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D MAT H

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

NUMBER SENSE OPERATIONS PLE — AND —

SAM ATION C U D E ! Y L L Y L L RA A R . 9 9 888.

HTED. G I GIVEN R T Y O P N O N IS K IS C O I O S O S I B WAY. ERM PLE Y P M N A A . S R N THIS MASTE RODUCED I E N I L BLACK TO BE REP A T O K IT IS N THIS BOO FOR C O NNE C TE D T O T HE

C O M M O N C O R E S TA N D A R 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

D

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN KLI ECT EBEDRETPOR T H E C A L C O NN B OT A K TO IT IS N THIS BOO OR CFOM 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 Manipulatives or Act Out Use a Formula or Rule Guess and Check Make it Simpler Make Estimates Look for a Pattern Write a Number Sentence, Use Ratio or Proportion In the Independent Practice section, students respond to four problems ED. math T EN H V I G I G for each student expectation on their own. NOT OPYR

IS C K ION IS AY. O S O S I B M E Y Wgrade level as In each book, there are student expectations from PER the particular MPL N A A . S R N I E S I THstudentNexpectations MAST UCEDthe previous grade that well as, when appropriate, from D E O I R L P K BE RtoE review. are important building Tblocks A BLACfor students O T O K N IT IS IS BOO H T R The RALLY! Math Strands FO are connected to the Common Core State Standards: • Operations & Algebraic Thinking • Number & Operations in Base Ten • Number & Operations—Fractions • Measurement & Data • Geometry

ISBN 978-1-4204-6261-6 R 6261-6 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 BAND: Number Systems . . . . 4

BAND: Operations . . . . . . . . 58

Grade 3

Grade 4

Student Expectation

Guided Practice

Independent Practice

Student Expectation

3.N.14. . . . . . . . . . . 5 . . . . . . . . 6 3.N.15 . . . . . . . . . . 10 . . . . . . . 11

4.N.14 4.N.15 4.N.16 4.N.17 4.N.18 4.N.19 4.N.20 4.N.21 4.N.22 4.N.23 4.N.24 4.N.25

Grade 4 Student Expectation

Guided Practice

Independent Practice

Guided Practice

. . . . . . . . . . 59 . . . . . . . . . . 62 . . . . . . . . . . 65 . . . . . . . . . . 68 . . . . . . . . . . 71 . . . . . . . . . . 74 . . . . . . . . . . 77 . . . . . . . . . . 80 . . . . . . . . . . 83 . . . . . . . . . . 86 . . . . . . . . . . 89 . . . . . H. T. E.D... 92

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

Independent Practice

. . . . . . . 60 . . . . . . . 63 . . . . . . . 66 . . . . . . . 69 . . . . . . . 72 . . . . . . . 75 . . . . . . . 78 . . . . . . . 81 . . . . . . . 84 . . . . . . . 87 . . . . . . . 90 . . . . E. N. . 93

4.N.1 . . . . . . . . . . . 15 . . . . . . . 16 4.N.2 . . . . . . . . . . . 18 . . . . . . . 19 4.N.3 . . . . . . . . . . . 20 . . . . . . . 21 4.N.4 . . . . . . . . . . . 22 . . . . . . . 23 4.N.5 . . . . . . . . . . . 24 . . . . . . . 25 4.N.6 . . . . . . . . . . . 26 . . . . . . . 28 4.N.7 . . . . . . . . . . . 30 . . . . . . . 31 GIV T YRIG 4.N.8 . . . . . . . . . . . 33 . . . . . . . 34 O P N O C IS K IS Estimation ISSION Y. W. .AY... . . . 97 4.N.9 . . . . . . . . . . . 36 . . . . . . . 37 PLE BOOBAND:ER M AM ER. P 4 UCED IN AN 4.N.10 . . . . . . . . . . 41 . . T. H. I.S. S. 42 MASTGrade LINE EPROD Student Guided Independent R 4.N.11 . . . . . . . . . . 45 . . A. .B.LA . C. K46 E B O T T O Expectation Practice Practice K N OO 4.N.12 . . . . . . . I.T.I.S49 . . . .H.IS. .B50 T 4.N.26 . . . . . . . . . . 98 . . . . . . . 99 FOR 4.N.27. . . . . . . . . . 101 . . . . . . 102 BAND: Number Theory . . . . 54 Grade 4 Student Expectation

Guided Practice

Independent Practice

4.N.13 . . . . . . . . . . 55 . . . . . . . 56

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 Student Expectation 3.N.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Explore equivalent fractions 3.N.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Compare and order unit fractions

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

4.N.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Skip count by 1,000’s. 4.N.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Read and write whole numbers to 10,000. 4.N.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Compare and order numbers to 10,000. 4.N.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 ED. Place value structure of the base ten number RIGHTsystem T GIVEN

COPY

IS NO

4.N.5. . . . . . . . . . . . . . . . .B.O.O.K. I.S. . . . . .IS. S. I.O.N. . . . . . A 24 Y. M E W L R E P Y P M N A A . Equivalent representations for numbers up to four digits IN IS S TER

TH

E MAS

DUCED

4.N.6. . . . . . . . L. A. C.K.L.IN. . . . . . . R . .EP .R . .O. . . . . . . . . . . . . 26 E B B A TO Associative IS NOTpropertyBOofOKmultiplication

IT

THIS

4.N.7. . .F.O.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Fractions as locations on number lines 4.N.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Recognize and generate equivalent fractions 4.N.9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Compare and order unit fractions 4.N.10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 Develop an understanding of decimals as part of a whole 4.N.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 Read and write decimals to hundredths 4.N.12. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Compare and order decimals in the context of money 4

© 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: Number Systems 3.N.14 Explore equivalent fractions (ᎏ21ᎏ, ᎏ31ᎏ, ᎏ41ᎏ). 1

2ᎏ of the figure below. Todd shaded ᎏ6

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

2ᎏ? Which rectangle is shaded to show a fraction equivalent to ᎏ6 HINT 2ᎏ and think about how it can Make It Simpler. Look at the fraction ᎏ6 be simplified. Then compare the simplified fraction to each of the N TED. answer choices. T GIVE YRIGH

A

B

NO COP S I S I N K O I LE BOO . PERMISS ANY WAY. P M A THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO C FOR

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 .


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

2

2ᎏ of the circles below. Lori shaded ᎏ4

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

2ᎏ? Which fraction is equivalent to ᎏ4 1ᎏ A ᎏ6 1ᎏ B ᎏ4 1ᎏ C ᎏ3 1ᎏ D ᎏ2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 3

4ᎏ of the figure below. Allen shaded ᎏ8

4ᎏ? Which rectangle is shaded to show a fraction equivalent to ᎏ8 A

B

C

D

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 .


Number NUMBER Sense and Operations SENSENumb AN 4

3ᎏ of the circles below. Tomas shaded ᎏ9

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

3ᎏ? Which fraction is equivalent to ᎏ9 A ᎏ1ᎏ 6 1ᎏ B ᎏ4 1ᎏ C ᎏ3 1ᎏ D ᎏ2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 5

2ᎏ of the figure below. Maria shaded ᎏ8

2ᎏ? Which rectangle is shaded to show a fraction equivalent to ᎏ8 A

B

C

D

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Band: 3.N.15

1

Number Systems 1ᎏ, ᎏ1ᎏ, ᎏ1ᎏ) and find their Compare and order unit fractions (ᎏ2 3 4 approximate locations on a number line.

Daniel made snack mix for lunch. The amounts of the three ingredients he used are shown in the table below.

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

Name of Ingredient

Amount Used

Raisins

1ᎏ cup ᎏ3

Oat Cereal

1ᎏ cup ᎏ2

. GHTED OT GIVEN I R Y P IS N IS COᎏ41ᎏ cup Peanuts N K O I O S O S I M WAY. LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN Which group of fractions shows KLI theBEamounts C A REPR of the ingredients used in L B A O T T order from least Oto greatest? K IT IS N THIS BOO FOR

HINT Use Manipulatives or Act Out. Draw 3 rectangles that are the same size and cut them out. Shade them to show the fractions in the table. Put the rectangles in order from least to greatest amount shaded.

A ᎏ1ᎏ ᎏ1ᎏ ᎏ1ᎏ 4 2 3

1ᎏ C ᎏ1ᎏ ᎏ1ᎏ ᎏ2 4 3

B ᎏ1ᎏ ᎏ1ᎏ ᎏ1ᎏ 3 4 2

1ᎏ D ᎏ1ᎏ ᎏ1ᎏ ᎏ4 2 3

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 Independent Practice Directions: Solve the problems on your own.

2

The distances that Roberto, Julie, and Dante walk to school are shown in the table below. DISTANCE WALKED TO SCHOOL Name of Student

Distance Walked

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

1ᎏ mile ᎏ4

Julie

1ᎏ mile ᎏ2

Dante

1ᎏ mile ᎏ3

Which list shows the students in order from shortest to longest distance from school? N TED. A B C D

YRIGH IS NOT GIVE P O C Julie, Dante, Roberto K IS O O ISSION Y WAY. B M E L R E P AM Roberto, Dante, Julie AN . P THIS S NE MASTER ODUCED IN R Dante, Julie, Roberto KLI C A L E REP B B A O T T Roberto, S NO DanteIS BOOK IT IJulie, H FOR 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 3

The lengths of three hiking trails at Crismon Park are shown in the table below. CRISMON PARK TRAILS Name of Trail

Length of Trail

Canyon

1ᎏ mile ᎏ2

Lookout

1ᎏ mile ᎏ4

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 1ᎏ mile ᎏ3

Treasure

Which list shows the trails in order from shortest to longest? A Canyon, Lookout, Treasure B Canyon, Treasure, Lookout

C Treasure, Lookout, Canyon

D Lookout, Treasure, Canyon

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Linda, Stephen, and Manuel each ordered the same size pizza. The table below shows what fraction of their pizza each student ate. PIZZAS Student

Fraction of Pizza Eaten

Linda

1ᎏ ᎏ2

Stephen

1ᎏ ᎏ4

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 1ᎏ ᎏ3

Manuel

Which group of fractions shows the amounts of pizza eaten in order from least to greatest? A ᎏ1ᎏ ᎏ1ᎏ ᎏ1ᎏ 3 4 2 1ᎏ ᎏ1ᎏ ᎏ1ᎏ B ᎏ4 3 2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . 1ᎏ ᎏ3 THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

1ᎏ ᎏ1ᎏ ᎏ1ᎏ C ᎏ2 3 4 1ᎏ ᎏ1ᎏ D ᎏ2 4

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 5

April, Joelle, and Omar each ordered the same size submarine sandwich. The table below shows what fraction of their sandwich each student ate. SUBMARINE SANDWICHES Student

Fraction of Sandwich Eaten

April

1ᎏ ᎏ3

Joelle

1ᎏ ᎏ2

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 1ᎏ ᎏ4

Omar

Which list shows the students in order from least to greatest fraction of sandwich eaten? A Omar, April, Joelle

B Joelle, Omar, April

C Omar, Joelle, April

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

D Joelle, April, Omar

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

Band: 4.N.1 1

Number Systems Skip count by 1,000’s.

In the pattern below, which number belongs in the box? 1,490; 2,490; 3,490;

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

HINT Look for a Pattern. Look at the pattern shown. Decide what the rule is for the pattern. Then use the rule to find the number that belongs in the box.

. GHTED OT GIVEN I R Y P 3,590 IS CO SSION IS N . K O O MI WAY LE B R E P 4,090 Y P M N A A . THIS S NE MASTER ODUCED IN 4,490 R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

A 3,491 B 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 .


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

2

In the pattern below, which number belongs in the box? 2,815; 3,815; 4,815;

A 4,816 B 5,815 C 5,851 D 6,815

3

What number is 1,000 more than 3,765? A 3,775 B 3,865 C 4,765

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN What number is 1,000 more R KLI than 5,120? C A L E REP B B A O T T A 6,120 IT IS NO BOOK S I H T FOR B 5,220 D 4,876

4

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

C 5,130 D 5,121

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 5

In the pattern below, which number belongs in the box? 2,225; 3,225; 4,225;

A 4,226 B 5,325 C 5,225 D 6,225

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Band: 4.N.2 1

Number Systems Read and write whole numbers to 10,000.

Which number is the same as two thousand six hundred four?

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 and think about how you would read each number. Which answer choice would you read as “two thousand six hundred four”?

A 264 B 2,064

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI 2,640 WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

C 2,604 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 .


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

2

The number of people at Friday’s baseball game was nine thousand twentytwo. What is another way to write the same number? A 922 B 9,022 C 9,202 D 9,220

3

Which number is the same as four thousand one hundred five? A 415 B 4,015 C 4,105

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . IN ER THItoS SwriteNEeight ASTthousand Which is another way two eighty? CEDhundred M U D O I R L P K E C A R L E A 284 OT A B BOOK TO B N S I IT HIS B 8,028 FOR T D 4,150

4

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

C 8,208 D 8,280

5

Which number is the same as six thousand seventy-six? A 6,067 B 6,076 C 6,607 D 6,706

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: 4.N.3 1

Number Systems Compare and order numbers to 10,000.

By how much would the value of 7,904 change if the digit 9 were replaced with the digit 4?

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

HINT Compute—Write a Number Sentence. Replace the 9 with a 4 and then write a number sentence to find the difference in the values of the two numbers.

A 4 B 5 C 400 D 500

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Which number has the greatest value in the thousands place? A 17,909 B 18,278 C 19,467 D 23,989

3

By how much would the value of 8,735 change if the digit 8 were replaced with the digit 9? A 1 B 9 C 900

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . S THISgreatest ASTEinR theOhundreds Which number has the value CED IN place? M U D E N I LACKL TO BE REPR B A T A 5,002 O K IT IS N THIS BOO B 7,934 FOR

D 1,000

4

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

C 8,243 D 9,889

5

By how much would the value of 3,815 change if the digit 1 were replaced with the digit 8? A 70 B 80 C 700 D 800 21

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: 4.N.4

1

Number Systems Understand the place value structure of the base ten number system: 10 ones = 1 ten; 10 tens = 1 hundred; 10 hundreds = 1 thousand; 10 thousands = 1 ten thousand

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

Which is the same as 9 hundreds?

HINT Compute—Write a Number Sentence. Think about the value of 9 hundreds. 9 hundreds: 9 ⫻ 100 = 900. Write similar number sentences for the answer choices. Which has a value of 900?

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K 90 ones O O MI WAY LE B R E P Y P M N A A . 90 tens THIS S NE MASTER ODUCED IN R KLI C A 900 tens L E REP B B A O T T O K IT IS N THIS BOO FOR

A 9 ones B C D

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 Independent Practice Directions: Solve the problems on your own.

2

Which is the same as 8 thousands? A 80 tens B 800 ones C 8 hundreds D 80 hundreds

3

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

Which is the same as 20 tens? A 20 ones

B 200 ones

C 20 hundreds D 2 thousands

4

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B Which is the same as 400 ones? R E P Y P M N A A . THIS S NE MASTER ODUCED IN A 40 ones R KLI C A L E REP B B A O T T B 4 tens IS NO BOOK IT S I H T FOR C 40 tens D 4 thousands

5

Which is the same as 10 thousands? A 10 tens B 100 ones C 10 hundreds D 100 hundreds

23 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: 4.N.5

1

Number Systems Recognize equivalent representations for numbers up to four digits and generate them by decomposing and composing numbers.

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

Which is the same as 2,400?

HINT Guess and Check. Look at the first answer choice. Find the sum of the numbers. Does the sum equal 2,400? Check each answer choice by finding the sum of the numbers.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K 2,000 ⫹ 400 O O MI WAY LE B R E P Y P M N A A . 2 ⫹ 400 THIS S NE MASTER ODUCED IN I R 2 ⫹ 4 ⫹ 100 A BLACKL E REP B O T T O K IT IS N THIS BOO FOR

A 1,000 ⫹ 200 ⫹ 200 B C D

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 Independent Practice Directions: Solve the problems on your own.

2

Which is the same as 535? A 500 ⫹ 30 ⫹ 5 B 500 ⫹ 300 ⫹ 5 C 300 ⫹ 50 ⫹ 5 D 5 ⫹ 35

3

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

Which is the same as 1,122? A 1,000 ⫹ 200 ⫹ 2 B 500 ⫹ 500 ⫹ 22

C 1,000 ⫹ 1,000 ⫹ 20 ⫹ 2 D 500 ⫹ 600 ⫹ 22

4

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI E B ⫹ 40 ⫹PE9? WAY Which is the same as 3,000M⫹PL200 R Y N A A . THIS S NE MASTER ODUCED IN A 3,209 R KLI C A L E REP B B A O T T B 3,249 IS NO BOOK IT S I H T FOR C 3,294 D 3,409

5

Which is the same as 500 ⫹ 120 ⫹ 10 ⫹ 5? A 525 B 535 C 615 D 635

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

Band: 4.N.6

1

Number Systems Understand, use, and explain the associative property of multiplication.

Mr. Lapin reads aloud the math problem below.

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

Three times four times five equals what number?

HINT Compute—Write a Number Sentence. First find the product of 3 and 4. Then multiply that product by 5 to solve the problem.

Part A

TED. GIVEN T O N C K IS ION IS AY. O S O S I B M E (3 ⫻ 4) ⫻ 5 ⫽ ? YW P ER MPL N A A . S R N I E S I TH CED to show the MAST sentence Ubelow D E Fill in both blanks in Daniel’s number O N I R L P K C BLAmath BE RE Athe O next step in solving problem. T T O K N IT IS IS BOO H T R (3 ⫻ 4) ⫻ 5 ⫽ ?FO Daniel wrote Mr. Lapin’s problem this way. OPYRIGH

⫻5⫽

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 Part B Sherry wrote Mr. Lapin’s problem this way. 3 ⫻ (4 ⫻ 5) ⫽ ? Fill in both blanks in Sherry’s number sentence below to show the next step in solving the math problem. 3 ⫻ (4 ⫻ 5) ⫽ ? 3⫻

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 .


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

2

Keisha wrote the expression below. (3 ⫻ 8) ⫻ 7 Which expression is equivalent to Keisha’s expression? A 3 ⫻ (8 ⫻ 7)

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

B 3 ⫻ (8 ⫹ 7) C (3 ⫻ 8) ⫹ 7 D (3 ⫹ 8) ⫻ 7

3

Which expression is equal to (12 ⫻ 15) ⫻ 17? A 12 ⫻ (15 ⫹ 17)

. GHTED OT GIVEN I R Y P C 12 ⫼ (15 ⫻ 17) IS CO SSION IS N . K O O MI WAY LE B R D 12 ⫹ (15 ⫻ 17) E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O OK Tyler wrote IS Nexpression BObelow. IT the S I H T FOR B 12 ⫻ (15 ⫻ 17)

4

(9 ⫻ 6) ⫻ 4

Which expression is equivalent to Tyler’s expression? A 9 ⫹ (6) ⫻ 4) B 9 ⫻ (6 ⫹ 4) C (9 ⫻ 6) ⫹ 4 D 9 ⫻ (6 ⫻ 4)

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 5

Mrs. Kirby reads aloud the math problem below. Two times five times eight equals what number?

Part A Jay wrote Mrs. Kirby’s problem this way. (2 ⫻ 5) ⫻ 8 ⫽ ? Fill in both blanks in Jay’s number sentence below to show the next step in solving the math problem.

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

(2 ⫻ 5) ⫻ 8 ⫽ ?

⫻8⫽

Part B

Linda wrote Mrs. Kirby’s problem this way.

. GHTED OT GIVEN I R Y P IS N IS CO below N K O I O S O Fill in both blanks in Linda’s number sentence to show S Y. next step I M WAthe LE B R E P Y P M N A A . in solving the math Tproblem. HIS S E MASTER CED IN U D O N I R KL E REP 2 ⫻ (5 ⫻ 8) ⫽ ? T A BLAC B O T IS NO HIS BOOK T I 2⫻ FOR T ⫽ 2 ⫻ (5 ⫻ 8) ⫽ ?

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 .


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

Band: 4.N.7

1

Number Systems Develop an understanding of fractions as locations on number lines and as divisions of whole 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

0

1 — 8

R

1 — 2

S

7 — 8

T 1

1ᎏ? Which point on the number line represents ᎏ4

HINT . GHTEDCheckOTeach I GIVEofN the R Guess and Check. Look at each answer choice. Y P N O C IS 1 K IS 1 ONless points on the number line. than AYᎏ.2ᎏ? MISSIor E BIsOᎏ4Oᎏ greater than

A B

YW P ER MPL N A A . S R N I E S I TH MAST UCED D E O N I R L P K E A BLAC K TO BE R T O N point PIT IS IS BOO H T R FO point R

C point S D point T

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

Points D, E, F, and G are graphed on the number line shown below. D 0

E 1 — 3

F 2 — 3

G 1

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

5ᎏ? Which point on the number line represents ᎏ6 A point D B point E C point F

D point G

3

. GHTED OT GIVEN I R Y P Point T is graphed on the number lineK shown IS N IS CO below. N O I O S O S I M WAY. LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN KLI EPTR C A R L E B B OT A K TO IT IS N THIS BOO 1 — 0 1 FOR 2 Which fraction is represented by point T? A ᎏ1ᎏ 8 3ᎏ B ᎏ8 C ᎏ4ᎏ 8 5ᎏ D ᎏ8

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 .


Number NUMBER Sense and Operations SENSENumb AN 4

Point X is graphed on the number line shown below. X 0

1 — 10

1 — 2

7 — 10

1

Which fraction is represented by point X? 3 A ᎏ 1ᎏ 0 2ᎏ B ᎏ5 1ᎏ C ᎏ2 9 D ᎏ 1ᎏ 0

5

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

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

. GHTED OT GIVEN I R Y P N O M N P OK IS C QN IS O I S O S I M WAY. LE B R E P Y P M N A A . THIS S1 NE MASTER 2ODUCED IN — R— 0 1 KLI C A L 3 E REP 3 B B A O T T O K IT IS N THIS BOO OR Which point on Fthe number line represents ᎏ1ᎏ? 2

A point M B point N C point P D point Q

32 © 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: 4.N.8

1

Number Systems Recognize and generate equivalent fractions (halves, fourths, thirds, fifths, sixths, and tenths) using manipulatives, visual models, and illustrations

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

The figures below are divided into equal parts.

A

B

C

D

. GHTED OT GIVEN I R Y P Which two figures are shaded to show equivalent IS N IS CO SSfractions? N K O I O O I M WAY. LE B R E P Y P M N A A . HINT THIS S NE MASTER ODUCED IN R LI or List. Organize—Make aCKChart A L E REPMake a list of the fractions shown B B A O T T O by Figures and BOOKD. Then write 2 or 3 equivalent fractions IT IS N A, B,THC, S I for each fraction FOR in your list. Look for the same fraction listed for 2 different figures.

A Figure A and Figure C B Figure A and Figure D C Figure B and Figure C D Figure B and Figure D

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

The figures below are divided into equal parts.

A

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

C

D

Which two figures are shaded to show equivalent fractions? A Figure A and Figure C

B Figure C and Figure D C Figure A and Figure B

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . S S into The figures below are STER parts. THIdivided Aequal CED IN M U D E O N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR D Figure B and Figure D

3

A

B

C

D

Which two figures are shaded to show equivalent fractions? A Figure A and Figure C B Figure B and Figure C C Figure A and Figure B D Figure C and Figure D

34 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 figures below are divided into equal parts.

A

B

C

D

Which two figures are shaded to show equivalent fractions?

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

A Figure A and Figure C

B Figure C and Figure D C Figure A and Figure B

D Figure B and Figure D

5

The figures below are divided into equal parts.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O A IT IS N BS BOOK C D I H T R FO Which two figures are shaded to show equivalent fractions? A Figure A and Figure C B Figure C and Figure D C Figure B and Figure C D Figure A and Figure D

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

Band: 4.N.9

1

Number Systems Use concrete materials and visual models to compare and order unit fractions or fractions with the same denominator (with and without the use of a number line)

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

Derek is practicing writing fractions on a number line. Which number line shows the fractions in the correct locations? HINT Draw a Picture or Diagram. Draw a number line from 0 to 2. Divide the number line into fourths and label all of the tick marks. Locate ᎏ1ᎏ 2ᎏ on your number line. Choose the answer that has ᎏ1ᎏ and 4 and 1ᎏ4 2ᎏ in the same locations as you show on your number line.4 1ᎏ4

A 0

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . 1 2 1 2 THIS 1S— ASTER ODUCED IN — — M 1— E N I R L 4 4 4 4 P K LAC E REC B B A O T T O K IT IS N THIS BOO FOR1 2 0 1 2 1 — 4

B 0

2 1— 4 1

1 — 4

D 2

0

2 1— 4 1

2

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 .


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

2

Fran is practicing writing fractions on a number line. Which number line shows the fractions in the correct locations? 1 1— 6

1 — 6

A

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

0

1

1 — 6

B

0

C

1

2

1 1— 6

2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . 1 1 K O — O 1— MI WAY L6E B R 6 E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T 0 1 2 T O K IT IS N THIS BOO FOR 1 1— 6

1 — 6

D 0

1

2

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 .


Number NUMBER Sense and Operations SENSENumb AN 3

Kayla is practicing writing fractions on a number line. Which number line shows the fractions in the correct locations? 1 — 4

1 — 3

1 — 2

A 1

0

1 1 — — 4 3

B

1 — 2

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

0

1 1 — — 2 3

C

1

1 — 4

. GHTED 1OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . 1IS S 1 TH— A1STER — CED IN — M U D E O N I R3 4 CK L 2 LA E REP B B A O T T O K IT IS N THIS BOO FOR 0 1 0

D

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 4

Misha is practicing writing fractions on a number line. Which number line shows the fractions in the correct locations? 2 — 8

3 1— 8

A 0

1

2

2 — 8

B

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

0

1

. GHTED 2OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . 3CED IN 2IS S TH— ASTER OD1U— M E N I R 8 8 CK L LA E REP B B A O T T O K IT IS N THIS BOO FOR 0 1 2 0

D

2

3 1— 8

2 — 8

C

3 1— 8

1

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

Adam is practicing writing fractions on a number line. Which number line shows the fractions in the correct locations? 1 — 8

1 — 5

1 — 2

A 0

1

1 — 2

B 0

1

1 — 2

1 — 8

. GHTED 1 OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . 1 — 1THIS S 1ASTER CED IN — — M U D E O N I 2 5 LACKL TO8 BE REPR B A T O K IT IS N THIS BOO FOR 0 1 0

D

1 — 8

E L P SAM ATION C U D E ! Y L RAL 99.RALLY . 8 8 8 1 — 5

C

1 — 5

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: Number Systems 4.N.10 Develop an understanding of decimals as part of a whole 1

Andrea drew a square and divided it into 10 equal parts. She shaded the square as shown below.

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

. GHTED OT GIVEN I R Y P IS N S CO thatSIisONshaded? Isquare K O What decimal describes the partE of the O S I M WAY. L B R E P Y P M N A A . THIS S NE MASTER ODUCED IN HINT KLI C A REPR L E B B A O T T Look for Write OOK a decimal to describe each number of IS NaOPattern. B T I S I H T shaded parts, FOR from 1 part to 10 parts: 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0 What pattern do you notice? Which decimal describes four shaded parts?

A 0.04 B 0.4 C 0.6 D 4

41 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

Brian shaded a hundreds grid as shown below.

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

What decimal describes the part that is shaded? A 0.025 B 0.2 C 0.25 D 2.5

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 3

Hannah shaded a hundreds grid as shown below.

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

What decimal describes the part that is shaded? A 0.43 B 0.57 C 4.3 D 43

4

D.

N Isaac drew a square and divided it into 10 equal parts. GHTE He shaded I GIVEthe R T Y O P N O C S square as shown below. SION I . OOK IS MIS WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

What decimal describes the part of the square that is shaded? A 0.07 B 0.3 C 0.7 D 7 43 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

Briana shaded a hundreds grid as shown below.

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

What decimal describes the part that is shaded? A 8 B 0.92 C 0.8 D 0.08

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 .


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

Band: 4.N.11

1

Number Systems Read and write decimals to hundredths using money as a context

Each square on the grids below equals $0.01.

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

. GHTED OT GIVEN I R Y P IS N IS COby theSSshaded N K O I O What is the total amount of money shown squares O I M WAY. on LE B R E P Y P M N A A . the grids? THIS S NE MASTER ODUCED IN KLI C A REPR L E B B A O T T HINT S NO OOK I B T I S I H T Guess andOCheck. Look at each answer choice. Think about what a F R completely shaded grid represents. Which of the answer choices include the completely shaded grid?

A $1.56 B $1.44 C $0.56 D $0.44

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 Independent Practice Directions: Solve the problems on your own.

2

Each square on the grids below equals $0.01.

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

What is the total amount of money shown by the shaded squares on the grids? A $1.29

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI $1.09 WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN $0.29 R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

B $1.19 C D

46 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 3

Each square on the grid below equals $0.01.

What is the total amount of money shown by the shaded squares on the grid? A $0.37 B $0.63 C $1.37 D $1.63

4

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

TED. GIVEN T O N O C K IS ION IS AY. O S O S I B M E YW P ER MPL N A A . S R N I E S I TH MAST UCED D E O N I R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO

Each square on the grids below equals $0.01.PYRIGH

What is the total amount of money shown by the shaded squares on the grids? A $0.06 B $0.60 C $1.06 D $1.60

47 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

Each square on the grid below equals $0.01.

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

What is the total amount of money shown by the shaded squares on the grid? A $1.82 B $1.18 C $0.82 D $0.18

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Band: Number Systems 4.N.12 Use concrete materials and visual models to compare and order decimals (less than 1) to the hundredths place in the context of money

1

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

Each square on the grid below equals $0.01.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . N What amount of money by the STERthe amount THIS isS greater Athan CED Ishown M U D E O N I R shaded squares on the Lgrid? A CK L E REP B B A O T T IS NO HIS BOOK T I HINT FOR T

Draw a Picture or Diagram. Draw a number line from $0.00 to $1.00. Place a dot on the number line to show the amount shown on the grid. Then place 4 more dots to show the amounts in the answer choices. Which is the greatest amount?

A $0.45 B $0.50 C $0.55 D $0.75

49 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

Each square on the grid below equals $0.01.

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

What amount of money is less than the amount shown by the shaded squares on the grid? A $0.63

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI $0.75 WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN $0.81 R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

B $0.72 C D

50 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 3

Each square on the grid below equals $0.01.

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

What amount of money is greater than the amount shown by the shaded squares on the grid? A $0.39 B $0.37 C $0.29 D $0.27

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

51 © 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

Steve, Theresa, and Bill have the coins shown below.

Steve

Theresa

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

Which group of decimals shows the amounts of money in order from least to greatest? A $0.41

D

$0.45

$0.45

$0.55

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K $0.55 $0.41 $0.45 O O MI WAY LE B R E P Y P M N A A . S $0.45 $0.55 THIS$0.41 ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

B $0.41 C

$0.55

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 5

Joan, Michael, and Barbara have the coins shown below.

Joan

Michael

Barbara

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

Which group of decimals shows the amounts of money in order from least to greatest? A $0.62

D

$0.58

$0.46

$0.62

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K $0.46 $0.58 $0.62 O O MI WAY LE B R E P Y P M N A A . S $0.62 $0.58 THIS$0.46 ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

B $0.58 C

$0.46

53 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

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

Student Expectation

4.N.13. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Develop an understanding of the properties of odd/even numbers as a result of multiplication.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

54 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: Number Theory 4.N.13 Develop an understanding of the properties of odd/even numbers as a result of multiplication.

1

Which kind of numbers, when multiplied together, have a product that is an odd number?

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

HINT Compute—Write a Number Sentence. For each answer choice, replace the word odd with an odd number and the word even with an even number. Write number sentences to determine which product is an odd number.

A B C D

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K odd ⫻ odd ⫻ odd O O MI WAY LE B R E P Y P M N A A . even ⫻ even ⫻ even THIS S NE MASTER ODUCED IN R KLI C odd ⫻ even ⫻ even A L E REP B B A O T T O odd BOOK IS N⫻ even ⫻ ITodd HIS FOR T

55 © 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 kind of numbers, when multiplied together, have a product that is an odd number? A even ⫻ even B even ⫻ odd C odd ⫻ odd

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

D even ⫻ odd

3

Which number sentence always results in an answer that is an odd number?

䊐 B odd number ⫻ odd number ⫽ 䊐 . C even number ⫻ even number ⫽ 䊐 GHTED OT GIVEN I R Y P D even number ⫻ odd number ⫽ 䊐 IS CO IS N N K O I O S O S I M WAY. LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI multiplied Which kind of numbers, when C A L E REPtogether, have a product B B A O T T O that is an even BOOK IT IS Nnumber? S I H T R FOodd A odd ⫻ odd ⫻ A odd number ⫻ even number ⫽

4

B odd ⫻ odd C even ⫻ odd D odd ⫻ odd ⫻ odd ⫻ odd

56 © 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

Which kind of numbers, when multiplied together, have a product that is an odd number? A even ⫻ even ⫻ even B odd ⫻ odd ⫻ even C even ⫻ even ⫻ odd D odd ⫻ odd ⫻ odd ⫻ odd

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

57 © 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

Operations Student Expectation 4.N.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Add and subtract numbers up to 10,000 4.N.15. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 Computational and operational methods to solve problems

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

4.N.16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Understand various meanings of multiplication and division. 4.N.17. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Use multiplication and division as inverse operations 4.N.18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . T.E.D.. . . . . 71 EN IGH GIV T YRnumbers O P Multiply two-digit numbers by one-digit N O C IS S

KI O O ISSION Y WAY. B M E L R E P 4.N.19. . . . . . . . . S. A.M. . . . . . . . .R.. . P E . . . .U.C.E.D. I.N. A. N. . . . 74 IS T H S T A M Multiply two-digit numbers two-digit numbers KLINE by EPROD C A R L E B B OT A K TO 4.N.20. IT IS N. . . . .T.H.IS. .B.O.O. . . . . . . . . . . . . . . . . . . . . . . . . 77 Multiplying FORand dividing multiples of 10 and 100 4.N.21. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 Multiplying and dividing multiples of 10 and 100 4.N.22. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Multiplying and dividing multiples of 10 and 100 4.N.23. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Multiplying and dividing multiples of 10 and 100 4.N.24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 Multiplying and dividing multiples of 10 and 100 4.N.25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 Multiplying and dividing multiples of 10 and 100 58

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: Operations 4.N.14 Use a variety of strategies to add and subtract numbers up to 10,000.

1

Becky, Melba, and Tom play a number guessing game.

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

Melba’s number is 2,000 more than Tom’s number. Tom’s number is 2,500 less than Becky’s number. Becky’s number is 9,700. What is Melba’s number?

HINT Work Backwards. Start with Becky’s number. Use the given facts to work backwards from Becky’s number to find Tom’s number and then EN HTED. Melba’s number. OT GIV PYRIG

IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI Show your work. C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

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 Independent Practice Directions: Solve the problems on your own.

2

When the number square below is completed, any three numbers in line will add up to 180. The three numbers can be added across, up, down, or diagonally.

96

72

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

60

108

24

What number belongs in Box A?

. GHTED OT GIVEN I R Y P B 24 IS CO SSION IS N . K O O MI WAY LE B R E P Y P C 36 M N A A . THIS S NE MASTER ODUCED IN D 84 R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR On Friday and Saturday, the art museum had a special show. On Friday, A 12

3

3,912 people attended the show. On Saturday, 5,833 people attended. What is the total number of people that attended the show on Friday and Saturday? A 1,921 B 2,921 C 8,745 D 9,745

60 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

Mr. Ritz is driving from Phoenix to San Diego. The total distance is 359 miles. After driving 187 miles, he stops to rest. How many more miles must Mr. Ritz drive to get to San Diego? Show your work.

Answer

5

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

Matthew is exactly 5 years older than Kayla. Kayla is 11 years old today. How old will Matthew be in 3 years? Show your work.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

years old

61 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 4.N.15 Select appropriate computational and operational methods to solve problems.

1

Ryan placed his marbles in 6 rows, with 9 marbles in each row, as show below.

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O I Mnumber E Bfind the Ptotal WAY Lto R Which expression can be used of marbles E P Y M N A A . THIS S NE MASTER ODUCED IN Morris has? R KLI C A L E REP B B A O T T O K HINT IT IS N THIS BOO R FOCheck. Guess and Look at the array of marbles. Find how many marbles are in the array. Then check each answer choice to find the expression that has a value equal to the number of marbles in the array.

A 6⫹9 B 6 ⫹ 6 ⫹ 6 ⫹6 ⫹6 ⫹ 6 C 9⫻9⫻9⫻9⫻9⫻9 D 6⫻9

62 © 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

Alexis, Mary, Luis, and Thomas together earned $54.00 mowing lawns. They will share the money equally. Which number sentence could they use to find out how much money they will each get?

䊐 $54.00 ⫺ 4 ⫽ 䊐 $54.00 ⫻ 4 ⫽ 䊐 $54.00 ⫼ 4 ⫽ 䊐

A $54.00 ⫹ 4 ⫽ B C D

3

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

Ms. Williams bought 120 pencils for her students. The pencils came in packages of 8 pencils in each package. Which number sentence can be used to find the number of packages of pencils Ms. Williams bought?

䊐 HTED. G I GIVEN R T Y O P B 120 ⫼ 8 ⫽ 䊐 N O C K IS ION IS AY. O S O S I B M E C 8 ⫹ 䊐 ⫽ 120 YW P ER MPL N A A . S R N I E S I MAST UCED D 120 ⫺ 䊐 ⫽ 8 TH D E O N I R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO a day for 21 days to train for a race. Which expression Jewel jogged 3 miles A 8 ⫻ 120 ⫽

4

can be used to find the total number of miles Jewel jogged? A 3⫹3⫹3 B 21 ⫹ 21 ⫹ 21 C 21 ⫻ 3 D 21 ⫼ 3

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 5

Victor and Milo together earned $50.00 walking dogs. They will share the money equally. Which number sentence could they use to find out how much money they will each get?

䊐 $50.00 ⫺ 2 ⫽ 䊐 $50.00 ⫻ 2 ⫽ 䊐 $50.00 ⫼ 2 ⫽ 䊐

A $50.00 ⫹ 2 ⫽ B C D

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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: Operations 4.N.16 Understand various meanings of multiplication and division. 1

Jay is building a fence that has 8 sections. There are 5 boards in each section. How many boards are there in the fence?

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

HINT Draw a Picture or Diagram. Draw the fence that is described in the problem. Use your drawing to find the number of boards in the fence.

A 5 B 8 C 40 D 48

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 Independent Practice Directions: Solve the problems on your own.

2

There are 7 cars in the Whirlwind ride at the park. Each car holds 6 people. How many people does the Whirlwind ride hold? A 6 B 7 C 36 D 42

3

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

Mr. Landry hiked 35 miles during his vacation. He hiked an equal number of miles each day for 5 days. How many miles did Mr. Landry hike each day? A 5 B 7 C 30 D 175

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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 4

Claude puts 81 toy planes on 9 shelves. He places an equal number of planes on each shelf. How many toy planes does Claude place on each of the 9 shelves? A 9 B 10 C 72 D 90

5

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

Julie earned $72 last week for walking 6 dogs. She earned an equal amount for each dog she walked. How much did Julie earn for each of the 6 dogs? A $6 B $9 C $12 D $66

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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

Band: Operations 4.N.17 Use multiplication and division as inverse operations to solve problems.

1

Mrs. Turner prepared the same number of meals each day for 7 days. She prepared a total of 42 meals. How many meals did Mrs. Turner prepare each day?

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

HINT Compute—Write a Number Sentence. You need to find how many meals Mrs. Turner prepared on each of the 7 days. Think about whether you should add, subtract, multiply, or divide.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . Show your work. K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

meals

Fill in the blanks below to make a number sentence that will check your answer. Number sentence

68 © 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

David’s teacher wrote this number sentence on the board. 32 ⫼ 4 ⫽ 8 Which number sentence could David use to check the one his teacher wrote?

䊐 4⫻8⫽䊐 4 ⫻ 32 ⫽ 䊐 8 ⫻ 32 ⫽ 䊐

A 8⫼4⫽ B C D

3

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

If 180 ⫼ 15 ⫽ 12, which equation must also be true? A 12 ⫹ 15 ⫽ 180

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O C 12 ⫻ 15 ⫽ 180 MI WAY LE B R E P Y P M N A A . SS ASTER ODUCED IN D 15 ⫼ 12 ⫽ 180 THI M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO R this number sentence on the board. Mariah’s teacherFOwrote B 12 ⫻ 12 ⫽ 180

4

132 ⫼ 11 ⫽ 12 Which number sentence could Mariah use to check the one her teacher wrote?

䊐 12 ⫼ 11 ⫽ 䊐 11 ⫻ 132 ⫽ 䊐 132 ⫻ 12 ⫽ 䊐

A 11 ⫻ 12 ⫽ B C D

69 © 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

Diane washed the same number of windows each day for 6 days. She washed 7 windows every day. What is the total number of windows Diane washed in 6 days? Show your work.

Answer

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

Fill in the blanks below to make a number sentence that will check your answer. Number sentence

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

70 © 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: Operations 4.N.18 Use a variety of strategies to multiply two-digit numbers by one-digit numbers (with and without regrouping).

1

Jessica decorates picture frames with seashells. She uses 42 seashells for each picture frame. How many seashells does Jessica need to decorate 5 picture frames?

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

HINT Compute—Write a Number Sentence. Jessica uses 42 seashells on each of the 5 frames. Think about whether you should add, subtract, multiply, or divide to find the total number of seashells.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . Show your work. K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

seashells

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 Independent Practice Directions: Solve the problems on your own.

2

Mr. Sims is painting the doors in his house. It takes him 40 minutes to paint one door. How many minutes will it take Mr. Sims to paint 8 doors? A 48 B 320 C 328 D 360

3

A machine in a juice factory can cap 85 bottles in 1 minute. How many bottles can the machine cap in 8 minutes? A 595 B 672

. GHTED OT GIVEN I R Y P IS CO SSION IS N . D 688 K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R college 4 days a week. The KLIat the Bcommunity C A L Mrs. Collins drives to school E REP B A O T T NO house toBOthe OK college is 21 kilometers. What is the total distance from IT IS her S I H T FOR Mrs. Collins drives to the college and back home in distance, in kilometers, C 680

4

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

one week? Show your work.

Answer

kilometers 72

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

On Monday, 5 school buses take students to the zoo. Each bus carries 39 students. How many students take the bus to the zoo on Monday? Show your work.

Answer

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

73 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 4.N.19 Use a variety of strategies to multiply two-digit numbers by two-digit numbers (with and without regrouping)

1

Jaime and Timothy go to an amusement park with their families. If the price of a ticket is $37.00, what is the total cost for 12 tickets?

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

HINT Compute—Write a Number Sentence. You need to find the total cost for 12 tickets that cost $37.00 each. Think about whether you should add, subtract, multiply, or divide.

. GHTED OT GIVEN I R Y P $444.00 IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N $454.00 A A . THIS S NE MASTER ODUCED IN R $456.00 KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

A $49.00 B C D

74 © 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 members of the drama club go to see a play. If the price of one ticket is $15.00, what is the total cost for 32 tickets? A $480.00 B $380.00 C $370.00 D $47.00

3

The Plant Place Nursery has 40 trays of tomato plants. If there are 24 plants in each tray, what is the total number of tomato plants at the nursery? A 64 B 860

. GHTED OT GIVEN I R Y P IS CO SSION IS N . D 960 K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI bought C A L During her vacation, Ms. Harper E REP13 postcards. If each postcard B B A O T T K IS NOis theHIStotal cost $0.25, Ms. Harper spent on postcards? BOOamount IT what T FOR C 950

4

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

A $3.25 B $3.15

C $2.15 D $0.38

75 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

The members of the travel club take a ferry boat trip from Maine to Newfoundland. If the price of a ticket is $65.00, what is the total cost for 19 tickets? A $650.00 B $1,195.00 C $1,235.00 D $1,245.00

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

76 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: Operations 4.N.20 Develop fluency in multiplying and dividing multiples of 10 and 100 up to 1,000.

1

There are 40 fruit baskets at a farmer’s market. There are 9 pieces of fruit in each basket. What is the total number of pieces of fruit in the baskets?

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

HINT Compute—Write a Number Sentence. There are 40 baskets and each one has 9 pieces of fruit. Think about whether you should add, subtract, multiply, or divide to find the total number of pieces of fruit.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Show your work.

Answer

pieces of fruit

77 © 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

There are a total of 300 alligators in 10 ponds at the alligator farm. Each pond has the same number of alligators. How many alligators are there in each pond? A 3 B 30 C 300 D 3,000

3

There are 40 boxes of crackers on a store shelf. There are 12 crackers in each box. What is the total number of crackers on the shelf? A 300

. GHTED OT GIVEN I R Y P C 480 IS CO SSION IS N . K O O MI WAY LE B R E P Y D 600 P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K a patio in his yard. He made 9 rows of Mr. West Iused BtoOOmake T IS Nstone Ttiles S I H R each row. He used 150 tan tiles. The rest of the tiles FOin tiles, with 30 tiles B 400

4

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

were brown. How many brown tiles did Mr. West use? Show your work.

Answer

brown tiles 78

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

A car dealer has 800 cars on his lot. There are 20 rows of cars. Each row has the same number of cars. How many cars are there in each row? Show your work.

Answer

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

79 © 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 4.N.21 Use a variety of strategies to divide two-digit dividends by one-digit divisors (with and without remainders).

1

In Bob’s Hobby Shop, there are a total of 72 train cars on 8 shelves. Each shelf has the same number of train cars. How many train cars are on each shelf?

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

HINT Compute—Write a Number Sentence. The 72 train cars have been put into 8 equal groups. Think about whether you should add, subtract, multiply, or divide to find how many train cars are in each group.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . Show your work. K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

train cars

80 © 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

Ellen has 65¢. Erasers cost 9¢ each. What is the greatest number of erasers Ellen can buy? A 6 B 7 C 8 D 9

3

79 ⫼ 7 ⫽ A 10 R 6 B 11 C 11 R 2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . TER the wire D INpieces that are each HISofS wire.E He AScuts Louis has a 50-inch Troll CEinto M U D O N I L PR Louis have? LACK6-inch 6 inches long. HowAmany pieces E REdoes B B O T T IS NO BOOK Show yourITwork. OR THIS F D 11 R 3

4

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

Answer

pieces

81 © 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

Maria has 45 party gifts and 9 gift bags. She puts an equal number of party gifts in each gift bag. How many party gifts does Maria put in each gift bag? Show your work.

Answer

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

82 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: Operations 4.N.22 Interpret the meaning of remainders. 1

Ross has 65 stickers. He places 9 stickers on each page of an album. There are 7 pages in his album. How many stickers does Ross have left over?

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

HINT Use Manipulatives or Act Out. Use counters to represent the stickers. Draw 7 circles on a piece of paper to represent the pages. Act out the problem. How many counters are left over?

Show your work.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

Answer

stickers

83 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

Chloe makes 116 cookies. She divides the cookies into 14 bags for the bake sale. She puts 8 cookies in each bag. How many cookies does Chloe have left over? A 3 B 4 C 5 D 6

3

Hector has 31 pencils. He gives 6 pencils to each of his 5 friends. How many pencils does Hector have left over? A 1

. GHTED OT GIVEN I R Y P C 3 IS CO SSION IS N . K O O MI WAY LE B R E P Y D 4 P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T NO 50 ounces Ms. Cannon BOOofK fruit juice. She has 6 cups. She pours IT ISbuys S I H T R into each cup. How many ounces of fruit juice 8 ounces of fruitFOjuice B 2

4

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

does Ms. Cannon have left over? Show your work.

Answer

ounces 84

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

Jasmine has 47 feet of rope. She cuts the rope to make 6 jump ropes. Each jump rope is 7 feet long. How much rope does Jasmine have left over? Show your work.

Answer

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

85 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 4.N.23 Add and subtract proper fractions with common denominators 1

1ᎏ of his baseball cards to John and ᎏ2ᎏ of his baseball cards Hector gives ᎏ8 8 to Mark. What fraction of his baseball cards does Hector give away?

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 rectangle and divide it into 8 equal parts. Shade 1 part to represent ᎏ1ᎏ. Then shade 2 parts 8 2ᎏ. What fraction of the rectangle to represent ᎏ8 is shaded?

A ᎏ1ᎏ 16 3 B ᎏ 1ᎏ 6 3ᎏ C ᎏ8 1ᎏ D ᎏ2

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

86 © 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

2ᎏ of the pizza. Jennifer Kayla and Jennifer eat pizza for lunch. Kayla eats ᎏ6 3ᎏ of the pizza. How much of the pizza did they eat in all? eats ᎏ6 5ᎏ A ᎏ6 B ᎏ3ᎏ 6 5 C ᎏ 1ᎏ 2 1ᎏ D ᎏ6

3

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

2ᎏ of the fence and April Carl and April are painting a fence. Carl paints ᎏ5 1ᎏ of the fence. How much more of the fence does . Carl paint paints ᎏ5 GHTED OT GIVEN I R Y P N O than April? K IS C ON IS 3ᎏ A ᎏ5 3 B ᎏ 1ᎏ 0 C ᎏ2ᎏ 5

ISSI BOO M E WAY. L R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

D ᎏ1ᎏ 5

87 © 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

3ᎏ cup of flour. He uses ᎏ1ᎏ cup of the flour in a recipe. How Mr. Collins has ᎏ4 4 much flour does Mr. Collins have left? 1ᎏ cup A ᎏ4 1ᎏ cup B ᎏ2 C ᎏ5ᎏ cup 8 3ᎏ cup D ᎏ4

5

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

3ᎏ of the sandwich Dylan and Olivia share a submarine sandwich. Dylan eats ᎏ8 4ᎏ of the sandwich. How much of the sandwich did they eat and Olivia eats ᎏ8 in all? 1ᎏ A ᎏ8 1ᎏ B ᎏ2 12 C ᎏ 1ᎏ 6 7ᎏ D ᎏ8

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

88 © 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: Operations 4.N.24 Express decimals as an equivalent form of fractions to tenths and hundredths

1

1ᎏ mile from his house to the bus stop. What decimal is equal Mick walks ᎏ2 1ᎏ? to ᎏ2

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. Read the decimal and 1ᎏ. write it as a fraction. Choose the fraction that is equivalent to ᎏ2

A 0.02 B 0.05 C 0.2 D 0.5

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

89 © 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

6ᎏ of his math problems and then took a break. What decimal José did ᎏ8 is equal to ᎏ6ᎏ? 8 A 0.08 B 0.25 C 0.68 D 0.75

3

9 of the questions on her quiz. What decimal Brittany correctly answered ᎏ 1ᎏ 0 9 is equal to ᎏᎏ? 10 A 0.01

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K C 0.9 O O MI WAY LE B R E P Y P M N A A . D 0.99 THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS24N THIS BOO OR Burt inflated ᎏ 5ᎏ 0Fof the balloons for his cousin’s birthday party. What B 0.09

4

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

2ᎏ? 4 decimal is equal to ᎏ 50 A 0.24 B 0.26 C 0.48 D 0.50

90 © 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

4ᎏ of her model car. What decimal is equal to ᎏ4ᎏ? Rhonda painted ᎏ5 5 A 0.04 B 0.08 C 0.4 D 0.8

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

91 © 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 4.N.25 Add and subtract decimals to tenths and hundredths using a hundreds chart

1

Each square on the grids below equals 0.01.

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

. GHTED OT GIVEN I R Y P CO IS N ISshaded N K O I O S What number sentence is shown by the squares on W the O S I AY.grids? M LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN HINT KLI C A REPR L E B B A O T T Compute—Write Sentence. Count the number of squares OOK IS NO HISaBNumber T I T that are shaded FOR light gray. Then count the number of squares that are shaded dark gray. Write a number sentence using those numbers.

A 0.25 ⫹ 0.19 ⫽ 0.44 B 1.00 ⫹ 0.19 ⫽ 1.19 C 1.00 ⫹ 0.25 ⫽ 1.25 D 1.25 ⫹ 0.19 ⫽ 1.44

92 © 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

Each square on the grid below equals 0.01.

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

What number sentence is shown by the shaded squares on the grid? A 0.58 ⫹ 0.23 ⫽ 0.81

. GHTED OT GIVEN I R Y P 0.68 ⫹ 0.23 ⫽ 0.91 IS CO SSION IS N . K O O B WAY RMI E Y 0.68 ⫹ 0.32 ⫽ 1.00 SAMPLE P N A . THIS ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

B 0.68 ⫹ 0.22 ⫽ 0.90 C D

93 © 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

Each square on the grids below equals 0.01.

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

What number sentence is shown by the shaded squares on the grids? A 1.00 ⫺ 0.19 ⫽ 0.81 B 1.00 ⫺ 0.18 ⫽ 0.82 C 1.37 ⫺ 0.18 ⫽ 1.19

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

D 1.37 ⫺ 0.10 ⫽ 1.27

94 © 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

Each square on the grids below equals 0.01.

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

What number sentence is shown by the shaded squares on the grids? A 0.7 ⫹ 0.5 ⫽ 1.2

B 0.8 ⫹ 0.5 ⫽ 1.3

C 1.0 ⫹ 0.5 ⫽ 1.5

D 1.2 ⫹ 0.5 ⫽ 1.7

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

95 © 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

Each square on the grids below equals 0.01.

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

What number sentence is shown by the shaded squares on the grids? A 1.00 ⫺ 0.25 ⫽ 0.75 B 1.00 ⫺ 0.35 ⫽ 0.65 C 0.75 ⫺ 0.25 ⫽ 0.50

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

D 0.75 ⫺ 0.35 ⫽ 0.40

96 © 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

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

Student Expectation

4.N.26. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 Round numbers less than 1,000 to the nearest tens and hundreds. 4.N.27. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Check reasonableness of an answer by using estimation.

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

97 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: Estimation 4.N.26 Round numbers less than 1,000 to the nearest tens and hundreds.

1

Mr. Able’s motor scooter weighs 267 pounds. What is 267 rounded to the nearest 100?

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

HINT Use a Formula or Rule. Think about the rules for rounding. Look at the digit to the right of the hundreds place. Is it less than, equal to, or greater than 5? Does the digit 2 stay the same or does it increase by 1? OR Draw a Picture or Diagram. Draw a number line from 200 to 300, TED. line. EN GHnumber I divided into intervals of 10. Place 267 P on the GIVWhich R T Y O N O C IS hundred is 267 closer to? BOOK IS ISSION AY.

A 100 B 200

MPLE TER. PERM IN ANY W A S S I TH MAS UCED D E O N I R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO

C 250 D 300

98 © 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

Zoe has 63 stuffed animals in her collection. What is 63 rounded to the nearest 10? A 50 B 60 C 70 D 80

3

Ms. Dixon’s car weighs 1,984 pounds. What is 1,984 rounded to the nearest 100? A 1,900 B 1,950

. GHTED OT GIVEN I R Y P IS CO SSION IS N . D 2,000 K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R LI KHillside C A L There are 796 students at Elementary. E REP What is 796 rounded to the B B A O T T O K nearest 10? IT IS N THIS BOO FOR C 1,990

4

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

A 700 B 790 C 800 D 810

99 © 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

There were 3,526 people at Friday’s basketball game. What is 3,526 rounded to the nearest 100? A 3,500 B 3,530 C 3,600 D 4,000

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

100 © 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 4.N.27 Check reasonableness of an answer by using estimation. 1

Mr. Dixon went shopping on Tuesday. He spent $62.40 for groceries, $47.22 for clothing, and $28.13 for books. Which statement is reasonable?

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

HINT Make Estimates. Estimate the total amount Mr. Dixon spent. Then pick the answer choice that is closest to your estimate.

A Mr. Dixon spent a total of $90.53 on Tuesday.

B Mr. Dixon spent a total of $109.62 on Tuesday.

HTED. GIVEN T O N C IS K on ION IS AY. O S O S I B Mr. Dixon spent a total ofP$275.50 Tuesday. M E YW P ER M L N A A . S R N I E S I TH MAST UCED D E O N I R L P K E A BLAC K TO BE R T O N IT IS IS BOO H T R FO

G C Mr. Dixon spent a total of $137.75 on Tuesday. OPYRI D

101 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

Ms. Knight went on a trip last week. On Monday she drove 322 miles, on Tuesday she drove 430 miles, and on Wednesday she drove 208 miles. Which statement is reasonable? A On her trip last week, Ms. Knight drove a total of 530 miles. B On her trip last week, Ms. Knight drove a total of 960 miles.

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

C On her trip last week, Ms. Knight drove a total of 1,522 miles. D On her trip last week, Ms. Knight drove a total of 2,880 miles.

3

Three buses are used for a field trip to the museum. There are 45 students on each bus. Which statement is reasonable? A There is a total of 45 students on the buses.

. GHTED OT GIVEN I R Y P O There is a total of 135 students on the IS N IS Cbuses. N K O I O S O S I WAY. RM E PLE B on the Y There is a total of 400SA students buses. P M N A . THIS ASTER ODUCED IN M E N I LACKL TO BE REPR B A T O K IT IS N THIS BOO FOR

B There is a total of 90 students on the buses. C D

102 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 craft show was held for 4 days. The table below shows the attendance at the craft fair. CRAFT FAIR ATTENDANCE Day

Number of People

Thursday

1,212

Friday

1,825

Saturday

3,595

Sunday

3,146

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

Which statement is reasonable?

A A total of 9,778 people attended the craft fair.

B A total of 7,978 people attended the craft fair.

C A total of 6,741 people attended the craft fair.

D A total of 3,037 people attended the craft fair.

5

. GHTED OT GIVEN I R Y P N CO IS feet IS Bridge N K O I The main span of the Verrazano-Narrows is 4,260 long. O S O S Y. The main I B A M E W L R E P Y P AM AN main span of the span of the Brooklyn HBridge than IN the ER. shorter D STfeet E T IS S isNE2,664 A C M U Verrazano-Narrows Bridge. statement I KLWhich EPROisD reasonable? C A R L E B B K TO Bridge is 596 feet long. NOT ofA the Brooklyn O O A The main B IT ISspan S HI FORofTthe Brooklyn Bridge is 1,596 feet long. B The main span C The main span of the Brooklyn Bridge is 5,856 feet long. D The main span of the Brooklyn Bridge is 6,924 feet long.

103 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

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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

104 © 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

. GHTED OT GIVEN I R Y P IS CO SSION IS N . K O O MI WAY LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR


D

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 Probability OOK IS

. GHTED OT GIVEN I R Y P CO IS N N O I S S I M WAY. LE B R E P Y P M N A A . THIS S NE MASTER ODUCED IN R KLI C A L E REP B B A O T T O K IT IS N THIS BOO FOR

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