, Relations and Functions 7.A.10 Write an equation to represent a function from a table of values 1

Carlton conducted an experiment on the growth rate of mold. The table below shows his results.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 GROWTH RATE OF MOLD

Number of Hours (h)

Mold Spores (m)

0

30

1

68

2

106

STER. A M E ACKLIN L B A Write a function rule for the number of mold spores, h hours. O BE S NOTm, after I T T K I O . GHTED OR THIS BO I R Y P HINT IS CO IVEN F Y WAY. K G O T O O B Look for Find N differenceINinANthe number of mold spores from MPLaE Pattern. N ISthe A O I S S S S UCEDsee? Then think about how you will use I I hour to hour. What pattern do you D TH O R ERM P P E the beginning numberRof mold spores, 30, in your function rule. 3

144

Answer What will the number of mold spores be after 6 hours? Show your work.

Answer

mold spores

39 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

Independent Practice Directions: Solve the problems on your own.

2

The table below shows a relationship between x and y. x

y

2

10

6

14

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 8

16

9

17

12

20

What equation represents the relationship between x and y? A y ⫽ 2x

STER. A M E CKLIN A L B A y⫽x⫹8 S NOT OK TO BE I T I . y ⫽ 2x ⫹ 6 GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

B y ⫽ 5x C D

40 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

3

The table below shows a relationship between x and y. x

y

2

3

4

7

6

11

8

15

10

19

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

What equation represents the relationship between x and y? A y ⫽ 2x

B y⫽x⫹1

C y ⫽ 2x ⫹ 1 D y ⫽ 2x – 1

41 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

4

The table below shows the number of teachers, y, needed for a certain number of students, x, on a school field trip. SCHOOL FIELD TRIP Number of Students (x)

36

54

72

108

Number of Teachers (y)

4

6

8

12

Write an equation that represents the relationship between the number of teachers needed and the number of students going on the field trip. Answer

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

How many teachers will be needed for a field trip that has 198 students? Answer

teachers

42 ÂŠ R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

5

Anton puts money into a savings account each month. The table below shows his savings account balance for the last four months. ANTON’S SAVINGS ACCOUNT Month (m)

Savings Balance (b)

1

$191

2

$307

3

$423

4

$539

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Write a function rule for the savings balance, b, after m months. Answer

How much money will Anton have in his savings account after 12 months? Show your work.

Answer $

43 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

44 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

45 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

46 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

47 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

48 © R A L LY ! E D U C AT I O N . N O PA R T O F T H I S D O C U M E N T M AY B E R E P R O D U C E D W I T H O U T W R I T T E N P E R M I S S I O N O F T H E P U B L I S H E R .

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

G

Strand Strand BY

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8

Math Strand-by-Strand provides instructional practice in math problem-solving. Students are taught several different problem-solving strategies. Each of the 5 math strands are in a separate book: • • • • •

Number Sense and Operations Algebra Geometry Measurement Statistics and ProbabilityIGHTED.

STER. A M E ACKLIN L B A E OT IT IS N BOOK TO B THIS YR R P O O F C GIVEN NY WAY. OK IS T O O B N E L IN A MP N IS A D O I S E S C S S U I I D TH PERM REPRO

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