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G MAT H

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

NUMBER SENSE OPERATIONS — AND —

E L P M SA N O I T A C U D E ! Y L L Y L A L R A R . 9 9 . 888

TER. S A M KLINE C A L B NOT A K TO BE S I T I O . GHTED OR THIS BO I R Y P EN F IS CO V I K AY. G O W T O Y O B N N E A AMPL D IN ON IS THIS S PERMISSI EPRODUCE R 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

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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

NUMBER SENSE OPERATIONS — AND —

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


Number NUMBER Sense and Operations SENSENumb AN 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 Work Backwards Use a Formula or Rule

Make a Chart or List, Graph, Sort Data Use Manipulatives or Act Out Write a Number Sentence, Use Ratio or Proportion Make it Simpler Look for a Pattern

Guess and Check Make Estimates

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 ANY W grade that are important LE BOexpectations S NOfrom 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 978-1-4204-6264-7 R 6264-7 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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Contents – Number Sense and Operations Number Systems . . . . . . . . . . . . 4

Estimation . . . . . . . . . . . . . . . . 62

Grade 7

Grade 7

Student Expectation

Guided Practice

Independent Practice

Student Expectation

7.N.1 . . . . . . . . . . . . . 5 . . . . . . . . . 6 7.N.2 . . . . . . . . . . . . . 8 . . . . . . . . . 9 7.N.3. . . . . . . . . . . . . 11 . . . . . . . . 12 7.N.4. . . . . . . . . . . . . 14 . . . . . . . . 15 7.N.5. . . . . . . . . . . . . 17 . . . . . . . . 18 7.N.6. . . . . . . . . . . . . 20 . . . . . . . . 21 7.N.7. . . . . . . . . . . . . 23 . . . . . . . . 24

Guided Practice

Independent Practice

7.N.18. . . . . . . . . . . . 63 . . . . . . . . 64 7.N.19. . . . . . . . . . . . 65 . . . . . . . . 67

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

Number Theory . . . . . . . . . . . . 27 Grade 7 Student Expectation

Guided Practice

Independent Practice

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 Operations . . . . . . . . . . . .O.K. I.S. C37 IVEN F Y WAY. G T O O B MPLE SSION IS N UCED IN AN Grade 7 A S S I I D TH Student Guided PERM Independent REPRO 7.N.8. . . . . . . . . . . . . 28 . . . . . . . . 29 7.N.9. . . . . . . . . . . . . 30 . . . . . . . . 31 7.N.10. . . . . . . . . . . . 32 . . . . . . . . 34

Expectation

Practice

7.N.11. . . . . . . . . . . . 38 7.N.12. . . . . . . . . . . . 41 7.N.13. . . . . . . . . . . . 46 7.N.14. . . . . . . . . . . . 52 7.N.15. . . . . . . . . . . . 55 7.N.16. . . . . . . . . . . . 58 7.N.17. . . . . . . . . . . . 60

Practice

. . . . . . . . 39 . . . . . . . . 43 . . . . . . . . 48 . . . . . . . . 53 . . . . . . . . 56 . . . . . . . . 59 . . . . . . . . 61

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 .


Number NUMBER Sense and Operations SENSENumb AN

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

Student Expectation

7.N.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers.)

ER.

7.N.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . 8MAST N I L Recognize the difference between rational and irrational BLACK E A T O N of π.)K TO B numbers (e.g., explore different approximations O . IT IS

GHTED OR THIS BO I R Y P 7.N.3. . . . . . . . K . . I.S. C. O . . . . . . . .I.V.E.N. F. . . . . . . . .Y. . . . . . . . 11 O TG O Y WA Onumbers B N N E PlaceMrational and irrational (approximations) on a A L S I P N I N A D O I S E S C S S U I I D and justify the placement of the numbers TH number Pline ERM REPRO

7.N.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 Develop the laws of exponents for multiplication and division 7.N.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Write numbers in scientific notation 7.N.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Translate numbers from scientific notation into standard form 7.N.7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Compare numbers written in scientific notation

4 Š 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 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.1

1

Number Systems Distinguish between the various subsets of real numbers (counting/natural numbers, whole numbers, integers, rational numbers, and irrational numbers.)

The set below contains only which type of numbers?

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 ᎏᎏ (⫺6, 0, 8ᎏ1ᎏ, 17, 25.2, 33, √6 4, 100) 2

HINT Organize—Make a Chart or List, Graph, Sort Data. Make four columns and label them with the four types of numbers shown in the answer choices. Sort each number in the set above into one or more of the types of numbers. Choose the type that has all of the numbers listed underSTit.ER.

A B C

E MA N I L K C A BLA BE T O N . IT IS IS BOOK TO D E T H mixed numbers PYRIG EN FOR TH . O C S I rational numbersOOK AY GIV W T Y O B N N E A L AMP ION IS ODUCED IN whole S S I M THIS Snumbers P ER REPR

D counting numbers

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

Which number is an irrational number? A 4.8 3ᎏ B ᎏ5 C ⫺2 ᎏᎏ D √13

3

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

The set below contains only which type of numbers? (⫺5, ⫺3, ⫺1, 0, 1, 3, 5, 7)

STER. A M E CKLIN A L B A mixed numbers S NOT OK TO BE I T I . whole numbers GHTED OR THIS BO I R Y P counting numbersOK IS CO IVEN F Y WAY. G T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

A integers B C D

4

Which number is a counting number? A 12 B ⫺13.5 C ᎏ7ᎏ 11 1 D ᎏᎏ √ᎏ 9

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 ND ber Sense OPERATIONS and Operations Number Sense 5

The set below contains only which type of numbers? (0, 17, 95, 100, 275, 650, 990) A mixed numbers B counting numbers C whole numbers D irrational numbers

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

7 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.2

1

Number Systems Recognize the difference between rational and irrational numbers (e.g., explore different approximations of π.)

Which number is an irrational number?

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

HINT Guess and Check. Remember that an irrational number cannot be represented as an exact ratio of two integers; and the decimal form of the number never terminates and never repeats. Use what you know about rational and irrational numbers to check each answer choice.

A B C

STER. A M E ᎏᎏ √3 2 ACKLIN L B A S NOT OK TO BE I T I . ⫺ᎏ 1 ᎏ GHTED OR THIS BO I R 5 Y P O IVEN F Y WAY. K IS C G O T O O B 1.6 苶 MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO ᎏ

D ⫺√9

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Which number is a rational number? ᎏᎏ A √2 5 ᎏ ᎏ B √29 ᎏ C ⫺√5 ᎏᎏ D ⫺√1 5

3

苶 A 2.3 3ᎏ B ⫺4ᎏ4

STER. A M E ACKLIN L B A ᎏ S NOT OK TO BE I D ⫺√7 T I . GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B IS N IN AN Nnumber? AMPisLEa rational D O I S WhichHInumber E S C S S U I D T PERM REPRO C 1.98

4

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

Which number is an irrational number?

1 A ᎏ ᎏᎏ ᎏ √1 0 1 B ᎏ ᎏ ᎏ √ᎏ 36 3 C ᎏ ᎏ ᎏ √ᎏ 11 ᎏᎏ D ⫺√85

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 .


Number NUMBER Sense and Operations SENSENumb AN 5

Which number is an irrational number? ⫺ᎏ 3 A ᎏ 7 ᎏ B √3 C 1.1 ᎏᎏᎏ D ⫺√144

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.3

1

Number Systems Place rational and irrational numbers (approximations) on a number line and justify the placement of the numbers

Points P, R, S, and T are graphed on the number line shown below.

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

P 1

R

1.5

S

2

T

2.5

3

ᎏ? Which point on the number line represents √5

STER.

HINT E MA N I L K C LAᎏ Make Estimates. Estimate a decimal equivalent OT AforB √5. ThenE choose the

T IS N BOOK TO B I T YRIGH N FOR THIS P O C AY. GIVE OK IS W T O Y O B N N E A L AMP D IN ON IS point THIS SP PERMISSI EPRODUCE R point that is closest to your estimate. ED.

A

B point R C point S D point T

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

Points A, B, C, and D are graphed on the number line shown below.

A 3

B 3.5

C

D 4

4.5

5

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

ᎏᎏ Which point on the number line represents √1 7? A point A B point B C point C D point D

3

STER. A M E ACKLIN L B A Point T is graphed on the number line shown below. S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P O TOOK IS C IVEN F Y WAY. G T O B MPLE SSION IS N UCED IN AN A S S I D TH RMI E P REPRO 0 21 1

Which rational number is represented by point T? A ⫺0.625 B ⫺0.25 C 0.625 D 0.25

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense 4

Point X is graphed on the number line shown below.

X 6

8

7

Which irrational number is represented by point X? ᎏ A √7 ᎏᎏ B √5 0 ᎏᎏ C √7 1 ᎏᎏ D √9 0

5

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

Points K, M, N, and P are graphed on the number line shown below.

STER. A M E ACKLIN L B A 22 21 0 S NO1T OK TO B2E I T I . GHTED OR THIS BO I R Y P O F IVEN⫺1.25? K IS Cline represents AY. G Which point on theBO number O W T Y O N N E A L AMP D IN ON IS A point THIS SK PERMISSI EPRODUCE R K

M

N

P

B point M C point N D point P

13 © 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.4 1

Number Systems Develop the laws of exponents for multiplication and division

Simplify the expression below. 43 ⫻ 42

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

HINT Use a Formula or Rule. You can use the law of exponents for multiplication: abac = ab + c.

A 1,024

STER. A M E ACKLIN L B A 80 S NOT OK TO BE I T I . 16 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 256 C D

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Simplify the expression below. 33 ⫻ 32 A 9 B 81 C 243 D 729

3

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

Simplify the expression below.

65 ⫼ 63

A 7,560

STER. A M E ACKLIN L B C 36 A S NOT OK TO BE I T I . D 12 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 213

4

43 ⫻ 41

A 16 B 64 C 128 D 256

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 .


Number NUMBER Sense and Operations SENSENumb AN 5

Simplify the expression below. 108 ⫼ 104 A 100 B 10,000 C 100,000 D 1,000,000,000,000

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

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.5 1

Number Systems Write numbers in scientific notation

The maximum distance between the sun and Mercury is 43.4 million miles. What is 43.4 million written in scientific notation?

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

HINT Guess and Check. Write 43.4 million in standard form. Then write it in scientific notation. Check each answer choice for the one that matches your number in scientific notation.

TER. S A M E 4.34 ⫻ 107 ACKLIN L B A 43.4 ⫻ 108 S NOT OK TO BE I T I . GHTED OR THIS BO I 4.34 ⫻ 108 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 43.4 ⫻ 107 B C D

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

In the year 2006, approximately 240,000,000 personal computers were in use in the United States. What is 240,000,000 written in scientific notation? A 24 ⫻ 107 B 24 ⫻ 108 C 2.4 ⫻ 107

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

D 2.4 ⫻ 108

3

The minimum distance between Earth and Jupiter is 366 million miles. What is 366 million written in scientific notation? A 3.66 ⫻ 108 B 3.66 ⫻ 107

STER. A M E ACKLIN L B 7 A D 36.6 ⫻ 10 S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P F CO IS our Y. old. What is 13.7 IVisEN13.7 Kthat Ayears G O W T O Some scientists Lbelieve universe billion Y O B N N E A P N IS IOnotation? ED IN S C billion S SAM in scientific S U I D M THIwritten O P ER REPR 10 C 36.6 ⫻ 108

4

A 137 ⫻ 10

B 13.7 ⫻ 1011 C 1.37 ⫻ 1011 D 1.37 ⫻ 1010

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense 5

In the year 2006, approximately 10,500,000,000 bushels of corn were produced in the United States. What is 10,500,000,000 written in scientific notation? A 10.5 ⫻ 1010 B 10.5 ⫻ 1011 C 1.05 ⫻ 1010 D 1.05 ⫻ 1011

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

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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.6 1

Number Systems Translate numbers from scientific notation into standard form

The table below shows geographical information about Asia. ASIA

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

1.19 ⫻ 107 square miles

Lowest elevation

⫺1.348 ⫻ 103 feet

Write the numbers, in standard form, for the area and the lowest elevation of Asia.

HINT R. Compute—Write a Number Sentence. Write a numberNEsentence MASTE

LI

CK and to find the value of 1.19 ⫻ 107. Write 107 in standard BLAform A T O BE N then multiply. OK TO . IT IS

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 Answer area lowest elevation

square miles feet

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

In 2006, the population of New York City was about 8.21 ⫻ 106. What is this number written in standard form? A 8,210,000 B 82,100,000 C 821,000,000

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

D 8,210,000,000

3

North Dakota has a total land area of 7.07 ⫻ 104 square miles. What is this number written in standard form? A 707 B 7,070

STER. A M E ACKLIN L B A 707,000 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 70,700 D

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 .


Number NUMBER Sense and Operations SENSENumb AN 4

The table below shows geographic information about the Pacific Ocean. PACIFIC OCEAN Approximate area

6.42 ⫻ 107 square miles

Lowest elevation

⫺3.584 ⫻ 104 feet

Write the numbers, in standard form, for the area and the lowest elevation of the Pacific Ocean.

Answer area

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

lowest elevation

5

square miles

feet

TER.

S The table below shows geographic information about the Mediterranean NE MA Sea. ACKLI L B A MEDITERRANEAN SEA S NOT OK TO BE I T I . GHTED 6OR THIS BO I R Y P Area IS CO 2.512 ⫻EN kilometers IV 10F square K AY. G O W T O Y O B N N 3 E A L ⫺5.15 MP elevation ALowest D IN⫻ 10 meters ON IS THIS S PERMISSI EPRODUCE R

Write the numbers, in standard form, for the area and the lowest elevation of the Mediterranean Sea.

Answer area lowest elevation

square miles feet

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 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.7 1

Number Systems Compare numbers written in scientific notation

The table below shows the average surface temperature for Mercury and Earth.

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

Planet

Temperature (in °F)

Mercury

3.33 ⫻ 102

Earth

5.9 ⫻ 101

How much warmer, in °F, is the surface temperature of Mercury than TER. S the surface temperature of Earth? Write your answer in standard INE MA CKLform.

A BLA BE T O N . IT IS IS BOOK TO HINT D E T H G H need to find how much Compute—Write Sa CNumber OR TYou OPYRI Sentence. F N E I V I MercuryYisWthan AY. the surface temperature Gof OK temperature T O warmer the surface O B N N E A L N IS in standard IOnumber SAMP WriteMeach ED IN form and then think about whether S C S U IS Earth. I D THof O P ER REPR you should add, subtract, multiply, or divide.

Show your work.

Answer

°F

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

Andrew wrote the four numbers below in scientific notation. 9.9 ⫻ 103

7.5 ⫻ 106

1.2 ⫻ 1010

3.1 ⫻ 109

Which number has the greatest value? A 9.9 ⫻ 103 B 7.5 ⫻ 106

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

C 1.2 ⫻ 1010 D 3.1 ⫻ 109

3

Selena is researching the storage capacity for four types of digital audio players. The data are shown in the table below.

STER. A M E Player Amount of Storage (in bytes) ACKLIN L B A 1 1.0 ⫻ 10 S 9NOT OK TO BE I T I . ED BO GHT2.0 10THIS I R Y 2 ⫻ 10 R P O O IVEN F 8Y WAY. K IS C G O T O O B IN⫻ A10N MPLE 3 SSION IS N UC5.12 A D S E S I I D 8 TH PE4RM REPRO 1.6 ⫻ 10 Selena wants to buy the player with the most storage. Which player should she buy? A Player 1 B Player 2 C Player 3 D Player 4

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense 4

The table below shows the number of square miles of land area for New York and Alaska. LAND AREA State

Land Area (in Square Miles)

New York

4.72 ⫻ 104

Alaska

5.72 ⫻ 105

How much greater, in square miles, is the land area of Alaska than the land area of New York? Write your answer in standard form.

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

Show your work.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . Answer square miles 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

25 © 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 .


Number NUMBER Sense and Operations SENSENumb AN 5

The table below shows the number of people in the world who speak Spanish and the number of people who speak Korean. LANGUAGE SPOKEN (2005) Language

Number of People

Spanish

3.22 ⫻ 108

Korean

6.7 ⫻ 107

How many more people speak Spanish than Korean? Write your answer in standard form.

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

Show your work.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . Answer people IGHTED HIS BO T R Y R P O 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

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense

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

Student Expectation

7.N.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Find the common factors and greatest common factor of two or more numbers 7.N.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 ER. Determine multiples and least common multiple of two or E MAST KLIN more numbers A BLAC

S NOT OK TO BE I T I . 7.N.10. . . . . . . . . . . . . . . . .IG . .H.T.E.D. . . . . . . H . I.S. .B.O. . . . . . . 32 T R Y R P O O Determine the prime number Y. and IVEofN aF givenY W K IS Cfactorization A G O T O O B writeMinPexponential LE IS N IN AN Nform A D O I S E S C S S U I I D TH PERM REPRO

27 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.8

1

Number Theory Find the common factors and greatest common factor of two or more numbers

What is the greatest common factor of 48, 80, and 96?

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

HINT Organize—Make a Chart or List. List the factors of each number. Then circle the factors that all three numbers have in common. Choose the greatest of the common factors.

STER. A M E 12 ACKLIN L B A 16 S NOT OK TO BE I T I . GHTED OR THIS BO I 24 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 4 B C D

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

What is the greatest common factor of 54, 81, and 135? A 3 B 9 C 13 D 18

3

A 9 B 15 C 18

STER. A M E ACKLIN L B A BE NOT O S I T T K I O . What is the greatest common factor of T88, 240? GH ED 120,ORand HIS BO I T R Y P O A 24 IVEN F Y WAY. K IS C G O T O O B LE N IS N UCED IN AN B 12 S SAMP O I S S I I D TH PERM REPRO C 10 D 45

4

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

What is the greatest common factor of 45, 63, and 126?

D 8

5

What is the greatest common factor of 42, 70, and 98? A 7 B 14 C 28 D 42

29 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.9

1

Number Theory Determine multiples and least common multiple of two or more numbers

What is the least common multiple of 3, 5, and 6?

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

HINT Organize—Make a Chart or List. List the first 10 multiples of each number. Then circle the multiples that all three numbers have in common. Choose the least of the common multiples.

STER. A M E 30 ACKLIN L B A 60 S NOT OK TO BE I T I . GHTED OR THIS BO I 90 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 15 B C D

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

What is the least common multiple of 8, 10, and 12? A 2 B 80 C 120 D 240

3

A 5 B 35 C 70

STER. A M E ACKLIN L B A BE NOT O S I T T K I O . What is the least common multiple of 6, D and 42?HIS BO GHTE12, I R Y P OR T O F C N S E I A 168 V AY. GI OK W T O Y O B N N E A L B 84 S SAMP ION IS ODUCED IN S S I M THI P ER REPR C 72 D 105

4

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

What is the least common multiple of 5, 15, and 21?

D 6

5

What is the least common multiple of 7, 11, and 13? A 77 B 91 C 143 D 1,001

31 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: Number Theory 7.N.10 Determine the prime factorization of a given number and write in exponential form

1

Mr. Duffy assigns homework to his mathematics class. The assignment requires students to find the prime factorization of 875.

Part A

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

What is the prime factorization of 875?

HINT Draw a Picture or Diagram. You can use a factor tree to find the prime R.

TE

S and 35. factors of 875. Start the tree with any two factors of 875 such asA25 INE M

A CK L L B A S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P Show your work. 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

Answer

32 Š 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 ND ber Sense OPERATIONS and Operations Number Sense Part B Write the result of the prime factorization of 875 in exponential form.

Answer

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

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

What is the prime factorization of 500 written in exponential form? A 22 ⫻ 53 B 23 ⫻ 52 C 23 ⫻ 53 D 24 ⫻ 52

3

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

What is the prime factorization of 324 written in exponential form? A 22 ⫻ 42 B 23 ⫻ 33 C 23 ⫻ 42

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

D 22 ⫻ 34

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense 4

Mr. Carrillo assigns homework to his mathematics class. The assignment requires students to find the prime factorization of 1,125.

Part A What is the prime factorization of 1,125? Show your work.

Answer

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 Write the result of the prime factorization of 1,125Nin BE O form. S OTexponential I T T K I O . GHTED OR THIS BO I R Y P O Answer 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

Part B

35 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN 5

Mrs. Zigler assigns homework to her mathematics class. The assignment requires students to find the prime factorization of 784.

Part A What is the prime factorization of 784? Show your work.

Answer

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 T Write the result of the prime factorization of 784 inNO BE Oform. S exponential I T T K I O . GHTED OR THIS BO I R Y P O Answer 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

Part B

36 Š 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 ND ber Sense OPERATIONS and Operations Number Sense

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

Student Expectation

7.N.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Simplify expressions using order of operations. 7.N.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Add, subtract, multiply and divide integers

STER. A M E 7.N.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .B.L.A.C.K.L.IN . 46 A T O Add and subtract two integers (with andISwithout the use N O BE T T K I O . of a number line.) GHTED OR THIS BO I R Y P O IVEN F . Y. .W. .A.Y.. . . . . . . . 52 K IS C 7.N.14. L. E. .B.O. O . . . . . . . S. .N.O. T. .G. . . . . . . A. N I P N negative and ION understanding ED Iof S C S SAM aEconceptual S U I D M THIDevelop O P R with aRbase EPR of ten and relate to fractions zero exponents and decimals. 7.N.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Recognize and state the value of the square root of a perfect square (up to 225) 7.N.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Determine the square root of non-perfect squares using a calculator 7.N.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Classify irrational numbers as non-repeating/ non-terminating decimals

37 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.11

1

Operations Simplify expressions using order of operations. Note: Expressions may include absolute value and/or integral exponents greater than 0

Simplify the expression below.

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 5(25 ⫺ 22)

HINT Use a Formula or Rule. Remember to use the order of operations. 1. 2. 3. 4.

A B C

Simplify within grouping symbols such as parentheses or brackets. Apply exponents. Multiply and divide from left to right. STER. A M E Add and subtract from left to right. CKLIN

A BLA BE T O N . IT IS IS BOOK TO D E T H G H OPYRI IVEN FOR T Y. C S 0 I OT G IN ANY WA BOOK N E L S I P M 8 A D ON THIS S PERMISSI EPRODUCE 28 R

D 140

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Simplify the expression below. 13 ⫹ 23 ⫺  ⫺4 ⫻ 5 A 16 B 14 C 10 D 0

3

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

Simplify the expression below.

10(52 + 53) ⫼ 25

A 4

STER. A M E ACKLIN L B C 60 A S NOT OK TO BE I T I . D 1,500 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 16

4

72 + 23

A 9 B 57 C 81 D 729

39 © 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 .


Number NUMBER Sense and Operations SENSENumb AN 5

Simplify the expression below.  ⫺2 ⫹ 2(33 ⫹ 62) A 36 B 63 C 128 D 164

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

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.12 1

Operations Add, subtract, multiply and divide integers

The school band raised $2,345 by selling tickets for a spaghetti dinner. Five different teams sold the tickets. Todd’s team sold 68 tickets, Kendra’s team sold 152 tickets, Mario’s team sold 87 tickets, Faith’s team sold 59 tickets, and Scott’s team sold 103 tickets.

Part A

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

Each ticket was the same price. What was the price of one ticket?

HINT STER. to A M Compute—Write a Number Sentence. First write a number sentence E IN

KL

BLAC sentence find the total number of tickets sold. Then write a number to find A T E O B N O S I T the price of one ticket. OK . IT

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 Show your work. I I D TH PERM REPRO

Answer $

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 .


Number NUMBER Sense and Operations SENSENumb AN Part B What is the difference between the amount of money raised by the team that sold the greatest number of tickets and the amount of money raised by the team that sold the least number of tickets? Show your work.

Answer $

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

42 Š 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 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

The temperature on a winter night in Schenectady is 10° Fahrenheit. The temperature decreases by 20° Fahrenheit. What is the new temperature, in degrees Fahrenheit? A 30°F B ⫺30°F C 10°F D ⫺10°F

3

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

Carl earned $25 mowing lawns on Friday. On Saturday he raked leaves for 3 hours at a rate of $6 per hour. On Sunday he went to the movies and spent $12 on a movie and popcorn. How much money did Carl have left after going to the movies? TER.

E MAS N I L K C A BLA BE T O N $31 . IT IS IS BOOK TO D E T H G H $43 OPYRI IVEN FOR T Y. C S I OT G IN ANY WA BOOK $55 N E L S I P M A D ON THIS S PERMISSI EPRODUCE R

A $19 B C D

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 .


Number NUMBER Sense and Operations SENSENumb AN 4

Emma made $741 at the crafts festival by selling pieces of pottery that she makes. She sold four different types of pottery. She sold 13 mugs, 12 plates, 5 vases, and 9 pots.

Part A Each piece of pottery was the same price. What was the price of one piece of pottery? Show your work.

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 Part B T I . GHTED OR THIS BO I R Y P What is the difference between on the type of CO the amount ENofF moneyWEmma Y. made IVsales A G OK IS number T O Y O B pottery that hadLEthe greatest of and the amount of money she made AN SN I P N I M N A D O I S E S had theOleast S of pottery on the ISthat DUC number of sales? THItype PERM REPR Answer $

Show your work.

Answer $

44 Š 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 ND ber Sense OPERATIONS and Operations Number Sense 5

Canyon Jeep Tours sold 76 tour tickets on Friday. They sold the same number of tour tickets on Saturday as they did on Sunday. The total number of tour tickets sold for the three days was 282.

Part A How many tour tickets did Canyon Jeep Tour sell on Saturday? Show your work.

Answer

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

STER. A M E ACKLIN L Part B B A S NOT OK TO BE I T I . Canyon Jeep Tours made $7,050 on ticket BO days. Each ticket was IS three GHTEDsalesORforTHthe I R Y P the same price. What is the difference between CO EN F the amount Y. of money made on IVon K ofISmoney A G O W T O Y O B Sunday and theLamount made Friday? MP E SSION IS N UCED IN AN A S S I D THyour work.PERMI Show REPRO

Answer $

45 Š 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 .


Number NUMBER Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.13

1

Operations Add and subtract two integers (with and without the use of a number line.)

The temperature in Fairbanks, Alaska, was ⫺3°F on February 2 and 11°F on February 3.

Part A

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

On the number line below, plot the temperatures for February 2 and February 3. Be sure to label both points with the appropriate date.

STER. A M E ACKLIN L B A T 214 212 210 28 26 24 22 0 2IT IS4NO 6 O8K TO10BE 12 14 . 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

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense Part B How many degrees warmer was it on February 3 than on February 2?

HINT Use Manipulatives or Act Out. On your number line, count the units from the lower temperature to the higher temperature to find how many degrees warmer it was.

Show your work.

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

Answer

°F

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 .


Number NUMBER Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

The normal mean temperature in January for Barrow, Alaska, is ⫺14°F. The normal mean temperature in January for Duluth, Minnesota, is 8°F.

Part A On the number line below, plot the normal mean temperatures in January for Barrow and Duluth. Be sure to label both points with the appropriate city.

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

214 212 210 28 26 24 22

0

2

4

6

8

10

12

14

STER. A M E ACKLIN L B A Part B S NOT OK TO BE I T I . HIS BO in January IGHTEDmean T YRnormal How many degrees warmer CisOthe temperature R P O EN F IS for Barrow, IVAlaska? Kthan AY. G O W for Duluth, Minnesota, T O Y O B N N E A L MP ION IS ODUCED IN S S IS SAwork. I M THyour Show P ER REPR

Answer

°F

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 .


4 ND ber Sense OPERATIONS and Operations Number Sense 3

The elevation of Death Valley, California, is ⫺282 feet. The elevation of Los Angeles, California is 330 feet.

Part A On the number line below, plot the elevations for Death Valley and Los Angeles. Be sure to label both points with the appropriate name.

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

2350 2300 2250 2200 2150 2100 250

Part B

0

50

100 150 200 250 300 350

How many feet higher is Los Angeles than Death Valley?

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

Show your work.

Answer

feet

49 © 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 .


Number NUMBER Sense and Operations SENSENumb AN 4

The temperature at the top of a mountain is ⫺20°F. The temperature at the base of the mountain is ⫺2°F.

Part A On the number line below, plot the temperatures for the top of the mountain and the base of the mountain. Be sure to label both points with the appropriate location.

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

228 224 220 216 212 28 24

Part B

0

4

8

12

16

20

24

28

How many degrees warmer is the temperature at the base of the mountain than . the temperature at the top of the mountain? ASTER

LINE M K C A L Show your work. OT A B TO BE N S I T BOOK TED. I S H I G H I T R COPY GIVEN FOR S I K AY. O W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R

Answer

°F

50 © 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 ND ber Sense OPERATIONS and Operations Number Sense 5

In the spring, the water level of a lake was 5 feet above normal. After a dry summer, the water level is 4 feet below normal.

Part A On the number line below, plot the level of the river in the spring and the level of the river after the summer. Let 0 represent the normal level. Be sure to label both points with the appropriate season.

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

26 25 24 23 22 21

Part B

0

1

2

3

4

5

6

How many feet lower was the lake in the summer than in the spring?

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

Show your work.

Answer

feet

51 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: Operations 7.N.14 Develop a conceptual understanding of negative and zero exponents with a base of ten and relate to fractions and decimals 1ᎏ.) (e.g., 10⫺2 = .01 = ᎏ 100

1

Which decimal is equivalent to 10⫺1?

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

HINT Look for a Pattern. Think about powers of 10 with positive exponents: 104 = 10,000, 103 = 1,000, 102 = 100, and 101 = 10. What pattern do you see? Use the pattern to find the decimal equivalent to 10⫺1.

A B C D

STER. A M E 0.1 ACKLIN L B A 0.01 S NOT OK TO BE I T I . 0.001 GHTED OR THIS BO I R Y P O IVEN F Y WAY. 0.0001 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

52 © 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 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Which fraction is equivalent to 10⫺4? 1 A ᎏ 1ᎏ 0 1ᎏ B ᎏ 100 1 C ᎏ 1,0ᎏ 00 1ᎏ D ᎏ 10,000

3

Which decimal is equivalent to 10⫺2? A 0.0001

STER. A M E ACKLIN L B C 0.01 A S NOT OK TO BE I T I . D 0.1 GHTED OR THIS BO I R Y P O IVEN F Y WAY. K IS C G O T O O B NtoIS10N⫺2? UCED IN AN AMPisLEequivalent O I S WhichHIfraction S S S I D T PERM REPRO B 0.001

4

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

1 A ᎏ 1ᎏ 0 1ᎏ B ᎏ 100 1 C ᎏ 1,0ᎏ 00 1ᎏ D ᎏ 10,000

53 © 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 .


NUMBER Number Sense and Operations SENSENumb AN 5

Which decimal is equivalent to 10⫺3? A 0.1 B 0.01 C 0.001 D 0.0001

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

54 © 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 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.15

1

Operations Recognize and state the value of the square root of a perfect square (up to 225)

Dominique is decorating her bedroom. The floor of the bedroom is square. Dominique covers the floor with 196 square feet of carpet tile. How long, in feet, is one side of the bedroom floor?

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. Find the square of the number and compare the square to 196.

A B C D

STER. A M E 8 ACKLIN L B A 12 S NOT OK TO BE I T I . 14 GHTED OR THIS BO I R Y P O IVEN F Y WAY. 16 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

55 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

Mr. Silva builds a square patio. He uses 121 square feet of brick. How long, in feet, is one side of the patio? A 9 B 10 C 11 D 12

3

Mrs. Malone covers a square window with frosted window film. She uses 225 square inches of window film. How long, in inches, is one side of the window? A 25 B 15

STER. A M E ACKLIN L B A D 10 S NOT OK TO BE I T I . GHTED OR THIS BO I R Y P F CO VENkitchen IThe K IShis AY.is square. Mr. Andrews G O W T O Mr. Andrews is remodeling kitchen. floor Y O B N N E A L N long, in feet, is one side of the MP with 169 ON IS feetDofUCtile. Isquare ED IHow S covers S SAfloor S I M THIthe O ER REPR kitchen floor? P C 12

4

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

A 7 B 9 C 11 D 13

56 Š 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 ND ber Sense OPERATIONS and Operations Number Sense 5

Xavier cuts a piece of wood to make a wall plaque. The piece of wood is square. He covers the piece of wood with 100 square inches of glass tile. How long, in inches, is one side of the piece of wood? A 10 B 11 C 15 D 20

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

57 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: Operations 7.N.16 Determine the square root of non-perfect squares using a calculator

1

ᎏᎏ What is the value of √5 0 to the nearest tenth?

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. Find the square of the number and compare the square to 50.

A 7.1

STER. A M E 8.1 ACKLIN L B A S NOT OK TO BE I 8.9 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 7.9 C D

58 © 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 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

ᎏᎏ What is the value of √1 3ᎏ 0 to the nearest tenth? A 10.4 B 10.9 C 11.4 D 11.9

3

A 12.2 B 12.8 C 13.2

STER. A M E ACKLIN L B A BE NOT O S I T ᎏ ᎏ T K I O . √1 What is the value of 2 to the nearest Ttenth? GH ED OR THIS BO I R Y P O A 4.1 IVEN F Y WAY. K IS C G O T O O B LE N IS N UCED IN AN B 4.5 S SAMP O I S S I I D TH PERM REPRO C 3.1

D 13.8

4

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

ᎏᎏ What is the value of √1 6ᎏ 5 to the nearest tenth?

D 3.5

5

ᎏᎏ What is the value of √3 0ᎏ 0 to the nearest tenth? A 17.3 B 17.7 C 18.3 D 18.7

59 © 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 .


NUMBER Number Sense and Operations SENSENumb AN Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.17

1

Operations Classify irrational numbers as non-repeating/ non-terminating decimals

Which number is an irrational number?

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

HINT Look for a Pattern. Remember that an irrational number is a nonrepeating/non-terminating decimal. Look for repeating patterns in the answer choices. Which one does not have a repeating pattern?

STER. A M E 5.385164807 . . . ACKLIN L B A 1.011011011 . . . S NOT OK TO BE I T I . GHTED OR THIS BO I ⫺3.333333333 . . . 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 2.111111111 . . . B C D

60 © 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 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Which number is an irrational number? A 10.25 B ⫺2.5 C 1.228 D ⫺3.31662479 . . .

3

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

Which number is an irrational number? A 4.795831523 . . . B 0.166666666 . . . C 0.275

STER. A M E ACKLIN L B A BE NOT O S I T T K I O . Which number is an irrational number?TED GH HIS BO I T R Y R P O A 4.123123123 . . . OK IS CO IVEN F Y WAY. G T O O B MPLE . . . SSION IS N UCED IN AN B ⫺8.75757575 A S S I I D TH PE.R. M. REPRO C 20.12346348 D 0.583333333 . . .

4

D 0.667667667 . . .

5

Which number is an irrational number? A 0.03 B ⫺1.25873469 . . . C 15.00625 D 3.083333333 . . .

61 © 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 .


NUMBER Number Sense and Operations SENSENumb AN

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

Student Expectation

7.N.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line)

ER.

7.N.19. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E 65MAST N I L K Justify the reasonableness of answers using estimation A BLAC

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

62 Š 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 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: Estimation 7.N.18 Identify the two consecutive whole numbers between which the square root of a non-perfect square whole number less than 225 lies (with and without the use of a number line)

1

ᎏᎏ Between what two whole numbers is +√9 5?

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

HINT Work Backwards. Start with the numbers in the first answer choice. Work backwards by finding the square of each number. Then compare those to 95.

A B C D

STER. A M E 9 and 10 ACKLIN L B A 10 and 11 S NOT OK TO BE I T I . 11 and 12 GHTED OR THIS BO I R Y P O IVEN F Y WAY. 12 and 13 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

63 © 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 .


NUMBER Number Sense and Operations SENSENumb AN Independent Practice Directions: Solve the problems on your own.

2

ᎏᎏ Between what two whole numbers is +√2 0ᎏ 0? A 13 and 14 B 14 and 15 C 15 and 16 D 16 and 17

3

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

ᎏᎏ Between what two whole numbers is +√8 0? A 6 and 7 B 7 and 8 C 8 and 9

STER. A M E ACKLIN L B A BE NOT O S I T ᎏ ᎏ ᎏ +√1 T K I O . Between what two whole numbers is TE5D6? GH HIS BO I T R Y R P O O A 9 and 10 IVEN F Y WAY. K IS C G O T O O B MPLE SSION IS N UCED IN AN B 10 and 11 A S S I D TH ERMI REPRO C 11 and 12 P D 9 and 10

4

D 12 and 13

5

ᎏᎏ Between what two whole numbers is +√5 3? A 7 and 8 B 5 and 6 C 8 and 9 D 3 and 5

64 © 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 ND ber Sense OPERATIONS and Operations Number Sense Guided Practice Directions: Use the hint to help you solve the problem.

Band: 7.N.19 1

Estimation Justify the reasonableness of answers using estimation

The Walters are buying new carpet for their house. They need about 1,725 square feet of carpet. The carpet they buy is sold by the square yard.

Part A

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

Estimate the number of square yards of carpet the Walters need for their house.

HINT Make It Simpler. Make the problem simpler by using compatible numbers R.

MASTE E N I L BLACK E A T O T IS N BOOK TO B I . D E T YRIGH N FOR THIS P Show your work. O C AY. GIVE OK IS W T O Y O B N N E A L AMP D IN ON IS THIS S PERMISSI EPRODUCE R to estimate the number of square yards of carpet.

Answer

square yards

65 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN Part B One the lines below, describe a strategy the Walters should use to correctly estimate the number of square yards of carpet they need for their house.

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

66 Š 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 ND ber Sense OPERATIONS and Operations Number Sense Independent Practice Directions: Solve the problems on your own.

2

Mr. Gunn is buying new grass sod for his yard. He needs about 582 square yards of grass sod. The grass sod he buys is sold by the square foot.

Part A Estimate the total number of square feet of grass sod Mr. Gunn needs

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

for his yard.

Show your work.

STER. A M E ACKLIN L B A S NOT OK TO BE I T I . GHTED OR THIS BO Answer square feet 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 Part B TH D PERM REPRO On the lines below, describe a strategy Mr. Gunn should use to correctly estimate the number of square feet of grass sod he needs for his yard.

67 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN 3

Mrs. Collato is buying new tile for her kitchen counter. She needs about 4,350 square inches of tile. The tile she buys is sold by the square foot.

Part A Estimate the number of square feet of tile Mrs. Collato needs for her kitchen counter. Show your work.

Answer

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

STER. A M E ACKLIN L Part B B A S NOT OK TO BE I T I . On the lines below, describe a strategyHTMrs. should IS BO use to correctly estimate G ED Collato H I T R Y R P O the number of square feetSofCO tile she needs for her kitchen counter. IVEN F Y WAY. KI G O T O O B MPLE SSION IS N UCED IN AN A S S I I D TH PERM REPRO

68 Š 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 ND ber Sense OPERATIONS and Operations Number Sense 4

The Taylors are painting the outside of their house. They have about 232 square yards of wall surface to paint. One gallon of paint will cover about 400 square feet of wall surface.

Part A Estimate the number of gallons of paint the Taylors need for their house. Show your work

Answer

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

STER. A M E ACKLIN L Part B B A S NOT OK TO BE I T I . D Taylors Hshould One the lines below, describe a strategy IS BO use to correctly estimate GHTEthe I T R Y R P O the number of gallons of point for their house. O they need 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

69 Š 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 .


NUMBER Number Sense and Operations SENSENumb AN 5

Mrs. Ortiz is making chicken salad for a large group of people. She needs to buy 625 ounces of chicken for the salad. The chicken is sold by the pound.

Part A Estimate the number of pounds of chicken Mrs. Ortiz needs for the chicken salad. Show your work

Answer

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

STER. A M E ACKLIN L Part B B A S NOT OK TO BE I T I . D Ortiz should One the lines below, describe a strategy IS BOuse to correctly estimate GHTEMrs. H I T R Y R P O the number of pounds of chicken for the chicken salad. O she needs 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

70 Š 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 ND ber Sense OPERATIONS and Operations Number Sense

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

71 © 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 .


NUMBER Number Sense and Operations SENSENumb AN

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

72 © 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

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


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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


Math sbs g numbers sample