dr. karen c. fuson - iusd.org

Volume 1

This material is based upon work supported by the

National Science Foundation under Grant Numbers

ESI-9816320, REC-9806020, and RED-935373.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the

National Science Foundation.

Developed byThe Children’s Math Worlds

Research ProjectPROJECT DIRECTOR AND AUTHOR

Dr. Karen C. Fuson

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ii

Copyright © 2006 by Houghton Mifflin Company. All rights reserved.

No part of this work may be reproduced or transmitted in any form or by any means,electronic or mechanical, including photocopying or recording, or by any informationstorage or retrieval system without the prior written permission of the copyright ownerunless such copying is expressly permitted by federal copyright law. With the exception ofnonprofit transcription into Braille, Houghton Mifflin is not authorized to grant permissionfor further uses of this work. Permission must be obtained from the individual copyrightowner as identified herein. Address requests for permission to make copies of HoughtonMifflin material to School Permissions, Houghton Mifflin Company, 222 Berkeley Street,Boston, MA 02116.

Printed in the U.S.A.

ISBN-13: 978-0-618-50984-3ISBN-10: 0-618-50984-4

2 3 4 5 6 7 8 9 KDL 11 10 09 08 07 06

CreditsCover art: (scale) © HMCo./Richard Hutchings. (elephant) © Art Wolfe/Stone/Getty Images.(chipmunk) © David W. Hamilton/The Image Bank/Getty Images.

Illustrative art: Robin Boyer/Deborah Wolfe, LTDTechnical art: Nesbitt Graphics, Inc.Photos: Nesbitt Graphics, Inc.

Special ThanksSpecial thanks to the many teachers, students, parents, principals, writers, researchers, andwork-study students who participated in the Children’s Math Worlds Research Project overthe years.

Teacher Reviewers

KindergartenPatricia Stroh SugiyamaWilmette, Illinois

Barbara WahleEvanston, Illinois

Grade 1Sandra BudsonNewton, Massachusetts

Janet PecciChicago, Illinois

Megan ReesChicago, Illinois

Grade 2Molly DunnDanvers, Massachusetts

Agnes LesnickHillside, Illinois

Rita SotoChicago, Illinois

Grade 3Jane CurranHonesdale, Pennsylvania

Sandra TuckerChicago, Illinois

Grade 4Sara Stoneberg LlibreChicago, Illinois

Sheri RoedelChicago, Illinois

Grade 5Todd AtlerChicago, Illinois

Leah BarryNorfolk, Massachusetts

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VOLUME 1 CONTENTS iii

Unit 1 Place Value and Multi-Digit Addition and Subtraction

Understand Place Value

1 Make Place Value Drawings . . . . . . . . 1FAMILY LETTER . . . . . . . . . . . . . . 3

2 Build Numbers and Represent MoneyAmounts. . . . . . . . . . . . . . . . . . . . . . . 7

Secret Code Cards . . . . . . . . . . . . . . . 7Going Further . . . . . . . . . . . . . . . . . 12

3 Place Value in Word Problems . . . . . . 134 Practice with Place Value . . . . . . . . . 15

Going Further . . . . . . . . . . . . . . . . 17

Grouping to Add

5 Explore Multi-Digit Addition . . . . . . . 19FAMILY LETTER . . . . . . . . . . . . . 21

6 Discuss Addition Methods . . . . . . . . . 237 Addition with Dollars and Cents . . . . 258 The Grouping Concept in Addition . . 27

Going Further . . . . . . . . . . . . . . . . 289 Practice Addition . . . . . . . . . . . . . . . 29

Going Further . . . . . . . . . . . . . . . . 30

Ungrouping to Subtract

10 Ungroup to Subtract . . . . . . . . . . . . . 3111 Subtract Across Zeros . . . . . . . . . . . . 3312 Discuss Methods of Subtracting. . . . . 3713 Relate Addition and Subtraction . . . . 3914 Subtraction Practice . . . . . . . . . . . . . 4115 Addition and Subtraction Practice . . . 43

Going Further . . . . . . . . . . . . . . . . 43UNIT 1 Test . . . . . . . . . . . . . . . . . . . 45

Mini Unit A Lines, LineSegments and Quadrilaterals

1 Measure Line Segments and Perimetersof Figures . . . . . . . . . . . . . . . . . . . . . 47

FAMILY LETTER . . . . . . . . . . . . . 51

2 Parallel and Perpendicular Lines andLine Segments . . . . . . . . . . . . . . . . . 53

3 Parallelograms, Rectangles, Squares,and Rhombuses . . . . . . . . . . . . . . . . 57

Going Further . . . . . . . . . . . . . . . . 614 Draw Parallelograms and

Rectangles . . . . . . . . . . . . . . . . . . . . 655 Classify Quadrilaterals . . . . . . . . . . . . 67

UNIT A Test . . . . . . . . . . . . . . . . . . . 69

Unit 2 Addition andSubtraction Word Problems

Solve Word Problems

1 Addition and Subtraction Situations . 71FAMILY LETTER . . . . . . . . . . . . . 75

2 Word Problems with Unknown Partners . . . . . . . . . . . . . . . . . . . . . . 77

3 Word Problems with Unknown Starts . . . . . . . . . . . . . . . . . . . . . . . . 79

4 Comparison Problems . . . . . . . . . . . . 815 Comparison Problems with

Misleading Language . . . . . . . . . . . . 83

Solve Multi-Digit Word Problems

6 Multi-Digit Unknown Partner andUnknown Start Problems . . . . . . . . . 85

7 Multi-Digit Comparison Problems . . . 89Going Further . . . . . . . . . . . . . . . . 91

8 Mixed Multi-Digit Word Problems . . . 93Going Further . . . . . . . . . . . . . . . . 95

UNIT 2 Test . . . . . . . . . . . . . . . . . . . 97

VOLUME 1 CONTENTS

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VOLUME 1 CONTENTS (CONTINUED)

Mini Unit B Figures, Angles,and Triangles

1 Symmetry and Congruence . . . . . . . 99FAMILY LETTER . . . . . . . . . . . 105

2 Label Figures and Draw Diagonals . . . . . . . . . . . . . . . . . . . 107

3 Angles and Triangles . . . . . . . . . . . 1114 Angle Measures . . . . . . . . . . . . . . 117

UNIT B Test . . . . . . . . . . . . . . . . . 121

Unit 3 Use Addition andSubtraction

Round, Estimate, and Compare

1 Round to the Nearest Hundred . . . 123FAMILY LETTER . . . . . . . . . . . 125

2 Round to the Nearest Ten . . . . . . . 127Going Further. . . . . . . . . . . . . . . 130

3 Compare Whole Numbers . . . . . . . 131

Use Money

4 Money Values . . . . . . . . . . . . . . . . 1335 Represent Money Amounts in

Different Ways . . . . . . . . . . . . . . . 1376 Make Change . . . . . . . . . . . . . . . . 1397 Round Money Amounts . . . . . . . . 141

Going Further. . . . . . . . . . . . . . . 144

Tables, Complex Word Problems, andBar Graphs

8 Ask Addition and SubtractionQuestions from Tables . . . . . . . . . . 145

Going Further. . . . . . . . . . . . . . . 147

9 Complete Tables . . . . . . . . . . . . . . 149Going Further. . . . . . . . . . . . . . . 151

10 More Practice with Tables . . . . . . . 15311 Word Problems with Extra or

Hidden Information . . . . . . . . . . . 15512 Word Problems with Not

Enough Information . . . . . . . . . . . 157Extra Practice . . . . . . . . . . . . . . . 160

13 Solve Two-Step Word Problems . . . 16114 Solve Multi-Step Word Problems . . 163

Going Further. . . . . . . . . . . . . . . 16515 Read and Create Bar Graphs . . . . . 167

Going Further. . . . . . . . . . . . . . . 16916 Read and Create Bar Graphs

with Multi-Digit Numbers . . . . . . . 17117 Data Day. . . . . . . . . . . . . . . . . . . . . . *

UNIT 3 Test . . . . . . . . . . . . . . . . . 175

Mini Unit C Patterns

1 Motion Geometry Patterns . . . . . . 179FAMILY LETTER . . . . . . . . . . . 183

2 Repeating Patterns . . . . . . . . . . . . 1853 Growing and Shrinking Patterns . . 187

UNIT C Test . . . . . . . . . . . . . . . . . 191

Glossary . . . . . . . . . . . . . . . . . . . . . S1

iv VOLUME 1 CONTENTS * This lesson consists only of activities from the Teacher’s Guide.

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1–1 Name Date

UNIT 1 LESSON 1 Make Place Value Drawings 1

� Practice Place Value Drawings to 999

1. 2.

5. 6.

3. 4.

Write the number for each drawing.place value

7. 86 8. 587

Make a place value drawing for each number.

Write the number for each dot drawing.

Vocabularyplace value

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1–1 Name Date

2 UNIT 1 LESSON 1 Make Place Value Drawings

� Practice with the Thousand Model

Write the number for each place value drawing.

9. 10.

11. 2,368 12. 5,017

Make a drawing for each number.

� Write Numbers for Word Names

Write the number for the words.

13. eighty-two

14. ninety-nine

15. four hundred sixty-seven

16. nine hundred six

17. one thousand, fifteen

18. eight thousand, one hundred twenty

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Dear Family,

Your child is learning math in an innovative program called Math Expressions. This program interweaves abstractmathematical concepts with everyday experiences of children. Thisapproach helps children to understand math better.

In Math Expressions your child will learn math and have fun by:

• working with objects and making drawings of math situations

• working with other students and sharing problem-solvingstrategies with them

• writing and solving problems and connecting math to daily life

• helping classmates learn

Your child will have math homework almost every day. He or sheneeds a Homework Helper. The helper may be anyone — you, anolder brother or sister (or other family member), a neighbor, or afriend.

Please decide who the main Homework Helper will be and askyour child to tell the teacher tomorrow.

Make a specific time for homework and provide your child with aquiet place to work. Encourage your child to talk about what heor she is doing in math class. If your child is having problems withmath, please talk to me to see how you might help.

To make the concepts clearer, the Math Expressions program usessome special methods and activities. Two are described on theback of this letter.

Thank you. You are vital to your child’s learning.

Sincerely,Your child’s teacher

continued �

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• Place Value Drawings: Students learn to represent numberswith drawings that show how many hundreds, tens, and onesare in the numbers. Hundreds are represented by boxes. Tensare represented by vertical line segments. Ones arerepresented by small circles. The drawings are also used tohelp students understand regrouping in addition andsubtraction. Here is a place value drawing for the number 178.

The 7 ten sticks and 8 circles are grouped in 5s so you can seethe quantities easily and avoid errors.

• Secret Code Cards: Secret Code Cards are a set of cards forhundreds, tens, and ones. Students learn about place value byassembling the cards to show two- and three-digit numbers.Here is how the number 148 would be assembled.

1 hundred 7 tens 8 ones

100

1 0 0100

1 0 0Hundreds card Tens card Ones card Assembled cards

40

4 040

4 0 000008

8008

8

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Estimada familia:

Su niño está aprendiendo matemáticas por medio de unprograma innovador llamado Math Expressions. Este programarelaciona conceptos matemáticos abstractos con la experienciadiaria de los niños. Esto ayuda a los niños a entender mejor lasmatemáticas.

Con Math Expressions su niño aprenderá matemáticas y sedivertirá mientras:

• trabaja con objetos y hace dibujos de problemas matemáticos

• trabaja con otros estudiantes y comparte con ellos estrategiaspara resolver problemas

• escribe y resuelve problemas, y relaciona las matemáticas consu vida diaria

• ayuda a sus compañeros a aprender.

Su niño tendrá tarea de matemáticas casi todos los días. Le haráfalta una persona que le ayude con la tarea. Esa persona puedeser usted, un hermano mayor (u otro familiar), un vecino o unamigo.

Por favor, decida quién será el ayudante principal y dígale a suniño que se lo informe al maestro mañana.

Establezca una hora para hacer la tarea y ofrezca a su niño unlugar tranquilo donde trabajar. Anime a su niño a comentar loqué está aprendiendo en la clase de matemáticas. Si su niño tieneproblemas con las matemáticas, por favor comuníquese conmigopara ver cómo puede ayudarlo.

Para presentar los conceptos de manera más clara, el programaMath Expressions usa métodos y actividades especiales. Dos deellos se describen en el reverso de esta carta.

Gracias. Su ayuda es muy importante en el aprendizaje de su niño.

Atentamente,El maestro de su niño

continúa �

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• Dibujos de valor posicional: Los estudiantes aprenden arepresentar números por medio de dibujos que muestrancuántas centenas, decenas y unidades contienen. Las centenasestán representadas con casillas, las decenas con segmentosde recta verticales y las unidades con círculos pequeños. Losdibujos también se usan para ayudar a los estudiantes a quecomprendan cómo se reagrupa en la suma y en la resta. Éstees un dibujo de valor posicional para el número 178.

Los palitos de decenas y los círculos se agrupan en grupos de5 para que puedan ver las cantidades más fácilmente y evitenerrores.

• Tarjetas de código secreto: Las tarjetas de código secreto sonun conjunto de tarjetas con centenas, decenas y unidades. Losestudiantes aprenden acerca del valor posicional organizandolas tarjetas de manera que muestren números de dos y de tresdígitos. Así es como se puede armar el número 148.

1 centena 7 decenas 8 unidades

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Tarjetade centenas

Tarjetade decenas

Tarjetade unidades

Tarjetas organizadas

100

1 0 0100

1 0 040

4 040

4 0 000008

8008

8

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UNIT 1 LESSON 2 Secret Code Cards 1–100 7

100

1 0 090

9 0

80

8 070

7 0

60

6 050

5 0

40

4 030

3 0

20

2 010

1 01

12

23

34

45

56

67

78

89

9

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Copyright © Houghton Mifflin Company. All rights reserved. 8 UNIT 1 LESSON 2 Secret Code Cards 1–100

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UNIT 1 LESSON 2 Secret Code Cards 200–1,000 9

200

2 0 0300

3 0 0400

4 0 0500

5 0 0600

6 0 0700

7 0 0800

8 0 0900

9 0 01000

1 0 0 0

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10 UNIT 1 LESSON 2 Secret Code Cards 200–1,000Copyright © Houghton Mifflin Company. All rights reserved.

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UNIT 1 LESSON 2 Build Numbers and Represent Money Amounts 11

3-4 Name Date1–2

� Money Drawings on the Dot Array

On the dot side of your MathBoard, make a drawing to represent each money amount.

1. $1.84 2. $4.17 3. $3.03

� Money Drawings Without Dots

On the blank side of your MathBoard, make a drawing to represent each money amount.

4. $3.58 5. $6.29 6. $16.17

Write the money value for each drawing.7. 8.

9. 10.

11. 12.

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12 UNIT 1 LESSON 2 Build Numbers and Represent Money Amounts

Write the place of the underlined digit. Then write its value.

1-2

� Numbers Through Ten Thousands

Name Date

1. 12,345

3. 58,436

2. 35,740

4. 89,782

Write the word name for each number.

5. 43,875

6. 75,086

7. 98,502

Write each number in .

8. 14,762

9. 27,013

10. 79,874

Write the number in .

11. 40,000 � 3,000 � 500 � 20 � 7

12. 50,000 � 4,000 � 300 � 8

13. 7 ten thousands � 6 hundreds � 5 ones

14. 9 ten thousands � 8 thousands � 4 hundreds � 7 tens

15. seventeen thousand, three-hundred ninety five

16. eighty nine thousand, one hundred five

standard form

expanded form

Vocabulary

expanded formstandard form

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1–3 Name Date

UNIT 1 LESSON 3 Place Value in Word Problems 13

� Solve and Discuss Use a place value drawing to help you solve eachproblem. Label your answers.

� Read and Write Numbers


11. On the Back Write your own place value word problem. Make a drawing to show how to solve your problem.

1. two hundred twelve

3. nine hundred ninety-one

2. two thousand, eight

4. six thousand, fifty one

Mario and Rosa baked 89 corn muffins. Theyput the muffins in boxes of 10.

Zoe’s scout troop collected 743 cans of food todonate to a shelter. They put the cans in boxesof 10.

5. Scott baked a batch of rolls. Hegave a bag of 10 rolls to eachof 7 friends. He kept 1 roll forhimself. How many rolls did hebake in all?

6. Sixty-two bags of hotdog bunswere delivered to the schoolcafeteria. Each bag had 10buns. How many buns weredelivered?

7. How many boxes did they fill? 8. How many muffins were left over?

9. How many boxes did they fill? 10. How many cans were left over

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Name Date

14 UNIT 1 LESSON 3 Place Value in Word Problems

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1–4 Name Date

UNIT 1 LESSON 4 Practice with Place Value 15

� Scrambled Place Value Names

Unscramble the and write the number. place values

1. 8 ones � 6 hundreds � 4 tens

3. 5 ones � 0 tens � 7 hundreds

5. 2 tens � 2 hundreds � 2 ones

2. 9 hundreds � 7 tens � 1 one

4. 5 tens � 4 ones � 3 hundreds

6. 8 hundreds � 3 ones � 6 tens

Unscramble the place values and write the number.Then, make a place value drawing for the number.

7. 6 hundreds � 9 ones � 3 tens 8. 9 ones � 3 tens � 8 hundreds

9. 8 ones � 3 hundreds � 4 tens 10. 2 hundreds � 9 tens � 1 one

Vocabularyplace value

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1–4 Name Date

16 UNIT 1 LESSON 4 Practice with Place Value

� Solve and Discuss Solve each problem. Label your answer.

11. The bookstore received 35 boxes of books.Each box held 10 books. How many books didthe store receive?

12. How many baskets did they fill? 13. How many apples were left over?

14. How many bags did Aidee fill? 15. How many buttons were left over?

Aidee had 672 buttons. She put them in bagswith 100 buttons each.

Maya’s family picked 376 apples and put themin baskets. Each basket holds 10 apples.

16. How many piles of 100 didJoseph make?

17. How many extra pennies did hehave?

When Joseph broke open his piggy bank, therewere 543 pennies inside. He grouped thepennies into piles of 100.

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UNIT 1 LESSON 4 Practice with Place Value 17

� Numbers Through Hundred Thousands

Write the place of the underlined digit. Then write its value.

1. 345,127

3. 243,584

2. 453,407

4. 978,512

1-4 Name Date

Write the word name for each number.

5. 327,582

6. 408,681

7. 856,406

Write each number in expanded form.

8. 476,213

9. 528,036

10. 920,653

Write the number in standard form.

11. 300,000 � 20,000 � 5,000 � 200 � 30 � 6

12. 500,000 � 40,000 � 3,000 � 100 � 8

13. 7 hundred thousands � 6 ten thousands � 4 thousands

14. 9 hundred thousands � 5 thousands � 4 hundreds � 6 tens

15. two hundred seventy seven thousand, three-hundred ninety five

16. nine hundred ninety nine thousand, one hundred ten

17. On the Back Design your own ten thousand and hundred thousand bar to make a place value drawing for 125,436. Explain why you made them that way.

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18 UNIT 1 LESSON 4 Practice with Place Value

Name Date

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1–5 Name Date

UNIT 1 LESSON 5 Explore Multi-Digit Addition 19

� Solve and Discuss

Solve each problem. Label your answer. Use yourMathboard or a separate sheet of paper.

1. Elena made necklaces for her friends. She used586 green beads and 749 red beads. How manybeads did Elena use in all?

2. Fabrice has a collection of 485 basketball cardsand 217 baseball cards. How many sports cardsdoes Fabrice have in all?

� Introduce Addition MethodsTonya and Mark collect seashells. Tonya has 249 shells, and Mark has 386 shells. How many shells do they have in all?

Here are three ways to find the answer:

Show all totalsMethod

New GroupsBelow Method

New GroupsAbove Method

21419

� 386��

635

249� 386��

61315

249� 386��

500120

� 15��

635

Proof Drawing:

6 hundreds 3 tens 5 ones

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1–5 Name Date

20 UNIT 1 LESSON 5 Explore Multi-Digit Addition

� Practice Addition Methods

Solve each problem. Make proof drawings to show your answers are correct.

3. Ryan has two stamp albums. Onealbum has 554 stamps, and theother has 428 stamps. How manystamps does Ryan have in all?

4. One week Ashley read 269pages. The next week she read236 pages. What is the totalnumber of pages she read in thetwo weeks?

5. The video store has 445 comedyvideos and 615 drama videos.How many comedy and dramavideos does the store havealtogether?

6. Ali has 128 photos of her petsand 255 photos of her family.How many photos does Ali havealtogether?

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UNIT 1 LESSON 5 Explore Multi-Digit Addition 21

Dear Family,

Your child is currently participating in math activities that helphim or her to understand addition and subtraction of 2- and 3-digit numbers.

Addition Methods: Students may use the common U.S. method,referred to as the New Groups Above Method, as well as twoalternative methods. In the New Groups Below Method, studentsadd from right to left and write the new ten and new hundred onthe line. In the Show All Totals method, students add in eitherdirection, write partial sums and then add the partial sums to getthe total. Students also use proof drawings to demonstrategrouping 10 ones to make a new ten and grouping 10 tens tomake a new hundred.

Subtraction Methods: Students may use the common U.S. methodin which the subtraction is done right to left, with the ungroupingdone before each column is subtracted. They also learn analternative method in which all the ungrouping is done before thesubtracting. If they do all the ungrouping first, students cansubtract either from left to right or from right to left.

Please call if you have any questions or comments.

Thank you.


New GroupsBelow:

Show All Totals: Proof Drawing:New GroupsAbove:

46+ 37

83

1

Add right to left.

46+ 37

831

the newten

the new ten

8 tens 3 onesthe new ten

Add left to right.

46+ 37

83

7013

463– 275

188

3 515

131. Ungroup first2. Subtract (from left to right or from right to left).

Ungroup 1 hundredto make 10 tens.

3 hundreds 15 tens 13 ones

Ungroup 1 ten tomake 10 ones.

The New Groups Below Method shows theteen number 13 better than does the NewGroups Above Method, where the 1 and 3are separated. Also, addition is easier inNew Groups Below, where you add the 2 numbers you see and just add 1.

The Ungroup First Method helps studentsavoid the common error of subtracting asmaller top number from a larger bottomnumber.

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22 UNIT 1 LESSON 5 Explore Multi-Digit Addition

Estimada familia:

En estos momentos, su niño está participando en actividadesmatemáticas que le ayudan a comprender la suma y la resta denúmeros de 2 y de 3 dígitos.

Métodos de suma: Los estudiantes pueden usar el método comúnde los EE. UU., conocido como método de grupos nuevos arriba, ydos métodos alternativos. En el método de grupos nuevos abajo,los estudiantes suman de derecha a izquierda y escriben la nuevadecena y la nueva centena en el renglón. En el método de mostrartodos los totales, los estudiantes suman en cualquier dirección,escriben sumas parciales y luego las suman para obtener el total.Los estudiantes también usan dibujos de prueba para demostrarcómo se agrupan 10 unidades para hacer una nueva decena, y 10decenas para hacer una nueva centena.

Grupos nuevosabajo:

Mostrar todoslos totales:

Dibujo de prueba:Grupos nuevosarriba:

46+ 37

83

1

Sumar de derecha a izquierda.

46+ 37

831

la decenanueva

la decena nueva

8 decenas 3 unidades

la decena nueva

Sumar de izquierda a derecha.

46+ 37

83

7013

463– 275

188

3 515

131. Desagrupa primero.2. Resta (de izquierda a derecha o de derecha a izquierda).

Desagrupar 1 centenapara formar 10 decenas.

3 centenas 15 decenas 13 unidades

Desagrupar 1 decena paraformar 10 unidades.

Métodos de resta: Los estudiantes pueden usar el métodocomún de los EE. UU., en el cual la resta se hace de derecha aizquierda, desagrupando antes de restar cada columna. Tambiénaprenden un método alternativo en el que desagrupan todo antesde restar. Si los estudiantes desagrupan todo primero, puedenrestar de izquierda a derecha o de derecha a izquierda.

Si tiene alguna pregunta o comentario, por favor comuníqueseconmigo. Gracias.


El método de Gruposnuevos abajo muestra elnúmero 13 mejor que elmétodo de Gruposnuevos arriba en el quese separan los números1 y 3. Además, es másfácil sumar con Gruposnuevos abajo, donde sesuma los dos númerosque se ven ysimplemente se añade 1.

El método deDesagrupar primeroayuda a los estudiantes aevitar el error común derestar un númeropequeño de arriba a unnúmero más grande deabajo.

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1–6 Name Date

UNIT 1 LESSON 6 Discuss Addition Methods 23


Solve each problem using a numerical method anda proof drawing.

1. There are 359 cars and 245 trucks in the parking garage. How many vehicles are in the garage?

2. The Creepy Crawler exhibit atthe science museum has 693spiders and 1,592 centipedes.How many spiders andcentipedes are there in all?

3. On Saturday, 1,590 people wentto the art fair. On Sunday, itrained, and only 355 went to thefair. How many people went tothe fair altogether?

4. There were 1,120 people on theferry yesterday. Today the ferryhad 967 people. How manypeople did the ferry have in allduring the past two days?

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Name Date1–6

24 UNIT 1 LESSON 6 Discuss Addition Methods

� The Puzzled Penguin

Dear Math Students:

Today I found the answer to 163 + 78, but I don’t know if I

added correctly. Please look at my work. Is my

answer right? If not, please correct my work

and tell what I did wrong.

Thank you,

The Puzzled Penguin

168

948

+781

� Line Up the Places to Add

Write each addition vertically. Line up the places correctly. Then add and make a proof drawing.

5. 179 � 38 � 6. 1,250 � 345 � 7. 907 � 877 �

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1–7 Name Date

UNIT 1 LESSON 7 Addition With Dollars and Cents 25

Use the pictures above to solve. Use a MathBoardor a separate sheet of paper.

1. Maria wants to buy milk and cheese. How muchwill the two items cost?

2. Arturo wants to buy a tomato and a steak. Howmuch will Arturo’s groceries cost?

3. Tamika wants to buy bananas and awatermelon. How much will she spend?

4. Choose two items. Which items did you choose?How much do they cost together?

$3.49 $1.89 $0.75 $4.20

$0.99 $2.35 $1.49 $0.40

� Add Money

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1–7 Name Date

26 UNIT 1 LESSON 7 Addition With Dollars and Cents

5. How much would the two most expensive itemson your list cost altogether?

6. How much would the two least expensive itemscost in all?

7. What would be the total cost of your twofavorite items?

8. Which items would you buy if you had $5.00 tospend?

9. Use the grocery ad to write and solve a wordproblem involving money.

� Add Money Amounts from a Grocery Store Ad

Use an ad from a grocery store. List the names and prices of five or six items you would like to buy. Then answer the questions below.

Show your work.

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1–8 Name Date

UNIT 1 LESSON 8 The Grouping Concept in Addition 27

� Solve and DiscussUse the menu above to solve. Use a MathBoard ora separate sheet of paper.

1. Mr. Jackson ordered a grilled cheese sandwichand an iced tea. How much did his order cost?

2. Mrs. Lin ordered a glass of lemonade and achicken sandwich. How much did she spend?

3. Choose a Method Kurt and Ana ordered twosalads. Think of a fast way to find the total cost.Describe your method.

4. Number Sense Anne-Marie has only $1.50. Which two items could she buy?

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28 UNIT 1 LESSON 8 The Grouping Concept in Addition

� Use the Guess and Check Strategy

Use the pictures above to solve.

1. José bought two items. He paid with a $5 bill and two $1 bills, and got $0.50 change. Which items did he buy?

2. Explain how you found your answer.

Sneakers Socks Shirt

Shorts JacketCap

$4.65

$0.95$2.95

$5.45

$7.65

$1.85

1-8 Name Date

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1–9 Name Date

UNIT 1 LESSON 9 Practice Addition 29

You and your partner can take turns being a customerand a server at Carmen’s Café. Follow these steps:

• The customer chooses two items from the menu.

• The server writes down the names and prices ofthe two items and figures out the total cost.

• The customer checks to make sure the total iscorrect.

Show your work on a separate sheet of paper.


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30 UNIT 1 LESSON 9 Practice Addition

1. Jeremy bought a dog and a cat. How much didhe spend in all?

2. Keisha bought a horse. Juan bought a pig. Howmuch did they spend together?

3. Chan bought a cat, a duck, and a horse. Whatwas the total cost?

4. Choose a Method Rani wants to buy tworabbits. Think of a fast way to find the totalcost. Describe your method.

5. Number Sense Betty has $20.00. Is that enoughmoney for her to buy a cow and a horse?Explain why or why not.

� Add Larger Money Amounts

1–9 Name Date

$8.95

$6.38

$9.29 $7.39 $9.89$8.79 $12.69

$9.99

Use the pictures above to solve. Use your MathBoard or a separate sheet of paper.

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1–10 Name Date

UNIT 1 LESSON 10 Ungroup to Subtract 31

1. Make a place value drawing for 134. Take away 58.How many are left?

2. Write a numerical solution method for what youdid in the drawing.

3. Describe how you ungrouped to subtract.

Mr. Kim had 134 jazz CDs. He sold 58 of them at hisgarage sale. How many jazz CDs does he have now?

� Discuss Subtraction Methods

Solve this word problem.

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1–10 Name Date

� Subtraction DetectiveTo avoid making subtraction mistakes, look at the topnumber closely. Do all the you need tobefore you . The magnifying glass around thetop number helps you remember to be a “subtractiondetective.”

Subtract. Show your ungroupings numerically andwith proof drawings.

subtractungrouping

Dear Math Students:

Today I found the answer to 134 – 58, but I don’t know if I did it

correctly. Please look at my work. Is my answer right? If not,

please correct my work and tell what I did wrong.

Thank you,

The Puzzled Penguin

134

124

– 58

� The Puzzled Penguin

32 UNIT 1 LESSON 10 Ungroup to Subtract

Vocabularyungroupingsubtract

4. 5. 6. 7.

277– 68

459–175

163– 47

371– 86

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1–11 Name Date

UNIT 1 LESSON 11 Subtract Across Zeros 33

Solve each problem. Show your work numerically andwith proof drawings.

1. Lakesha bought a box of 500 paper clips. So far, shehas used 138 of them. How many are left?

2. A movie theater has 400 seats. At the noon show,329 seats were filled. How many seats were empty?

3. At the start of the school year, Seiko had a brandnew box of 300 crayons. Now 79 crayons arebroken. How many unbroken crayons does Seikohave?

� Ungroup to Subtract

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1–11 Name Date

34 UNIT 1 LESSON 11 Subtract Across Zeros

Solve each problem. Show your work numerically andwith proof drawings.

4. Armando brought $9.00 to the store. He bought agame for $3.42. How much money did he have left?

5. Shelby’s neighbor gave her $5 for pulling the weedsin his garden. She spent $1.79 on a jump rope. Howmuch money does she have left?

6. Harold got $4.00 for his allowance. He spent $2.68for an ice cream cone. How much money does hehave left?

� Subtract from Whole-Dollar Amounts

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1–11 Name Date

� Practice Subtracting Across ZerosSubtract. Make proof drawings for exercises 7–10.

7. 8.

9. 10.

11. 12.

13. 14. 3, 0 0 0� 6 5 4��

2, 0 0 0� 1 7 6��

1, 0 0 0� 3 9 7��

6 0 0� 5 7 5��

9 0 0� 8 1 8��

4 0 0� 2 1 7��

5 0 0� 3 3 3��

8 0 0� 3 9 1��

UNIT 1 LESSON 11 Subtract Across Zeros 35

15. On the Back Write a word problem that is solved by subtracting a 3-digit number from a number of thousands. Then solve the problem.

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36 UNIT 1 LESSON 11 Subtract Across Zeros

Name Date

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1–12 Name Date

UNIT 1 LESSON 12 Discuss Methods of Subtracting 37

Tony

Tony started ungrouping from theleft.

1. He has enough hundreds.

2. He does not have enough tens.He ungroups 1 hundred to make10 more tens.

3. He does not have enough ones.He ungroups 1 ten to make 10more ones.

4. Complete the subtraction.

Maria

Maria started ungrouping from theright.

1. She does not have enough ones.She ungroups 1 ten to make 10more ones.

2. She does not have enough tens.She ungroups 1 hundred to get10 more tens.

3. She has enough hundreds.

4. Complete the subtraction.

�Ungroup from Left or Right

Tony and Maria each solved this problem:

On Tuesday morning, a music store had 463 copies of the new School Daze CD. By the end of the day, they had sold 275 copies. How many copies were left?

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Name Date1–12

38 UNIT 1 LESSON 12 Discuss Methods of Subtracting

Imagine that you have the amount of money shown to spend at Andy’s Arts and Crafts Store each day.

Monday $8.00

Tuesday $7.25

Wednesday $6.50

Thursday $6.95

Friday $6.20

Here’s what to do for each day:

• Choose two, three, or four different items you want to buy.

• Find the total cost for the items.

• Figure out how much money you will have left for that day.



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1–13 Name Date

� Relate Addition and Subtraction

Solve each problem. Make a proof drawing.

1. There were 138 students in the gym for theassembly. Then, 86 more students came in. Howmany students were in the gym altogether?

2. There were 224 students in the gym for theassembly. Then, 86 students left. How manystudents were left in the gym?

3. Look at your addition, subtraction, and proofdrawings above. How are addition and subtractionrelated?

UNIT 1 LESSON 13 Relate Addition and Subtraction 39

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Name Date1–13

40 UNIT 1 LESSON 13 Relate Addition and Subtraction

4. Marly had 275 baseball cards. Her brother gaveher a collection of 448 baseball cards. Howmany baseball cards does Marly have now?

5. Write a subtraction word problem related to theaddition word problem in problem 4. Then findthe answer without doing any calculations.

6. Brian spent $5.17. He spent $3.29 on drawingpencils and the rest on paper. How much moneydid he spend on paper?

7. Write an addition word problem related to thesubtraction word problem in problem 6. Thenfind the answer without doing any calculations.


Solve. Label your answers. Show your work.

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1–14 Name Date

� Subtract and Check

Solve each problem.

1. Zane had $4.00. He bought a book for $3.76.How much money does he have left? Check bymaking a proof drawing.

2. Jasmine bought a cap. She paid with a $5.00 billand got $1.62 in change. How much did the capcost? Check by adding.

3. At the diner, Rita ordered the breakfast specialfor $2.91. She had $3.25 when she arrived at thediner. How much did she have after she paid herbill? Check by adding.

4. Bill bought a CD for $5.98. He paid with a $10.00 bill. What will his change be? Check by adding.

UNIT 1 LESSON 14 Subtraction Practice 41

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Name Date1–14

42 UNIT 1 LESSON 14 Subtraction Practice

5. Did she have to tomake more tens? Explain.

6. Did she have to ungroup tomake more ones? Explain.

ungroup

� Practice Deciding When to Ungroup

Answer each question.

Adair subtracted 595 from 834.

Beatrice subtracted 441 from 950.

7. Did she have to ungroup tomake more tens? Explain.

8. Did she have to ungroup tomake more ones? Explain.

Wan subtracted 236 from 546.

9. Did he have to ungroup tomake more tens? Explain.

10. Did he have to ungroup tomake more ones? Explain.

Vocabularyungroup

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UNIT 1 LESSON 15 Addition and Subtraction Practice 43

� Choose Mental Math, Pencil and Paper,or Calculator

Add or subtract. Then write what computation you used. Write (p) for paper-and-pencil, (c) for

, or (m) for .

1. 2. 3.

Method: Method: Method:

4. 5. 6.


7. 8. 9.


$23,000� 14,000��

12,534� 29,798��

$9,743� $5,221��

2,000� 5,700��

$9.25� $4.01��

495� 938��

537� 591��

79� 87��

$8.00� 7.50��

mental mathcalculator

method

1-15 Name Date

12. On the Back Play the Method Show-Down game.

Vocabulary

methodcalculatormental math

Solve each problem. Write whether you usedpaper-and-pencil, a calculator, or mental math.

10. Liz scores 20,000 points in her first turn. Shescores 19,000 points on her second turn. Howmany points did she score altogether?

11. There were 17,948 people at the basketballgame on Friday night. There were 16,777people at the game on Saturday night. Howmany more people were there on Friday nightthan on Saturday night?

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44 UNIT 1 LESSON 15 Relate Addition and Subtraction

� Method Show-Down GameWork in groups of three. Write the following methods on three separate index cards.

To play the game.

1. Each student writes an addition or subtraction exercise using numbers up to 5 digits on an index card. Put the cards in a paper bag.

2. One student mixes the three method cards and distributes them to the group, while another student picks an exercise card from the paper bag. Each student then uses the method on his or her card to solve the problem. The first student to get the correct answer scores 1 point. Mental math may be really difficult for problems with large numbers.

3. Mix the method cards and repeat the activity. The first student to earn 5 points wins the game.

calculatorpaper and

pencil mental math

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Name Date

UNIT 1 Test 45

1. 57 2. 392

1

Make a place value drawing for each number.

Unscramble the place values and write the number.

3. 9 ones � 6 hundreds � 4 tens

4. 5 hundreds � 2 ones � 3 tens

5. 5 ones � 7 hundreds � 1 thousand � 6 tens

6. 8 tens � 4 ones � 0 hundreds � 1 thousand


7. eight hundred seventy-two

8. five hundred four

9. one thousand fifty

Add or subtract.

10. 435 � 283 � 11. 962 � 87 �

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Name Date

46 UNIT 1 Test

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1

15. 16. 17. $10.00� 7.54��

$5.31� 0.32��

$3.29� 5.98��

18. Gordon baked 346 blueberry muffins and 287 bran muffins. How many muffins did he bake in all?

19. Write a subtraction word problem related to the addition word problem in problem 18. Then find the answer without doing any calculations.

20. Extended Response Veronica has 423 baseball cards. She put them in piles of 10 cards each.

How many piles of 10 cards did she make?

How many extra cards did she have?

Explain your reasoning.

12. 13. 14. 800� 684��

617� 549��

972� 129��

Add or subtract. Use extra paper if you need it.

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A–1 Name Date

UNIT A LESSON 1 Measure Line Segments and Perimeters of Figures 47

Vocabulary

line segmentcentimeter� Measure Line Segments

Measure each to the nearest .

1.

2. 3.

4.

centimeterline segment

5.

6.

cm

cm

cm

cm

cm

cm

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A–1 Name Date

48 UNIT A LESSON 1 Measure Line Segments and Perimeters of Figures

Vocabulary

horizontalvertical� Draw Line Segments of Given Lengths

Draw each line segment.

7. a line segment about 7 cm long

8. a line segment about 4 cm long

9. a slanted line segment about 13 cm long

10. a vertical line segment that is a little more than 2 cm long

11. a horizontal line segment that is a little less than 9 cm long

vertical

horizontal

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A–1 Name Date


Vocabulary

perimeter

12.

14.

13.

15.

� Measure the Perimeter of a Triangle

Find the of each triangle to the nearest centimeter.perimeter

16. Join the points to make a triangle. Find its perimeter.

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Vocabulary

quadrilateral

17. 18.

19. 20.

� Measure the Perimeter of a Quadrilateral

Find the perimeter of each to the nearest centimeter.quadrilateral

21. Join the points to make a rectangle. Find its perimeter.

78293.UAL01_047-052 3/23/06 12:20 PM Page 50


Dear Family,

Your child will be learning about geometry during this schoolyear. This first unit is about the geometric figures calledquadrilaterals. These get their name because they have four(quad-) sides (-lateral).

Students will learn about four different kinds of quadrilaterals inthis unit.

Each side of a quadrilateral is a part or a segment of a straightline. Your student will practice making careful measurements ofline segments.

Students will measure line segments in centimeters in this unit.Centimeters are a convenient size for measuring and they areclosely linked to the base 10 numeration system we use.

Your student will be able to recognize and describe differentquadrilaterals by their sides. Some sides may be of equal length.Some sides may be parallel: they do not meet no matter how farthey are extended. Some sides may be perpendicular: where theymeet is like the corner of a square.

If you have any questions, please call or write to me.Thank you.


10 2 3 4 5 6 7 8 9 10 11

Parallelogramopposite sides parallel

Rectangleopposite sides parallel

adjacent sides perpendicular

Squareopposite sides parallel

adjacent sides perpendicularall sides equal in length

Rhombusopposite sides parallel

all sides equal in length

78293.UAL01_047-052 3/23/06 12:20 PM Page 51


Estimada familia:

Durante este año escolar, su niño aprenderá geometría. Laprimera unidad se ocupa de figuras geométricas llamadascuadriláteros. Éstas se llaman así porque tienen cuatro lados.

En esta unidad los estudiantes aprenderán acerca de cuatro tiposdiferentes de cuadriláteros.

Cada lado de un cuadrilátero es parte de un segmento de recta.Su niño practicará cómo medir segmentos de rectacuidadosamente.

En esta unidad los estudiantes medirán segmentos de recta encentímetros. Los centímetros son una medida apropiada y estándirectamente relacionados con el sistema numérico de base 10que usamos.

Su niño podrá reconocer y describir diferentes cuadriláteros segúnsus lados. Algunos lados pueden tener la misma longitud.Algunos lados pueden ser paralelos: nunca se encuentran a pesarde lo largos que sean. Algunos lados pueden ser perpendiculares:cuando se encuentran, forman lo que podría ser el vértice de uncuadrado.



10 2 3 4 5 6 7 8 9 10 11

Paralelogramolados opuestos paralelos

Rectangulolados opuestos paralelos

lados adyacentes perpendiculares

Cuadradolados opuestos paralelos

lados adyacentes perpendicularestodos los lados de igual longitud

Rombolados opuestos paralelos

todos los lados de igual longitud

`

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3-4 Name DateA–2

� Define Lines and Line Segments

A is a straight path that goes on forever in bothdirections. When we draw a line, we put arrows on the ends to show that it goes on and on. Here aresome lines.

line

UNIT A LESSON 2 Parallel and Perpendicular Lines and Line Segments 53

A is part of a line. It has two ends,which are called . Here are some linesegments.

endpointsline segment

endpoint

endpoint

1. You can measure to find the length of a line segment, but you cannot measure to find the length of a line. Explain why.

Vocabulary

lineline segmentendpoint

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Name DateA–2

54 UNIT A LESSON 2 Parallel and Perpendicular Lines and Line Segments

Vocabulary

parallelperpendicular

2. What do you think it means for two lines to be parallel?

� Define Parallel Lines

The lines or line segments in thesepairs are .parallel

The lines or line segments in thesepairs are not parallel.

3. What do you think it means for two lines to be perpendicular?

� Define Perpendicular LinesThe lines or line segments in thesepairs are .perpendicular

The lines or line segments in thesepairs are not perpendicular.

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3-4 Name DateA–2

UNIT A LESSON 2 Parallel and Perpendicular Lines and Line Segments 55

Vocabulary

adjacentopposite� Identify Opposite and Adjacent Sides

Look at these quadrilaterals.

a

b d

cb

d

a c

a

db

c

c

d a

b

In all of the quadrilaterals, the sides labeled a and bare to each other. The sides labeled b and care also adjacent to each other.

4. What do you think it means for two sides to be adjacent?

5. Which other sides are adjacent to each other?

In all of the quadrilaterals, the sides labeled a and care each other.

6. What do you think it means for two sides to be opposite each other?

7. Which other sides are opposite each other?

opposite

adjacent

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Name DateA–2

56 UNIT A LESSON 2 Parallel and Perpendicular Lines and Line Segments

12. Draw a pair of parallel line segments.

13. First, draw a line segment 3 cm long. Then, draw a line segment 6 cm long that looks perpendicular to your first line segment.

14. Name two perpendicular adjacent sides in this figure.

15. Name two parallel opposite sides in the figure.

� Identify Types of LinesTell whether each pair of lines is parallel,perpendicular, or neither.

8. 9.

10. 11.

a

d

c

b

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A–3 Name Date

UNIT A LESSON 3 Parallelograms, Rectangles, Squares, and Rhombuses 57

Vocabulary

parallelogramquadrilateral� Define a Parallelogram

All of these figures are .parallelograms

A B C D E

These figures are not parallelograms.

FG H

IJ

1. A parallelogram is a

� Measure Parallelograms

For each parallelogram, measure the sides and label them with their lengths. Then, find the perimeter.

quadrilateral

2. cm 3. cm 4. cm

5. Look at the lengths of the sides. What patterns do you notice?

Complete the sentence.

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A–3 Name Date

58 UNIT A LESSON 3 Parallelograms, Rectangles, Squares, and Rhombuses

Vocabulary

rectanglesquarerhombus

� Define a RectangleAll of these figures are .rectangles

6. A rectangle is a parallelogram

7. A square is a rectangle

8. A rhombus is a parallelogram

Adel said, “Rectangles are special kinds of parallelograms.”

Takeshi said, “Squares are special kinds of rectangles.”

Cora said, “Rhombuses are special kinds of parallelograms.”

Complete the sentence.

Complete each sentence.

� Explore Squares and Rhombuses

These figures are . These figures are .rhombusessquares

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3-4 Name DateA–3

Vocabulary

rectanglesquare� Find the Perimeters of Rectangles and Squares

Find the perimeter of each figure without measuring allfour sides.

These figures are .rectangles


9. cm 10. cm

11. cm 12. cm

These figures are .squares

13. Write About It How are rectangles and squares the same? How are they different?

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A–3

Vocabulary

quadrilateralparallelogramrectanglesquare

� Describe Quadrilaterals

Use as many words below as possible to describe each figure.

quadrilateral parallelogram rectangle square

14.

15.

16.

17.

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UNIT A LESSON 3 Tangram Figures 61

A-3

� Tangram FiguresCarefully cut out each figure along the dotted lines.Make sure you cut as carefully and straight as you can.

Use your figures to create the patterns on StudentActivity Book page 63.

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62 UNIT A LESSON 3 Tangram FiguresCopyright © Houghton Mifflin Company. All rights reserved.

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0–0


A-3

Use your tangram figures from page 61 tomake this cat. When you finish, draw linesto show how you placed the figures.

On the Back Create your own pattern with tangramsand make a drawing of it.

Name Date

Try to create as manyof these patterns asyou can.

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UNIT A LESSON 4 Draw Parallelograms and Rectangles 65

Vocabulary

wordword

Vocabulary

oppositeparallelogram� Explore Parallelograms

1. Write what you know about the sides of a .

2. Draw three different parallelograms.

parallelogramopposite

a

b

d

c

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66 UNIT A LESSON 4 Draw Parallelograms and Rectangles

Vocabulary

rectangleadjacent� Review Rectangles

3. Write everything you know about the opposite sides of a .

4. What do you know about the sides of a rectangle?

5. Draw three different rectangles on the grid.

adjacent

rectangle

h

e

g

f

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UNIT A LESSON 5 Classify Quadrilaterals 67

�Describe Quadrilaterals

Place a check mark beside every name that describesthe figure.

1. 2. 3.

quadrilateral quadrilateral quadrilateralparallelogram parallelogram parallelogramrhombus rhombus rhombusrectangle rectangle rectanglesquare square square

4. 5. 6.

quadrilateral quadrilateral quadrilateralparallelogram parallelogram parallelogramrhombus rhombus rhombusrectangle rectangle rectanglesquare square square

7. For each figure, put Xs under the descriptions that are always true.

Four sides Both pairs of Both pairs of Four square All sides the opposite sides opposite sides corners same length

parallel the same length

Quadrilateral

Parallelogram

Rhombus

Rectangle

Square

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68 UNIT A LESSON 5 Classify Quadrilaterals

Use the finished chart on page 67 to complete each statement.

8. Parallelograms have all the features of quadrilaterals plus

9. Rectangles have all the features of parallelograms plus

10. Squares have all the features of quadrilaterals plus

11. Squares have all the features of parallelograms plus

12. Squares have all the features of rectangles plus

� Draw Quadrilaterals if Possible

Draw each figure if you can. If it is impossible, explain why.

13. Draw a quadrilateral that is not a parallelogram.

14. Draw a square that is not a rectangle.

15. Draw a parallelogram that is not a rectangle.

16. Draw a rectangle that is not a square.

17. Draw a rhombus that is not a parallelogram.

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UNIT A Test 69

1. 2.

A

Find the perimeter of each figure. Use a centimeter ruler.

3. 4.

Name each figure.

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70 UNIT A Test

Put a check mark beside every name that describes the figure.

9. Draw two perpendicular line segments on the dot array.

10. Extended Response Explain what it means for two line segments to be parallel.

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A

5.

quadrilateralnot a quadrilateralrectanglesquare

7.


6.


8.


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3-4 Name Date2–1

�Math Mountains and Equations

Complete.

1. Look at the Math Mountain and the 8 .What relationships do you see? In each equation,label each number as a (P) or the (T ).totalpartner

equations

UNIT 2 LESSON 1 Addition and Subtraction Situations 71

Vocabulary

partneraddendequation

totalsum

11 � 7 � 4 7 + 4 � 11

11 � 4 � 7 4 + 7 � 11

4 � 11 � 7 11 � 7 � 4

7 � 11 � 4 11 � 4 � 7

2. Write the 8 equations for this Math Mountain.Label each number as the total (T ) or a partner (P).

sumtotal11

7partneraddend

4partneraddend

14

8 6

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2–1 Name Date

72 UNIT 2 LESSON 1 Addition and Subtraction Situations

�Solve and Discuss

Solve each problem. Label your answers.

3. Change Plus Chris picked 8 apples. His motherpicked 6 more. How many apples do they havenow?

4. Change Minus Chris had 14 apples. He ate 8 ofthem. How many apples does he have now?

5. Put Together Alison has 7 juice boxes. Taylor has5 juice boxes. How many juice boxes do theyhave altogether?

6. Take Apart There are 12 juice boxes at thepicnic. Alison puts 7 on the table and leaves therest in the cooler. How many juice boxes are inthe cooler?

Show your work.

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2–1 Name Date


�Represent Word Problems with Math ToolsThe equations and Math Mountains below show theword problems on page 72.

7. Write the unknown numbers in the boxes.

8. How are these math tools the same? How are theydifferent?

9. On the Back Write a word problem for thisequation: 11 � 4 � . Then solve it.

Change Plus Change Minus

Put Together Take Apart

8 6

6Mom total

7 5

8Chris

� �

5Taylor total

7Alison

� �

8

14

8ate now

14total

� �

7table cooler

12total

� �

12totalcooler

7table

� �

7

12

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Dear Family,

In this unit, your child will solve addition and subtraction wordproblems involving a total and two partners.

• If one of the partners is unknown, it can be found bysubtracting the known partner from the total or by countingon from the known partner to the total.

• If the total is unknown, it can be found by adding the partners.

Math Mountains are used to show a total and two partners.Students can use the Math Mountain to write an equation andthen solve the equation to find the unknown.

Comparison Bars are used to solve problems that involve oneamount that is more than or less than another amount. MakingComparison Bars can help a student organize the information in theproblem in order to find the unknown smaller amount, largeramount, or the difference.

Please call or write if you have any questions or comments.


TOTAL13

8partner partner

?

8 � � 13

5 � 8 � 13

13 � 5 � 8

13 � � 5?

?

smaller amount difference

larger amount

7 4

11

partner partner total

78293.U02L01_071-076 3/23/06 12:34 PM Page 75


Estimada familia:

En esta unidad, su niño resolverá problemas verbales de suma yresta que contienen un total y dos partes.

• Si no se conoce una de las partes, se la puede hallar restando laparte conocida del total o contando hacia adelante desde laparte conocida hasta el total.

• Si no se sabe el total, se lo puede hallar sumando las partes.

Para mostrar un total y dos partes se usan montañasmatemáticas. Los estudiantes pueden usar montañas matemáticaspara escribir una ecuación y luego resolverla para hallar elnúmero desconocido.

Para resolver problemas que contengan una cantidad mayor omenor que otra se pueden usar barras de comparación. Estas barrasde comparación pueden ayudar al estudiante a organizar lainformación que se presenta en el problema para hallar la cantidadmás pequeña desconocida, la más grande o la diferencia.

Si tiene alguna pregunta o comentario, por favor comuníqueseconmigo.


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TOTAL13

8parte parte

?

8 � � 13

5 � 8 � 13

13 � 5 � 8

13 � � 5?

?

cantidad más pequeña diferencia

cantidad más grande

7 4

11

parte parte total

78293.U02L01_071-076 3/23/06 12:34 PM Page 76

Show your work.

2–2 Name Date

UNIT 2 LESSON 2 Word Problems with Unknown Partners 77

�Solve Unknown Partner Word Problems

Draw a Math Mountain and write and label anequation to solve each problem.

1. Put Together: Unknown Partner Stacy invited 9 girls and some boys to her party. 16 childrenwere invited in all. How many boys wereinvited?

2. Take Apart: Unknown Partner There were 15 people at the park. 7 were playing soccer.The others were playing softball. How manypeople were playing softball?

3. Change Plus: Unknown Partner Jan planted 8 tulips last week. Today she planted some lilies.Now she has 17 flowers. How many lilies did sheplant?

4. Change Minus: Unknown Partner Tim had 14 tennis balls. Then his brother borrowedsome. Now Tim has 6 tennis balls. How many did his brother borrow?

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any. A

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ts reserved.

78 UNIT 2 LESSON 2 Word Problems with Unknown Partners

�Represent Unknown Partners with Math ToolsThe equations and Math Mountains below show theword problems on page 77.


6. How are these math tools alike? How are theydifferent?

Put Together: Unknown Partner Take Apart: Unknown Partner

Change Plus: Unknown Partner Change Minus: Unknown Partner

16childrenboys

9girls

� �

17flowerslilies

8tulips

� �

7soccersoftball

15park

� �

6nowsome

14all

� �

boys

9girls

children16

softball

7soccer

park15

lilies

8tulips

flowers17

some

6now

all14

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UNIT 2 LESSON 3 Word Problems with Unknown Starts 79

Show your work.

�Solve Unknown Start Problems


1. Change Plus: Unknown Start Greta puts somebeads on a string. Then she puts on 7 more beads.Now there are 13 beads on the string. How manybeads did she put on the string to start?

2. Change Minus: Unknown Start Greta puts somebeads on a string. Seven of the beads fell off thestring. Six beads are still on the string. Howmany beads were there at first?

3. Change Plus: Unknown Start Patrick was carryingsome books. His teacher asked him to carry 3 more books. Now he has 11 books. How manybooks did he start with?

4. Change Minus: Unknown Start Patricia wascarrying some books. Her friend took 3 of them.Patricia has 8 books left. How many books wasshe carrying at first?

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80 UNIT 2 LESSON 3 Word Problems with Unknown Starts

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�Represent Unknown Start Problems with Math ToolsThe equations and Math Mountains below show the word problems on page 79.


6. How are these math tools alike? How are theydifferent?

Change Plus: Unknown Start Change Minus: Unknown Start

Change Plus: Unknown Start Change Minus: Unknown Start

7morestart

13now

� �

situation equation:

7

13

13� �

7� �

solution equations:

3morestart

11now

� �

situation equation:

3

11

11� �

3� �

solution equations:

7felloff

beads6

on� �

situation equation:

6 7� �

solution equation:

3friendstart

8now

� �

situation equation:

8 3� �

solution equation:

start

7more

now13

start

3more

now11

beads

7felloff

6on

start

3friend

8now

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2–4 Name Date

Show your work.

�Discuss Comparison Problems


1. How many more marbles does Ana have than David?

2. How many fewer marbles does David have than Ana?

Here are two ways to represent the comparisonsituation.

3. How many more marbles does Sasha have than Claire?

4. How many fewer marbles doesClaire have than Sasha?

5. How many fewer fishing lures does Rocky have than Megan?

Rocky has 7 fishing lures. Megan has 12 fishing lures.

Claire has 8 marbles. Sasha has 15 marbles.

Comparison Bars

David

Ana

5 ?

8

Comparison Drawing

David

Ana

David has 5 marbles. Ana has 8 marbles.

UNIT 2 LESSON 4 Comparison Problems 81

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82 UNIT 2 LESSON 4 Comparison Problems

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Show your work.

�Find an Unknown Larger or Smaller Amount


6. Unknown Larger Amount Maribel has 8 stickers.Arnon has 3 more stickers than Maribel. Howmany stickers does Arnon have?

7. Unknown Smaller Amount Arnon has 11 stickers.Maribel has 3 fewer stickers than Arnon. Howmany stickers does Maribel have?

8. Unknown Larger Amount Ivan has 9 goldfish.Milo has 5 more goldfish than Ivan. How manygoldfish does Milo have?

9. Unknown Smaller Amount Milo has 14 goldfish.Ivan has 5 fewer goldfish than Milo. How manygoldfish does Ivan have?

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2–5 Name Date

�The Puzzled Penguin

UNIT 2 LESSON 5 Comparison Problems with Misleading Language 83

�Solve Comparison Problems with MisleadingLanguage

Solve each problem on a separate piece of paper.

Dear Math Students,

As part of my math homework, I solved this problem:

Carlos has 9 fish. He has 4 fewer fish than Daniel. How many fish does Daniel have?

Here is what I did: 9 – 4 = 5 Daniel has 5 fish.

Is my answer right? If not, please correct my work, andtell what I did wrong.

Sincerely,The Puzzled Penguin

1. Unknown Smaller Amount Danielhas 13 fish. Daniel has 4 morefish than Carlos. How many fishdoes Carlos have?

3. Unknown Smaller AmountBettina ran 14 laps. Bettina ran 6more laps than Gina. How manylaps did Gina run?

2. Unknown Larger Amount Ginaran 8 laps. She ran 6 fewer lapsthan Bettina. How many laps didBettina run?

4. Sara read 8 books this month.She read 6 fewer books thanLupe. How many books did Luperead this month?

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84 UNIT 2 LESSON 5 Comparison Problems with Misleading Language

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Show your work.

�Solve Comparison Problems Without the Words More or Fewer


5. The coach brought 8 hockey sticks to practice.There were 13 players at practice. How manyplayers didn’t get sticks?

6. At a meeting, 5 people had to stand becausethere were not enough chairs. There were 12 chairs. How many people came to themeeting?

7. Jess had 16 apples. After he gave one to each ofhis cousins, he had 3 apples left. How manycousins does Jess have?

8. At the park, 4 of the children could not swingbecause there were not enough swings. Therewere 10 children at the park. How many swingswere on the swing set?

9. Maile took one step on each tile along thegarden path. After she took 14 steps, therewere 3 more tiles left to go. How many tileswere there along the path?

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2–6 Name Date

Solve each problem. Label your answers. Use yourMathBoard or another sheet of paper.

1. Amanda had 783 seashells in her collection. Shefound some more seashells at the beach. Nowshe has 912 seashells. How many seashells didshe find at the beach?

2. Michelle and Sanjay are playing pinball.Together they have scored 1,509 points. Michellehas scored 718 points. How many points hasSanjay scored?

3. Beth and Olivia are driving across the country.Beth drove 923 miles. Together they drove 1,586miles. How many miles did Olivia drive?

4. There were 1,936 people at a baseball game. Anumber of people left during the sixth inning.There were 856 people at the game after thesixth inning. How many people left during thesixth inning?

UNIT 2 LESSON 6 Multi-Digit Unknown Partner and Unknown Start Problems 85

�Solve Multi-Digit Problems with Unknown Partners

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86 UNIT 2 LESSON 6 Multi-Digit Unknown Partner and Unknown Start Problems

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Show your work.Solve each problem. Label your answers.

5. The students at Oakdale School collected somecans of food in May. They collected 978 cans offood in June. They collected 1,729 cans of foodin all in those two months. How many cans offood did they collect in May?

6. Mrs. Perez ordered some sheets of coloredpaper for her art class. Her students used 831sheets of colored paper. There are 369 sheetsleft over. How many sheets of colored paper didMrs. Perez order?

7. Today a grocer sold 682 melons. At the end ofthe day, 756 melons were left over. How manymelons did the grocer have at the beginning ofthe day?

8. Mr. Chung’s class earned some money sellingpizzas last month. This month, Mr. Chung’s classearned $562 more. Now they have $986. Howmuch money did the class earn last month?

�Solve Multi-Digit Problems with Unknown Starts

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2–6 Name Date

UNIT 2 LESSON 6 Multi-Digit Unknown Partner and Unknown Start Problems 87

Show your work.

�Solve Mixed Problems


9. A book has 876 pages. Maria has read 456 pages of the book. How many more pages must Maria read to finish the book?

10. Natalie polished some rocks in March. Shepolished 418 more rocks in April. She now has682 polished rocks. How many rocks did Nataliepolish in March?

11. Today the visitors at the library checked out atotal of 1,326 books. Of these books, 679 didnot come from the children’s section. Howmany books did come from the children’ssection?

12. Jeffrey has a nickel collection. He put 368nickels in the bank. He now has 283 nickels.How many nickels did Jeffrey start with?

13. On the Back Write a problem that can be solved using this equation: � 156 � 215.Then solve it.

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88 UNIT 2 LESSON 6 Multi-Digit Unknown Partner and Unknown Start Problems

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2–7 Name Date

Show your work.

�Solve Multi-Digit Comparison Problems


1. The Sunnytown Library has 1,052 history books.The Judson Library has 863 history books. Howmany more history books does the SunnytownLibrary have than the Judson Library?

2. Today the Daisy Café used 465 plates. They used197 fewer plates yesterday than they usedtoday. How many plates did the Daisy Café useyesterday?

3. José received 749 votes in the school election.Cora received 126 more votes than José. Howmany votes did Cora receive?

4. Marco earned $428 doing yard work. Troyearned $186. How much less money did Troyearn than Marco?

UNIT 2 LESSON 7 Multi-Digit Comparison Problems 89

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2–7 Name Date

90 UNIT 2 LESSON 7 Multi-Digit Comparison Problems

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�Solve Multi-Digit Comparison Problemswith Misleading Language

Solve each problem. Draw comparison bars tohelp you. Label your answers.

5. Billy has 679 pennies. He has 278 more penniesthan Lee. How many pennies does Lee have?

6. Rebecca drove 362 miles. She drove 439 fewermiles than Fiona. How many miles did Fionadrive?

7. The baseball team gave 250 caps to people whocame to the game today. There were 569 peopleat the game. How many people did not get acap?

8. The principal bought 975 pencils at thebeginning of the school year. Each student inthe school received one pencil. The principal had123 pencils left over. How many students are inthe school?

78293.U02L07_089-092 3/23/06 12:49 PM Page 90

UNIT 2 LESSON 7 Multi-Digit Comparison Problems 91

Show your work.

�Use Logical Reasoning to Solve Problems

Solve.

1. Darnell, Rita, and Mark each bought a CD. Markspent $3 less than Darnell. Rita spent $7 morethan Mark. Darnell spent $11. How much didRita spend?

2. Helmer, Lily, and Pete live on Maple Street.Pete's house number is twice Helmer's. Lily'shouse number is 251. Helmer's house number is45 less than Lily's. What is Pete's house number?

3. Luisa, Sally, and Tran each have a coin collection.Sally has 72 more coins than Luisa. Luisa has 126fewer coins than Tran. Sally has 429 coins. Howmany coins does each have?

4. Tonya, Seth, Ann, and Len were in a walk-a-thon.They walked 14 mi, 26 mi, 19 mi, and 10 mi. Sethwalked the farthest. Tonya walked farther thanLen. Ann walked 10 mi. How far did each walk?

5. Dave, Shawna, Liz, and Matt are friends. Liz istaller than Shawna. Dave is the tallest. Matt istaller than Liz. What is their order from shortestto tallest?

6. On the Back Explain the strategy you used tosolve problem 5.

2-7 Name Date

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92 UNIT 2 LESSON 7 Multi-Digit Comparison Problems

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�Solve Mixed Multi-Digit Word Problems


1. Jacob had 219 bottle caps in his collection. Thenhe found some more. Now he has 347 bottlecaps. How many bottle caps did Jacob find?

2. Yesterday Tamara stamped some invitations.Today she stamped 239 invitations. She stamped427 invitations in all. How many invitations didshe stamp yesterday?

3. Batai made 122 calls in the phone-a-thon. Ginamade 261 calls. How many more calls did Ginamake than Batai?

4. Greta has 449 feet of fencing for her dog run.Mitch has 110 fewer feet of fencing for his dogrun. How many feet of fencing does Mitchhave?

UNIT 2 LESSON 8 Mixed Multi-Digit Word Problems 93

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2–8 Name Date

94 UNIT 2 LESSON 8 Mixed Multi-Digit Word Problems

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Show your work.Solve each problem. Label your answers.

5. The Grove Street bus carried 798 passengerstoday. The Elm Street bus carried 298 morepassengers today than the Grove Street bus.How many passengers did the Elm Street buscarry today?

6. Park City Cycle has 876 bicycles in stock. This is134 more bicycles than Bentley’s Bike Shop hasin stock. How many bicycles does Bentley’s BikeShop have in stock?

7. At Sunflower Bakery’s grand opening, the first250 customers received a free bagel. There were682 customers at the grand opening. Howmany customers did not get a free bagel?

8. There were some chairs set up for a concert.Then Shantel set up 256 more chairs. Now 610chairs are set up. How many chairs were set upto start with?

78293.U02L08_093-096 7/8/05 5:45 AM Page 94

UNIT 2 LESSON 8 Mixed Multi-Digit Word Problems 95

�Find the Missing Digits

In each box, write the digit that makes a correct addition or subtraction.

2-8 Name Date

13. On the Back Write your own missing digitaddition and missing digit subtraction.

1.

4.

7.

10.

2.

5.

8.

11.

3.

6.

9.

12. 6 � 2 �� 1 � 8

3 8 2 2

� 6 4

� 3 � 8

9 5 �

�� 5

� 3 9 �� 0 2 3

7 �� 8

1 3 0

� 7 � 6

� 2 3 8 �4 � 4 0

5 � 7

� 2 6 �� 4 9

3 � 9

� � 7 �1 1 8 5

8 �� 4

5 7

9 � 2 8

�� 1 � 3

4 8 5 �

5 8 �� 6

4 3 6

1 � 5

� 4 �8 6

� 9

� 8 �1 2 6

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96 UNIT 2 LESSON 8 Mixed Multi-Digit Word Problems

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Name Date

UNIT 2 Test 97

Show your work.Solve each problem. Label your answer.

1. Helga is a dog walker. Today she walked 8 beagles and some terriers. Altogether she walked 14 dogs. How many terriers did she walk?

2. Li Wei had some apples. She gave 9 of theapples to her friends. She has 5 apples left. How many apples did she start with?

3. Luis received 6 cards. He received 7 fewer cards than Carlos received. How many cards didCarlos receive?

4. Wanda has 12 crayons. James has 9 crayons.How many more crayons does Wanda have than James?

5. On Tuesday, Rashid polished 143 rocks. Hepolished some more rocks on Wednesday. Hepolished 228 rocks altogether. How many rocksdid Rashid polish on Wednesday?

6. Some students were playing in the schoolyard.Then 119 students went into the school. Now thereare 286 students in the schoolyard. How manystudents were in the schoolyard to start with?

2

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98 UNIT 2 Test

Solve. Label your answer.

7. Pat has 425 pennies in his collection. Miguelhas 201 fewer pennies. How many penniesdoes Miguel have?

Write an equation and then solve each problem.Label your answer.

8. On Monday and Tuesday, Franco spent 5 hoursdoing homework altogether. He did homeworkfor 2 hours on Tuesday. How many hours didFranco spend doing homework on Monday?

9. Tony had some baseball cards. Jeremy gave him8 more. Then he had 19 baseball cards. Howmany did he have to start?

Show your work.

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2

10. Extended Response Elsa read 13 books this month.She read 6 fewer books than Cliff read.Draw Comparison Bars to represent the problem.

How many books did Cliff read?

Explain how you know who read more books, Elsa or Cliff.

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UNIT B LESSON 1 Symmetry and Congruence 99

�Review Quadrilaterals and Types of Lines

Place the letter Q on each quadrilateral. Then labeleach quadrilateral with all the names that describe itusing the letters from the Key.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

Key

Parallelogram (P)

Rectangle (R)

Square (S)

Rhombus (Rh)

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100 UNIT B LESSON 1 Symmetry and Congruence

Vocabulary

line of symmetry�Draw Lines of SymmetryA divides a figure in half so that ifyou fold along the line, the two halves match eachother exactly.

Draw all of the possible lines of symmetry on eachfigure. Cut out and fold the figures on page 101 tohelp you.

line of symmetry

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A

D

G

J

B

E

H

K

C

F

I

L

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A

D

G

J

B

E

H

K

C

F

I

L

� Draw Lines of Symmetry

Cut out these figures to help you with StudentActivity Book page 100.

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Copyright © Houghton Mifflin Company. All rights reserved. 102 UNIT B LESSON 1 Symmetry and Congruence

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� Identify Congruent Halves of FiguresTwo halves of a figure are if they are thesame size and shape.

Does the dashed line divide the figure into congruenthalves? Write yes or no.

congruent

Vocabulary

congruent

1. 2. 3.

4. 5. 6.

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� Identify Congruent FiguresTwo figures are if they are the same sizeand shape. If you can slide, flip, or turn one figure so that it fits exactly on top of the other, the figuresare congruent.

congruent

Write which two figures in each row are congruent.

7. Figures and are congruent.


A

B

Figures A and B are congruent.


BA EC D

BA EC D

BA EC D


Vocabulary

congruent

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Dear Family,

Your child is currently participating in math activities that helphim or her understand basic geometry in two dimensions.

Your child will be looking for lines of symmetry. If you fold afigure along a line of symmetry, the two halves will match eachother exactly.

Your child will also beidentifying congruent figures.Congruent figures are the same size and shape.

Encourage your child to look forcongruent figures in your home orneighborhood and to identify lines of symmetry in various two-dimensionalfigures.

Your child will be learning how to label,name, and describe geometric figures. Forexample, the line segment AC is a diagonalof the square ABCD.

Your child will learn that angles aremeasured in degrees and discover thatthe sum of the measures of the angles ina triangle is always 180 degrees (180°).

If you have any questions or comments,please call or write to me.

Thank you.


line of symmetry

A B

D C

60˚

30˚60� + 30� + 90� = 180�

78293.UBL01_099-106 3/23/06 12:53 PM Page 105


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Estimada familia:

En estos momentos su niño está participando en actividadesmatemáticas que le ayudan a entender la geometría básica en dosdimensiones.

Su niño buscará ejes de simetría. Si se dobla una figura a lo largode su eje de simetría, las dos mitades coincidirán exactamente.

Su niño también identificaráfiguras congruentes. Las figurascongruentes tienen el mismotamaño y forma.

Anime a su niño a buscar figurascongruentes en la casa o en el vecindario y a identificar los ejes de simetría de variasfiguras bidimensionales.

Su niño aprenderá a rotular, nombrar ydescribir figuras geométricas. Por ejemplo,el segmento de recta AC es una diagonaldel cuadrado ABCD.

Su niño aprenderá que los ángulos semiden en grados y descubrirá que lasuma de las medidas de los ángulos deun triángulo es siempre 180 grados(180°).

Si tiene alguna pregunta o comentario,por favor comuníquese conmigo.

Gracias.


eje de simetría

A B

D C

60˚

30˚60� + 30� + 90� = 180�

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B–2 Name Date

�Label Corners with Letters You can name figures by labeling their corners with letters.

Give two possible names for each figure.

1. 2.

N

M

L

G

D

F

E

4. Draw a rectangle. Name it MNOP.

3. Draw a triangle. Name it ABC.

UNIT B LESSON 2 Label Figures and Draw Diagonals 107

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108 UNIT B LESSON 2 Label Figures and Draw Diagonals

Vocabulary

diagonal�DiagonalsA line segment that connects two corners of a figureand is not a side is called a . diagonal

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5. Draw the diagonals in the square.

Draw diagonal AC. Draw diagonal BD. Draw both diagonals.A B

D C

A B

D C

A B

D C

F G

I H

F G

I H

F G

I H

6. What do you notice about the diagonals you drew?

7. What do you notice about the triangles that were formed by the diagonals you drew?

8. Draw the diagonals in the rectangle.

Draw diagonal FH. Draw diagonal GI. Draw both diagonals.

9. What do you notice about the diagonals and the triangles they formed?

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UNIT B LESSON 2 Label Figures and Draw Diagonals 109

10. Draw the diagonals in the quadrilateral.

Draw diagonal WY. Draw diagonal ZX. Draw both diagonals.

WX

ZY

WX

ZY

WX

ZY

K

L

M

N

K

L

M

N

K

L

M

N

11. What do you notice about the diagonals you drew and the triangles they formed?

12. Draw the diagonals in the parallelogram.

Draw diagonal KM. Draw diagonal LN. Draw both diagonals.

13. What do you notice about the diagonals you drew and the triangles they formed?

14. On the Back Draw a quadrilateral, label it, and draw all the diagonals. Name all of the sides and diagonals of your quadrilateral.

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110 UNIT B LESSON 2 Label Figures and Draw Diagonals

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UNIT B LESSON 3 Angles and Triangles 111

�Types of AnglesA is part of a line that has one endpoint and continues forever in one direction. To draw a ray, make an arrow to show that it goes on forever.

Two line segments or two rays that meet at an endpoint form an .

An angle that forms a square corner is called a .

An angle that is smaller than a right angle is called an .

An angle that is larger than a right angle is called an .

These angles are named with a letter in the corner.

1. Which of the angles are right angles?

2. Which of the angles are acute angles?

3. Which of the angles are obtuse angles?

VW

XY

Z

obtuse angle

acute angle

right angle

angle

ray

Vocabulary

rayangleright angle

acute angleobtuse angle

right angle

acute angle

obtuse angle

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112 UNIT B LESSON 3 Angles and Triangles

Vocabulary

right triangleacute triangleobtuse triangle

�Name Triangles by Sizes of Angles

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4. What do you think a right triangle is?

5. What do you think an acute triangle is?

6. What do you think an obtuse triangle is?

These are .right triangles

These are .acute triangles

These are .obtuse triangles

B

DC

E

GF

UV

W

L M

N

D

E K

L

MF G

H W

X

Y

C

O

P

Y

W

X

Q

S

R

F

H GN

You can name triangles according to the sizes of their angles.

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Vocabulary

equilateral triangleisosceles triangle scalene triangle

�Name Triangles by Lengths of SidesYou can also name triangles according to the lengthsof their sides.

7. What do you think an equilateral triangle is?

8. What do you think an isosceles triangle is?

9. What do you think a scalene triangle is?

These are .equilateral triangles

These are .isosceles triangles

These are .scalene triangles

B

Z Y

X

A

C T

S

F

GH

R

L

V U

TK

J FO

M

N

E

D

Q

V

X

WP

RD E

F

G

C

B

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114 UNIT B LESSON 3 Angles and Triangles

�Name Triangles by Sizes of Angles andLengths of Sides

Mark all the words that describe each triangle.

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10. 11. 12.

equilateralisoscelesscalenerightacuteobtuse



13. 14. 15.




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�Build Quadrilaterals from Triangles

Cut out each pair of triangles. Use each pair to makeas many different quadrilaterals as you can. (You mayflip a triangle and use the back.) On a separate pieceof paper, trace each quadrilateral that you make.

Obtuse Triangles

Right Triangles

Acute Triangles

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Copyright © Houghton Mifflin Company. All rights reserved. 116 UNIT B LESSON 3 Angles and Triangles

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�Introduce DegreesAngles are measured in units called . One degree is the measure of one very small rotation.

This angle has a measure of 1 degree.

The measure of an angle is the total number of 1-degree angles that fit inside it.

This angle measures 5 degrees.

The symbol for degrees is a small raised circle (°). Youcan write the measure of the angle above as 5°.

A has a measure of 90°. A 90°-rotation traces one quarter of a circle.

right angle

degrees

90˚

Vocabulary

degreestraight angleright angle

UNIT B LESSON 4 Angle Measures 117

A measures 180°. A 180°-rotation traces one half of a circle.

This angle measures 360°. A 360°-rotation traces a completecircle.

straight angle

180˚ 360˚

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118 UNIT B LESSON 4 Angle Measures

�Angle Measures

Find the size of each angle.

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1. This angle is half the size of aright angle.

2. If you put three of these anglestogether, you will get a rightangle.

? ?

3. This angle is the same size astwo of the angles in exercise 2put together.

4. This angle is the same size astwo of the angles in exercise 3put together.

? ?

5. This angle is the angle inexercise 1 added to a rightangle.

6. This angle is the angle inexercise 2 added to a straightangle.

?

?

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UNIT B LESSON 4 Angle Measures 119

�Join Angles of a Triangle

Draw a large triangle on a sheet ofunlined paper. You can draw any type oftriangle. Mark each corner with a dotand then cut out the triangle.

Tear each angle off the triangle, andplace the three angles together so thatthe dotted corners are touching.

7. Sketch your three angles joined at thedotted corners.

8. What kind of angle is formed when you put together the three angles of your triangle?

Compare your sketch with those of your classmates.

9. Is the sum of the measures of the three angles the same for every triangle?

Complete this statement.

10. The sum of the measures of the three angles in a triangle is .

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120 UNIT B LESSON 4 Angle Measures

�Find Missing Angle Measures

Find the missing angle measure in each triangle.

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11. 12. 13.

90˚

60˚

?120˚

20˚

?

70˚ 70˚

?

14. 15. 16.100˚

50˚

?

80˚

30˚

?

45˚

?

17. In an equilateral triangle, each angle has the same measure. What is the measure of each angle in this equilateral triangle?

?˚

?˚ ?˚

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UNIT B Test 121

B

1. Which two figures below are congruent?

Figures and are congruent.

A B C D E

2. Draw all the lines of symmetry on the figure.

3. Draw diagonal AC inthe rectangle.

A B

D C

Name each triangle by the lengths of its sides. Place a check mark next to all of the words thatdescribe the triangle.

4. 5. 6.

equilateralisoscelesscalene



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122 UNIT B Test

Name each triangle by the sizes of its angles. Place acheck mark beside the words that describe the triangle.

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B

7. 8. 9.

rightacuteobtuse

rightacuteobtuse

rightacuteobtuse

10. Extended Response Trace and cut out each pair ofcongruent triangles. Make as many quadrilaterals asyou can from each pair. Trace the quadrilaterals ona separate sheet of paper. Which pair of trianglesmakes more quadrilaterals? Explain why.

Isosceles triangles

Equilateral triangles

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3–1 Name Date

UNIT 3 LESSON 1 Round to the Nearest Hundred 123

Vocabulary

estimateround�Estimate

Solve the problem.

1. Tasha read three books over the summer. Here isthe number of pages in each book:

About how many pages did Tasha read? Explainhow you made your .

�Practice Rounding

each number to the nearest hundred. Usedrawings or Secret Code Cards if they help you.Round

estimate

Watership Down 494 pagesSounder 128 pagesThe Secret Garden 368 pages

2. 128

5. 649

8. 62

3. 271

6. 415

9. 1,481

4. 376

7. 550

10. 2,615

11. Explain Your Thinking When you round a numberto the nearest hundred, how do you knowwhether to round up or round down?

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�Solve Problems by Estimating

Solve by rounding to the nearest hundred.

12. At the Lakeside School, there are 286 secondgraders, 341 third graders, and 377 fourthgraders. About how many students are thereat the Lakeside School?

13. Last week, Mrs. Larson drove 191 miles on Monday, 225 miles on Wednesday, and 107 miles on Friday. About how many miles didshe drive altogether?

14. Of the 1,432 people at the hockey game, 292sat on the visiting team side. The rest sat onthe home team side. About how many peoplesat on the home team side?

�Reasonable Answers

Use rounding to decide if the answer is reasonable.Then find the answer to see if you were right.

Show your work.

124 UNIT 3 LESSON 1 Round to the Nearest Hundred

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15. 604 � 180 � 586

17. 268 � 17 � 107

19. 407 � 379 � 28

16. 377 � 191 � 568

18. 1,041 � 395 � 646

20. 535 � 287 � 642

78293.U03L01_123-126 7/14/05 4:36 AM Page 124

UNIT 3 LESSON 1 Round to the Nearest Hundred 125

Dear Family,

Your child has started a new unit on using addition andsubtraction. These are important math operations that we usealmost every day.

At the beginning of the unit, students learn to estimate sums anddifferences by rounding numbers. They also use estimates tocheck that actual answers are reasonable, and compare numbersusing the symbols for greater than (� ), less than (� ), or equal to (� ).

Students also identify and compare the values of a collection ofU.S. coins and bills, act out making purchases by counting out theexact amounts, and find out how much change they shouldreceive when giving more than the exact amount for a purchase.

Later in the unit, students learn to recognize word problems that contain hidden, extra, and not enough information. Theysolve problems with two or more steps and learn to analyzeinformation when it is presented in tables and graphs.

Your child is learning how math is used in the world around us.You can help your child learn by sharing shopping situations withthem and pointing out graphs and tables in the newspaper ormagazines. Encourage your child to spend time acting outshopping situations with coins and bills at home.

Thank you for helping your child learn important math skills.


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126 UNIT 3 LESSON 1 Round to the Nearest Hundred

Estimada familia:

Su niño ha comenzado una nueva unidad sobre suma y resta.Éstas son operaciones matemáticas importantes que usamos casitodos los días.

Al principio de esta unidad los estudiantes aprenden a estimarsumas y diferencias redondeando números. También usan laestimación para comprobar que las respuestas que dieron sonrazonables y comparan números usando los símbolos mayor que(� ), menor que (� ) o igual (� ).

Los estudiantes también identifican y comparan los valores de unacolección de monedas y billetes de los EE.UU., representancompras contando las cantidades exactas y aprenden cuántocambio deben recibir cuando dan más de la cantidad exactadurante una compra.

Más adelante en esta unidad, los estudiantes aprenden areconocer problemas verbales que contienen informaciónimplícita, exceso o falta de información. Resuelven problemas dedos o más pasos y aprenden a analizar la información presentadaen tablas y gráficas.

Su niño está aprendiendo cómo se usan las matemáticas en la vidadiaria. Usted puede ayudar a su niño compartiendo situaciones decompra y señalando gráficas y tablas en periódicos o revistas.Anime a su niño a representar en casa situaciones de compra conmonedas y billetes.

Gracias por ayudar a su niño a aprender destrezas matemáticasimportantes.


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UNIT 3 LESSON 2 Round to the Nearest Ten 127

�Round 2-Digit Numbers to the Nearest Ten

Round each number to the nearest ten.

1. 63

3. 78

5. 57

7. 42

2. 34

4. 25

6. 89

8. 92

�Round 3-Digit Numbers to the Nearest Ten

Round each number to the nearest ten.

9. 162

11. 309

13. 118

15. 503

10. 741

12. 255

14. 197

16. 246

17. Explain Your Thinking When you round a numberto the nearest ten, how do you know whether toround up or round down?

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�Estimate the Answer

Solve each problem.

18. The chart at the right showshow many smoothies the JuiceHut sold yesterday. By roundingeach number to the nearest ten,estimate how many smoothiesthe Juice Hut sold in all.

19. Ms. Singh has 52 rock CDs, 75jazz CDs, 36 classical CDs, and23 hip-hop CDs. Round eachnumber to the nearest ten, to find about how many CDsshe has.

21. Estimate the total number ofbooks the school received byrounding each number to thenearest hundred.

22. Estimate the total number ofbooks the school received byrounding each number to thenearest ten.

128 UNIT 3 LESSON 2 Round to the Nearest Ten

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20. Roz rented a video that is 123 minutes long. She watched 48 minutes of it. Round eachnumber to the nearest ten toestimate how many moreminutes she has to watch.

Smoothies Sold at Juice Hut

13 raspberry-peach smoothies

38 strawberry-banana smoothies

44 guava-mango smoothies

61 peach-blueberry smoothies

Use the table at the right to solve problems 21–23.

Jefferson Elementary SchoolBooks Received

Math 436

Reading 352

23. Find the total number of books.Which of your estimates is closerto the actual total?

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3–2 Name Date

�Reasonable Answers

Use rounding to decide if the answer isreasonable. Write yes or no on the line. Then findthe answer to see if you were right.

24. 58 � 37 � 131

25. 122 � 67 � 55

26. 28 � 45 � 53

27. 93 � 29 � 122

28. 113 � 57 � 140

29. 85 � 16 � 101

30. 182 � 65 � 117

UNIT 3 LESSON 2 Round to the Nearest Ten 129

Show your work.

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130 UNIT 3 LESSON 2 Round to the Nearest Ten

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�Different Ways to Estimate

Use clustering to estimate each sum.

1. 62 � 58 � 59

3. 375 � 402 � 412

2. 227 � 198 � 212

4. 498 � 512 � 475

Use front-end estimation to estimate each sum or difference.

Use the estimation strategies given in the tablebelow to estimate the sum of the numbers on theleft. Then find the actual sum.

5. 6. 7. 8. 321� 130��

625� 462��

1,806� 3,110��

4,327� 1,340��

3-2 Name Date

32928

776� 408��

9. 10. 11.

Round to thenearest hundred

Round to thenearest ten

Front-endestimation

12. Which estimation strategy above gave you theclosest estimate?

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3-4 Name Date3–3

�Compare Numbers

Compare the numbers. Write �, �, or � in each .

�Order Numbers

Write the numbers in order from greatest to least.

UNIT 3 LESSON 3 Compare Whole Numbers 131

1. 34 86

3. 653 663

5. 1,752 1,572

7. 1,932 1,951

9. 3,478 3,478

2. 97 67

4. 875 587

6. 1,572 1,527

8. 2,633 2,487

10. 4,786 4,876

11. 69, 20, 81 12. 381, 124, 197

Write the numbers in order from least to greatest.

13. 2,245, 1,642, 1,787 14. 1,982, 1,892, 1,782

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3–3 Name Date

�Multi-Step Comparisons

Compare. Write �, �, or � in each .

15. 35 � 28 23 � 39

16. 864 � 29 699 � 265

17. 273 � 641 850 � 57

18. 84 � 148 151 � 71

19. 38 � 165 572 � 365

20. 419 � 109 160 � 150

21. 241 � 157 175 � 86

22. 525 � 231 146 � 173

Show your work.

132 UNIT 3 LESSON 3 Compare Whole Numbers

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�Compare Using Number Sense

Compare without calculating. Write �, �, or �in each .

23. 888 � 5 888 � 5

25. 145 � 17 17 � 145

27. 143 � 68 96 � 71

29. 267 � 138 279 � 199

24. 510 � 0 510 � 0

26. 1,250 � 300 900 � 150

28. 421 � 103 347 � 98

30. 257 � 259 702 � 219

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3-4 Name Date3–4

�Coin EquivalentsWhat relationships do you see in this coin chart?

UNIT 3 LESSON 4 Money Values 133

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134 UNIT 3 LESSON 4 Money Values

�Count Coins and Bills

Find the value of each collection of coins and bills.

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1. 2.

3.

4.

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UNIT 3 LESSON 4 Money Values 135

�Compare Amounts of Money

Compare the two collections of coins and bills. Write �, �, or � in the answer box.

5.

6.

7.

�Solve Problems Involving Money

Solve each problem.

8. Kevin wants to buy a book that costs $1.50. He has3 quarters, 6 nickels, and 4 pennies. Does he haveenough money to buy the book?

9. Jade has 7 nickels, 2 dimes, and 5 quarters. Eliashas 8 dimes, 6 pennies, 2 quarters, and 3 nickels.Who has more money?

10. On the Back Explain how you solved problem 8.

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136 UNIT 3 LESSON 4 Money Values

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�Coins that Make a DollarLook at the two different combinations of coins thatmake a dollar. Can you think of some other coincombinations that make a dollar?

UNIT 3 LESSON 5 Represent Money Amounts in Different Ways 137

�Coin Combinations

Draw two different coin combinations for each amount.

=

=

1. 37¢ 2. $0.75

3. $0.88

5. 71¢

4. $0.43

6. $.95

Draw each amount with the fewest coins. Usequarters, dimes, nickels, or pennies.

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138 UNIT 3 LESSON 5 Represent Money Amounts in Different Ways

These items are for sale at Snappy School Supplies:

�Act It Out

You and your partner can take turns being thecustomer and the shopkeeper. Here’s what to do:

Step 1: The customer chooses two or three items tobuy.

Step 2: The shopkeeper writes down the prices andfinds the total cost.

Step 3: The customer pays the exact amount of moneyfor the items.

Step 4: The shopkeeper counts the money to makesure it is the right amount and draws the coinsand bill used.


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�Count On to Make ChangeImagine you are working at a sandwich shop. Acustomer pays for a sandwich that costs $2.78 with a$5 bill. Your cash register is broken and you don’thave a pencil. How can you figure out how muchchange to give the customer?

Start with $2.78. Count on until you get a whole-dollar amount, and then count on by whole dollars until you get to $5.00.

UNIT 3 LESSON 6 Make Change 139

$2.78

$2.79 $2.80 $2.90 $3.00 $4.00 $5.00

Add the coins and bills to find the total amount ofchange, $2.22.

�Practice Making ChangeFind the amount of change by counting on to theamount paid. Draw the coins and bills you counted.

1. Fernando paid for a $1.39 bottle of juice with two$1 bills. How much change did he get?

2. At a garage sale, Ana bought a $3.53 CD with a $5 bill. How much change did she get?

3. Valerie bought a $2.12 magazine with three $1 bills.How much change did she get?

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140 UNIT 3 LESSON 6 Make Change

The following items are for sale at the Beach Snack Shop:

� Act It Out

You and your partner can take turns being thecustomer and the shopkeeper. Here’s what to do:

Step 1: The customer chooses two items to buy.

Step 2: The shopkeeper writes down the prices andfinds the total cost.

Step 3: The customer pays with bills only.

Step 4: The shopkeeper counts on to find the change.Then the shopkeeper writes down the billsused to pay and the amount of change.


$1.1272¢

34¢

56¢

$1.20$1.49$2.35

95¢

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�Round Amounts of Money

Round each amount first to the nearest dime andthen to the nearest dollar.

Show your work.Solve each problem.

6. Carl spent $3.35 on a sandwich and $1.85 on adrink. Estimate the total amount he spent byrounding the prices to the nearest dollar andadding.

7. Rose spent 85¢ on a pen, 32¢ on an eraser, and78¢ on a pencil sharpener. Estimate the totalamount she spent by rounding the prices to thenearest dime and adding.

8. Aisha spent $4.12 on a book, $3.65 on amagazine, and $1.75 on a greeting card. Estimatethe total amount she spent by rounding the pricesto the nearest dollar and adding.

Rounded to thenearest dime

Rounded to thenearest dollar

1. $3.62

2. $5.09

3. $1.25

4. $2.99

5. $7.50

UNIT 3 LESSON 7 Round Money Amounts 141

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�Estimate with Money

142 UNIT 3 LESSON 7 Round Money Amounts

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Jess brought $5.00 to the store. She wantsto buy the items shown at the right. Sheneeds to make an estimate to see if shehas enough money.

Ben has $3.28. Faiz has $1.63. They want to combinetheir money to buy a model car that costs $5.00.

9. Estimate the total cost of theitems by rounding each price tothe nearest dollar and adding.Is your estimate $5.00 or less?

10. Find the actual cost of theitems. Does Jess have enoughmoney to buy the items?

12. Estimate the total amount theboys have by rounding eachamount to the nearest dollarand adding. Is your estimate$5.00 or more?

13. Find the actual total amount theboys have. Do they have enoughto buy the model?

11. How could Jess make an estimate to be sure she has enough money?

14. How could the boys make an estimate to be sure they have enough money?

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3–7 Name Date

Solve each problem.

15. How do you think Tang should make his estimate?What estimate do you get if you use your method?

16. Can Tang be sure he has enough money to buy the toys?

17. How do you think Lidia should make her estimate?What estimate do you get if you use your method?

18. Can Lidia be sure she will have enough money?

Lidia is selling the items shown at the right at agarage sale. She wants to estimate how muchmoney she will make to be sure she will haveenough to buy a video game that costs $10.

Tang has $1.20. He wants to buy the itemsshown at the right. He wants to estimate thetotal cost of the items to make sure he hasenough money.

UNIT 3 LESSON 7 Round Money Amounts 143

Lidia’s Garage Sale

Tom’s Toy Store

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144 UNIT 3 LESSON 7 Round Money Amounts

�Different Ways to Estimate with Money

Complete.

3. What is the actual cost of the notebook, marker,and baseball cap? Use your estimates above tocheck that your answer is reasonable.

4. What estimation strategy would you use to estimatethe cost of several items when shopping? Explain.

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Estimate the total cost of the notebook, marker, and baseball cap using the strategies given below.

Round to the nearest dollar

Use Mental Math

1. 2.

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3–8 Name Date

�Read a Table The Riverside School is taking orders for pizzas to raisemoney for field trips. This shows the number oforders the third graders took for each type of pizza.

table

Show your work.Use the table above to answer the questions.

1. How many cheese pizzas were ordered onSunday?

2. How many vegetable pizzas were ordered on Saturday?

3. How many supreme pizzas were orderedaltogether?

4. How many pizzas were ordered on Sunday?

UNIT 3 LESSON 8 Ask Addition and Subtraction Questions from Tables 145

Vocabulary

tablerowcellcolumn

Cheese Supreme Vegetable

Saturday 37 26 5

Sunday 19 28 15

Third Graders’ Pizza Orders

Agoesacross.

row

A goesup and down.

columnA is where acolumn and row meet.

cell

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�Use a Table

This table shows the number of animals aveterinarian treated over three months.

146 UNIT 3 LESSON 8 Ask Addition and Subtraction Questions from Tables

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Dogs Cats Birds ReptilesAll

Animals

January 68 118 25 11

February 94 106 8 19

March 122 77 19 26

3-Month Total

Animals Treated

5. Fill in the total for each column and row.

6. Write two addition questions about this table.

7. Write two subtraction questions about this table.

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�Find a Pattern in a Table

Complete the tables and answer the questions.

UNIT 3 LESSON 8 Ask Addition and Subtraction Questions from Tables 147

Row 1 Row 2 Row 3 Row 4 Row 5 Row 6 Row 7

8 Blocks 6 Blocks 5 Blocks 4 Blocks

Blocks in a Tower

Week 1 Week 2 Week 3 Week 4 Week 5 Week 6 Week 7

$300 $285 $255 $240

Money in Savings Account

Hour 1 Hour 2 Hour 3 Hour 4 Hour 5 Hour 6

Tank A 4 in. 5 in. 7 in. 8 in.

Tank B 6 in. 8 in. 10 in. 14 in.

Water Level in Tank

2. If the pattern continues, how much money do you predictwill be in the savings account in week 8? Explain.

1. What pattern did you use to complete the table?

3. How would you describe the pattern for each tank?

4. On the Back Create your own table with a pattern.Describe the pattern.

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148 UNIT 3 LESSON 8 Ask Addition and Subtraction Questions from Tables

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�Analyze TablesThis table shows the number of people who went ondifferent rides at an amusement park.

Use the table above to answer the questions.

1. What do the numbers in the row for Tuesdaystand for?

2. What do the numbers in the column for bumpercars stand for?

3. Find the cell with 106 in it. What does thisnumber stand for?

UNIT 3 LESSON 9 Complete Tables 149

Roller Coaster Ferris Wheel Bumper Cars

Monday 383 237 185

Tuesday 459 84 348

Wednesday 106 671 215

Number of People Who Went on Rides

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�Fill in the Tables4. This table shows the number of loaves of bread

baked and sold last week at the Lotsa DoughBakery. Fill in the empty cells.

150 UNIT 3 LESSON 9 Complete Tables

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Loaves Baked Loaves Sold Loaves Left

Monday 122 38

Tuesday 113 47

Wednesday 145 89

Thursday 96 38

Friday 91 44

Bread Sales at Lotsa Dough Bakery

5. This table shows the number of CDs andvideotapes sold at the Sound Out Music Storelast week. Fill in the empty cells.

CDs Videotapes Total

Monday 62 19 81

Tuesday 73 32

Wednesday 88 133

Thursday 26 120

Friday 155 223

Saturday 66 294

Sound Out Music Sales

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�Use Logical Reasoning

Solve each problem.

1. Jan, Bev, Luis, and Alex arewearing different color caps. Thecolors are red, blue, green, andyellow. Jan’s cap is not red orgreen. Alex’s cap is red. Bev’s capis not green or yellow. Whatcolor cap is each wearing?

2. Ty, Sal, Amy, and Lea were in arace. Amy did not finish eitherfirst or second. Lea finished last.Sal finished before Ty. In whatorder did they finish the race?

3. Mai, Abdul, Bill, and Rita eachplay different instruments. Theinstruments are violin, flute,harp, and guitar. Mai’sinstrument does not have strings.Bill plays the violin. Abdul doesnot play the harp. What doeseach person play?

UNIT 3 LESSON 9 Complete Tables 151

Red Blue Green Yellow

Jan

Bev

Luis

Alex

First Second Third Fourth

Ty

Sal

Amy

Lea

violin flute harp guitar

Mai

Abdul

Bill

Rita

4. On the Back Create your own problem like the onesabove.

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152 UNIT 3 LESSON 9 Complete Tables

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�Make a Table

Use the data the class collected to fill in the table.

�Use a Table1. Write a comparison question using data from the

table above and the word more. Answer yourquestion.

2. Write a comparison question using data from thetable above and the word fewer. Answer yourquestion.

3. Write a question using data from the table and theword altogether. Answer your question.

UNIT 3 LESSON 10 More Practice With Tables 153

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�Analyze Data

Fill in the missing information in the tables andanswer the questions.

This table shows the number of souvenirs theWildcats baseball team sold last weekend.

154 UNIT 3 LESSON 10 More Practice With Tables

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White Red Total

Caps 134 211

T-shirts 64 109

Pennants 59 151

Souvenir Sales for Wildcats Baseball Team

4. Which item above had the most total sales?

5. Which color T-shirt had the most sales?

This table shows the number of items the Green Thumb Garden Shop sold at their Spring sale.

Number Before Number Numberthe Sale Sold Left

Spades 232 185

Straw Hats 68 76

Small Pots 412 70

Big Pots 227 98

Spring Sale at Green Thumb Garden Shop

6. Which item had the most sales?

7. Which item has the least number left?

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UNIT 3 LESSON 11 Word Problems with Extra or Hidden Information 155

�Solve Problems with Extra Information

Read each problem. Cross out any extrainformation. Then solve.

1. Emma solved 9 math problems and answered 7reading questions. Her sister solved 8 mathproblems. How many math problems did theysolve in all?

2. Mark had 6 shirts and 5 pairs of pants. Today hisaunt gave him 4 more shirts and another pair ofpants. How many shirts does he have now?

3. A parking lot had 179 cars and 95 trucks. Then85 cars left the lot. How many cars are in theparking lot now?

4. Laura had some roses in a vase. From hergarden, she picked 7 more roses and 6 daisies.Now she has 12 roses in all. How many roses didshe have at first?

5. Nikko had 245 pennies and 123 nickels. Hisbrother gave him 89 more pennies and 25 morenickels. How many pennies does Nikko havenow?

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156 UNIT 3 LESSON 11 Word Problems with Extra or Hidden Information

�Solve Problems with Hidden Information

Read each problem. Circle the hidden information.Then solve.

6. Samuel had 16 horseshoes in the shedyesterday. Today he put a new set ofhorseshoes on his horse Betsy. How manyhorseshoes are left in the shed?

7. Maya is going on a vacation with her family fora week and 3 days. How many days will she beon vacation?

8. Julie bought a dozen eggs at the market. Shegave 3 of them to Serge. How many eggs doesJulie have left?

9. Lisa had 3 quarters and 2 dimes. Then shefound 3 nickels and 12 pennies. How manycents does she have now?

10. Marissa is moving away. She is going to moveback in a year and 21 days. How many days willshe be gone?

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�Solve Word Problems with Not Enough Information

Read each problem. Is there a way to solve it? Explain.

1. Sara bought 8 bananas at the fruit market. She put them in a bowl with some oranges. How many pieces of fruit are in the bowl?

2. Josh had some money in his pocket. He spent $1.25 on a bottle of juice. How much money does he have left?

Tell what information is needed to solve each problem.

3. Meg bought 3 mystery books and put them on the shelf with her other mystery books. How many mystery books are now on the shelf?

4. Our school has 5 soccer balls, 6 basketballs, and 4 footballs. Today, some of the footballs were lost. How many balls does the school have now?

UNIT 3 LESSON 12 Word Problems with Not Enough Information 157

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3–12 Name Date

Tell what information is needed to solve eachproblem.

5. A stepladder is 8 feet tall. Two of the steps arebroken. How many steps are not broken?

6. Rebecca did 112 dives in competition lastsummer. This summer, she did many more divesin competition. How many competition dives didshe do in the two summers?

7. Today, Maggie’s Café sold more hot chocolatethan yesterday. Yesterday, Maggie’s Café sold237 cups of hot chocolate. How many more cupswere sold today than yesterday?

8. A living room couch is 6 feet long. There are 4 blue pillows and several gray pillows on thecouch. How many pillows are on the couchaltogether?

158 UNIT 3 LESSON 12 Word Problems with Not Enough Information

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�Practice

Solve each problem if possible. If more informationis needed, rewrite the problem to include thenecessary information and then solve it.

9. Leah began fishing at 2 o’clock in theafternoon. She stopped at dinnertime. Howmany hours did Leah fish?

10. On Saturday, Maria handed out 646 flyers inthe morning and the same number of flyers inthe afternoon. How many flyers did Mariahand out on Saturday?

11. The Kitchen Store sold 532 pans and 294 pots.Then some pans were returned. How manypans were not returned?

12. There are 3 tables in the room with 4 legseach. One has a broken leg. How many tablelegs in the room are not broken?

UNIT 3 LESSON 12 Word Problems with Not Enough Information 159

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160 UNIT 3 LESSON 12 Word Problems with Not Enough Information

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�Extra Practice

Solve each problem if possible. If more informationis needed, rewrite the problem to include thenecessary information and then solve it.

13. The train traveled 476 miles on Tuesday. Ittraveled even more miles on Wednesday. Howmany miles did the train travel on Tuesday andWednesday?

14. The hikers walked 12 miles on Tuesday andcamped overnight. On Wednesday, they walkedback along the same route. How many milesdid they hike altogether?

15. One week, Rene cooked meals for 235 people.The next week, she cooked meals for 413people. How many people did Rene cook mealsfor in those two weeks?

16. Julio and Scott played 6 card games and 4 computer games today. How many hours did they play games?

3–12 Name Date

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�Solve Two-Step Word Problems


1. The Hillside bus had 14 passengers. When itstopped, 5 people got off and 8 people got on.How many people are riding the Hillside busnow?

2. There are 15 fish in a tank. 12 are goldfish, andthe others are angelfish. How many moregoldfish are there than angelfish?

3. Luther had 11 sheets of colored paper. 6 wereorange, and the rest were blue. Today he used 2 sheets of blue paper. How many sheets ofblue paper does Luther have now?

4. Sun Mi picked 14 apricots. Celia picked 5 fewerapricots than Sun Mi. How many apricots didSun Mi and Celia pick altogether?

5. Annie took 8 photographs at home and 7 photographs at school. Her sister Amandatook 6 fewer photographs than Annie. Howmany photographs did Amanda take?

UNIT 3 LESSON 13 Solve Two-Step Word Problems 161

Show your work.

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162 UNIT 3 LESSON 13 Solve Two-Step Word Problems

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�Solve and Discuss


6. There are 5 mice, 3 gerbils, and some hamstersin a cage. Altogether there are 15 animals inthe cage. How many hamsters are there?

7. A new library opened on Saturday. The librarylent out 234 books on Saturday. On Sunday,they lent out 138 books. That day, 78 bookswere returned. How many books were notreturned?

8. Katie had 8 dimes and some nickels in her duckbank. She had 4 more nickels than dimes. Shetook out 5 nickels to buy a newspaper. Howmany nickels are in her duck bank now?

9. Tony had 14 colored pencils. 9 of them neededsharpening, and the rest were sharp. Yesterday,his uncle gave him some new colored pencils.Now Tony has 12 sharp colored pencils. Howmany colored pencils did his uncle give him?

10. José ate 6 strawberries. Then he ate 7 more.Lori ate 9 strawberries. How many fewerstrawberries did Lori eat than José?

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3–14 Name Date

�Solve Multi-Step Word Problems


1. Isabel has 14 pieces of fruit. 6 are apples, 2 arebananas, and the rest are pears. Then she buysmore pears. Now she has 9 pears. How manypears does she buy?

2. Four jugglers were practicing. Ted was juggling3 balls, Ruby was juggling 6 balls, and Mai wasjuggling 4 balls. 5 of their balls fell. Then Tobystarted juggling 7 balls. What total number ofballs were they juggling then?

3. Travis had $3.06 and Marie had $1.42. ThenTravis earned $1.74 more and Marie earned$2.86 more. Who has more money now? Howmuch more?

4. Finn delivered 3 pizzas. Then he delivered 5more pizzas. He delivered 6 fewer pizzas thanLiz. How many pizzas did Liz deliver?

5. Majeed built 7 car models and 14 airplanemodels. Jasmine built 9 more car models thanMajeed and 6 fewer airplane models. Howmany models did Jasmine build in all?

UNIT 3 LESSON 14 Solve Multi-Step Word Problems 163

Show your work.

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3–14 Name Date

�Use a Strategy

Read the problem below and answer the questions.

164 UNIT 3 LESSON 14 Solve Multi-Step Word Problems

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Trick

Sit

Stay

Fetch

Come

Lie down

Roll over

Practice Needed

3 times

6 times

5 times

2 times

4 times

7 times

6. Marika has 12 treats. She would like to teach Rufus 4 tricks. Can she do it? Explain why or why not.

7. What are all the possible combinations of tricks she can teach with exactly 12 treats?

Marika wants to teach her dog Rufus some tricks.She will reward Rufus with a treat each time hepractices a trick. She has a book that lists how many times a dog usually has to practice each trickin order to learn it. The list is shown below.

78293.U03L14_163-166 7/14/05 4:22 AM Page 164

�Use the Work Backward Strategy


1. Marvin cut some new line for his fishing pole.Then he cut the new line into 2 equal pieces.Next he cut 8 inches off one piece of line. Thatgave him a piece of line that was 42 inches long.How long was the original piece of new line?

2. Sam weighed a bag of peanuts. Then he added2 more pounds of peanuts to the bag. Aftertaking 5 pounds of peanuts out, the bagweighed 6 pounds. How much did the bag ofpeanuts weigh in the beginning?

3. Tim has a collection of trading cards. Hisbrother gave him 4 more cards. Tim gave 6 cards to his neighbor. Then Tim bought 24 cards. Tim now has 42 cards. How many cards did he have to start with?

4. Jack had an amount of money. He spent $7 fora model car kit and $4 for paint. His mothergave him $5. Jack now has $11. How muchmoney did he have to begin with?

UNIT 3 LESSON 14 Solve Multi-Step Word Problems 165

Show your work.

3-14 Name Date

5. On the Back Write a word problem that needsto be solved by working backward.

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166 UNIT 3 LESSON 14 Solve Multi-Step Word Problems

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3-4 Name Date3–15

UNIT 3 LESSON 15 Read and Create Bar Graphs 167

Vehicles in Murray’sUsed Car Lot

Kind of Vehicle

Nu

mb

er o

f V

ehic

les

10

9

8

7

6

5

4

3

2

1

0Van Truck Car

�Read a Horizontal Bar Graph

Look at this andanswer the question.

horizontal bar graph

�Read a Vertical Bar Graph

Look at this andanswer the question.

vertical bar graph

Flowers in Mary’s Garden

Number of Flowers

Kin

d o

f Fl

ow

er Rose

Zinnia

Tulip

0 1 2 3 4 5 6 7 8 9 10

Vocabularyhorizontal bar graphvertical bar graph

1. What do the bars represent?

2. What do the bars represent?

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168 UNIT 3 LESSON 15 Read and Create Bar Graphs

�Create a Vertical Bar Graph

Use the information in this table to complete the vertical bar graph.

�Create a Horizontal Bar Graph

Use the information in this table to complete the horizontal bar graph.

Balls in the Gym

Type of Ball Number of Balls

Soccer ball 4

Basketball 6

Softball 9

Favorite Fruits

Type of Number WhoFruit Chose It

Apple 5

Banana 6

Orange 4

3.

4.

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UNIT 3 LESSON 15 Read and Create Bar Graphs 169

�Take a Survey and Record Results1. Choose a survey topic from the box or make

up one of your own. Then take a survey to find the favorite.

2. Use the tally chart to complete the horizontal bar graph.

3. On the Back Write two questions that can beanswered using the bar graph. Then answer them.

TopicsSports

AnimalsColors

School SubjectsSnacks

Which is your favorite?

Answer Choice Tally

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170 UNIT 3 LESSON 15 Read and Create Bar Graphs

Name Date

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�Horizontal Bar Graphs with Multi-Digit Numbers

Use this horizontal bar graph to answer the questions below.

UNIT 3 LESSON 16 Read and Create Bar Graphs with Multi-Digit Numbers 171

1. How many miles did Shahid drive?

2. Who drove the most miles?

3. How many miles did Aaron and Barbara drivealtogether?

4. How many more miles did Jing drive than Shahid?

5. How many fewer miles did Barbara drive than Jing?

6. Write two more questions that can be answered byusing the graph.

Spring Trip

Miles Driven

Dri

ver

Aaron

Jing

Shahid

Barbara

0 50 100 150 200 250 300 350 400

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172 UNIT 3 LESSON 16 Read and Create Bar Graphs with Multi-Digit Numbers

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�Vertical Bar Graphs with Multi-Digit Numbers

Use the vertical bar graph at the right to answer the questions below.

7. How many cans of peas are atTurner’s Market?

8. Which type of canned goods doesTurner’s Market have the least of?

9. How many cans of beans andpeaches are there altogether?

10. How many more cans of beans arethere than peas?

11. How many fewer cans of peachesare there than peas?

12. Write two more questions that canbe answered by using the graph.

Canned Goods atTurner’s Market

Canned Goods

Nu

mb

er o

f C

ans

1000

900

800

700

600

500

400

300

200

100

0Beans PeasPeaches

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UNIT 3 LESSON 16 Read and Create Bar Graphs with Multi-Digit Numbers 173

�Create a Vertical Bar Graph with Multi-Digit Numbers

2. Use the information in this table to make a vertical bar graph.

�Create a Horizontal Bar Graphwith Multi-Digit Numbers

1. Use the information in this table to make a horizontal bar graph.

3. On the Back Write twoquestions that can beanswered using one of thegraphs.

Joe’s Video Collection

Type Videos

Comedy 60

Action 35

Drama 20

Summer Bike Sales

Type of Bike Number Sold

Road Bike 200

Mountain Bike 600

Hybrid Bike 450

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174 UNIT 3 LESSON 16 Read and Create Bar Graphs with Multi-Digit Numbers

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3-4 Name Date

Compare the numbers. Write �, �, or � in each .

UNIT 3 Test 175

3

1. 742 724 2. 2,329 2,319

Write the numbers in order from least to greatest.

3. 598, 678, 590 4. 6,543, 7,585, 6,585

Round each number to the given place.

5. 1,352 to the nearest ten

7. $7.89 to the nearest dime

6. 567 to the nearest hundred

8. $6.29 to the nearest dollar

Solve. Label your answer.

9. Jason collects toy dinosaurs. He has 485 toydinosaurs in his collection. He plans to sell 243 toydinosaurs. Round each number to the nearest ten toestimate how many he will have left.

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176 UNIT 3 Test

Use the bar graph to answer questions 10 and 11.

3

0 1 2 3 4 5 6 7 8 9 10

Louis

Jim

Bella

Number of Rides

Roller Coaster Rides

Rid

er

This table shows the numbers of T-shirts of differentsizes a store had before a big sale, the number theysold, and the number they had left.

10. How many more rides did Louis take than Jim?

11. How many rides did Bella and Louis take altogether?

12. Fill in the blank cells.

13. How many more small T-shirts than large T-shirts did the store have before the sale?

T-shirt Sales

Number Before Number Number LeftSale Sold After Sale

Small 645 587

Medium 390 45

Large 462 29

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UNIT 3 Test 177

3

Solve. Cross out any extra information. Circle anyhidden information.

14. Becky has 20 fish and 2 hamsters. There are 8 angelfish and the rest of the fish aregoldfish. She gets 7 more goldfish. How manygoldfish does she have now?

15. Raj is going on vacation for a week and 5 days.How many days will Raj be gone?

Solve the problem if possible. If more informationis needed, rewrite the problem to include thenecessary information and then solve it.

16. Julie and Sam grew tomato plants. Julie’s plantgrew 16 inches. How much taller did Sam’splant grow?

Show your work.

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178 UNIT 3 Test

3

19. Uri bought a tube of toothpaste for $2.58. Hepaid with a $5.00 bill. Find the amount ofchange by counting on. Draw the coins and billsyou counted. How much change did he get?

20. Extended Response Alexa has $5.00. She wantsto order a sandwich for $3.65 and a drink for$1.48. How can she estimate to be sure she hasenough money?

What estimate do you get using your method?Can Alexa be sure she has enough money tobuy the sandwich and the drink?

Show your work.

Compare the two collections of coins and bills. Write �, �, or � in the .

17.

18. Draw two different coin combinations for 78¢.

Solve.

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C–1 Name Date

UNIT C LESSON 1 Motion Geometry Patterns 179

Vocabulary

flip� Draw Flips

When you a figure over a line, you get a mirror image.flip

1. 2.

Draw the flipped image of each figure.

3. 4.

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180 UNIT C LESSON 1 Motion Geometry Patterns

� Use Flips in Patterns

Draw the next figure in each pattern.

5.

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6.

7.

8. Look for flips in this pattern. Shade a figure and its flip. Draw four more figures to continue the pattern.

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Vocabulary

slide�Describe and Draw SlidesYou can a figure along a line.slide

9. 10.

11. 12.

Describe each slide. Draw the new figure.

This slide moves the figure to theright and down.

This slide moves the figure up andto the right.

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Vocabulary

turn

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�Describe and Draw TurnsYou can a figure around a point.turn

13. 14.

15. 16.

Describe each turn. Draw the new figure.

This is a quarter turn. This is a half turn.

78293.UCL01_179-184 7/13/05 1:56 PM Page 182


Dear Family,

Your child is studying patterns that grow, patterns that shrink,and patterns that repeat. Students will find pattern rules andcontinue patterns for both number and geometric patterns.Students will also use patterns to solve real-world problems.Repeating patterns from geometry are used everywhere: in art,tiling designs, quilts, and clothing. Slides (translations), flips(reflections), and turns (rotations) can be used to make tilingpatterns.

This diagram shows how copies of thisgeometric figure can fit together tomake a tiling pattern.

Turn the figurearound a point.

Flip the figureover a line.

Slide the figure upand to the left.

If you have any questions or comments, please call or write to me.

Thank you.


78293.UCL01_179-184 3/23/06 1:26 PM Page 183


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Estimada familia:

La unidad que su niño está estudiando trata de patrones:patrones que aumentan, patrones que disminuyen, patrones que se repiten. Los patrones geométricos que se repiten se usanen todas partes: en arte, en diseños de azulejos, en colchas y enropa. Los deslizamientos (traslaciones), las inversiones(reflexiones) y los giros (rotaciones), servirán para hacer patronesde azulejos.

Este diagrama muestra de qué manerapueden combinarse las copias de estafigura geométrica para formar unpatrón de azulejos.

Gira la figurasobre un punto.

Invierte lafigura por unborde.

Desliza la figura haciaarriba y la izquierda.


Atentamente, El maestro de su niño.

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UNIT C LESSON 2 Repeating Patterns 185

Vocabulary

repeating pattern � Explore Repeating Number PatternsSometimes a number pattern continues by repeating the same digits.

Continue each number pattern.

1. 2 7 2 7 2 7

2. 1 2 2 1 2 2 1 2 2

3. 1 3 2 1 3 2 1 3 2

4. 1 0 0 1 1 0 0 1 1 0 0 1

� Explore Repeating Patterns in Skip Counting

Complete.

5. Skip count by 2s.

2, 4, 6, 8, 10, , , , , , , ,

6. Show the pattern in the ones digits when you skipcount by 2s, starting at 2.

, , , , , , , , ,

7. Start at 1 and count by 2s.

1, 3, 5, , , , , , ,

8. Show the pattern in the ones digits in exercise 7.

, , , , , , , , ,

9. Skip count by 5s.

5, 10, 15, , , , , , , , ,

10. Show the pattern in the ones digits when you skipcount by 5s, starting at 5.

, , , , , , ,

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186 UNIT C LESSON 2 Repeating Patterns

� Explore Repeating Shape Patterns

This pattern repeats the same figures over and over. You can describe it as a triangle, flipped triangle, square, repeat.

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11.

Show two ways to make a repeating pattern with these starting figures.

14.

12.

13.

15.

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UNIT C LESSON 3 Growing and Shrinking Patterns 187

Vocabulary

growing patternshrinking pattern� Continue a Growing or Shrinking

Number PatternA number pattern can grow or shrink by the same amount.

Continue the pattern and write the rule.

1. 5, 8, 11, 14, 17, , , , , , ,

2. 30, 27, 24, 21, , , , , ,

A number pattern can grow or shrink by a changing amount. When this happens, look for a pattern in the changes.

Continue the pattern and write the rule.

3. 6, 7, 9, 12, 16, , , , , , ,

4. 2, 6, 11, 15, 20, 24, 29, , , , , ,

Make two patterns with these starting numbers. Write the rule.

5. 2, 4, , ,

2, 4, , ,

6. 50, 45, , ,

50, 45, , ,

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188 UNIT C LESSON 3 Growing and Shrinking Patterns

� Continue a Growing or Shrinking Shape Pattern

The figures in this pattern grow larger and larger.

7. How does the pattern grow?


8.

9.

10.

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UNIT C LESSON 3 Growing and Shrinking Patterns 189

� Solve a Simpler ProblemHow many small triangles will be in triangle number 10?One way to solve problems like this one is to solve a simpler problem and look for a pattern.

13. Draw figure 5 in the patternabove. In the table, record thenumber of triangles it has.

14. Describe how the pattern grows.

1 2 3 4

12. Complete the table to show how the number of small triangles grows.

15. Use this pattern to find how many small triangles are in triangle number 10.

Triangle Number of SmallNumber Triangles

1

2

3

4

5

Solve.

16. If 8 friends all shake hands with each otheronce, how many handshakes will take place?

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190 UNIT C LESSON 3 Growing and Shrinking Patterns

� Solve Real-World Problems

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Use a number pattern to solve each problem.

17. One cookie costs 50¢, a bag of two cookiescosts 59¢, and a bag of 3 cookies costs 68¢. Ifthe pattern continues how much will it cost tobuy a bag of 6 cookies?

18. This is the window pattern on a building. Howmany windows will be in the pattern if thereare 7 floors?

19. A floor has this tile pattern. If there are 4 ringsaround the center, how many tiles will there be in all?

4 floors3 floors2 floors1 floor

Center with 1 ring with 2 rings with 3 rings

78293.UCL03_187-190 7/13/05 1:58 PM Page 190

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UNIT C Test 191

C

1. Is the second figure the result of a slide, flip, or turn?

2. Draw the next figure in the pattern.

3. Continue the number pattern.

329329329329329

4. Draw the next figure in the pattern.

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192 UNIT C Test

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C

5. Write a rule for this pattern.

9. Write a rule for this pattern.

69, 64, 59, 54, 49, 44, 39

10. Extended Response In September, Elisa walks dogs for $1.25 per walk.In October, she charges $1.50 per walk. In November, she charges $1.75per walk. If the pattern continues, how much will she charge per walkin December and January? Describe the pattern rule you used to solvethe problem.

6. Continue this pattern.

65, 62, 59, 56, 53, 50, 47, , , , ,


12, 16, 20, 24, 28, 32, 36, , , , ,


5, 6, 8, 11, 15, 20, 26, , , , ,

78293.UCTEST_191-192 7/19/05 11:04 AM Page 192

acute angle An angle whose measure isless than 90°.

acute triangle A triangle in which themeasure of each angle is less than 90°.

addend A number to be added.Example: 8 � 4 � 12

addend addend

addition A mathematical operation thatcombines two or more numbers.Example: 23 � 52 � 75

addend addend sum

adjacent (sides) Two sides that meet ata point.Example: Sides a and b are adjacent.

A.M. The time period between midnightand noon.

angle A figure formed by two rays ortwo line segments that meet at anendpoint.

area The number of square units in aregion

The area of the rectangle is 6 squareunits.

array An arrangement of objects,pictures, or numbers in columns androws.

Associative Property of Addition(Grouping Property of Addition)

The property which states thatchanging the way in which addends aregrouped does not change the sum.

Example: (2 � 3) � 1 � 2 � (3 � 1)

5 � 1 � 2 � 4

6 � 6

Associative Property of Multiplication(Grouping Property of Multiplication)

The property which states thatchanging the way in which factors aregrouped does not change the product.

Example: (2 � 3) � 4 � 2 � (3 � 4)

6 � 4 � 2 � 12

24 � 24

a c

b

d

Glossary

Glossary S1

78294.EM01_001_014 3/30/06 12:51 PM Page S1

S2 Glossary

axis (plural: axes) A reference line for agraph. A bar graph has 2 axes; one ishorizontal and the other is vertical.

bar graph A graph that uses bars to show data. The bars may be horizontal orvertical.

base (of a geometric figure) Thebottom side of a 2-D figure or thebottom face of a 3-D figure.

calculator A tool used to perform mathematical operations.

capacity The amount a container canhold.

cell A rectangle in a table where acolumn and row meet.

centimeter (cm) A metric unit used tomeasure length.

100 cm � 1 m

circle A plane figure that forms a closedpath so that all points on the path arethe same distance from a point calledthe center.

circle graph A graph that representsdata as parts of a whole.

circumference The distance around acircle, about 3�

17� times the diameter.

column A vertical group of cells in atable.

Coin Toss

SamZoe

Heads Tails11 6

column

9 10

orange

Jacket Colors in Ms. Timmer’s Class

blue

yellow

green

Coin Toss

SamZoe

Heads Tails11 6 cell9 10

base

Canned Goods at Turner’s Market

Number of Cans

Can

ned

Go

od

s

Peaches

Beans

Peas

0 100 200 300 400 500 600 700 800


Number of Flowers

Kin

d o

f Fl

ow

er Rose

Zinnia

Tulip

0 1

axes

2 3 4 5 6 7 8 9 10

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Glossary (Continued)

78294.EM01_001_014 3/30/06 12:51 PM Page S2

Commutative Property of Addition(Order Property of Addition) The

property which states that changingthe order of addends does not changethe sum.

Example: 3 � 7 � 7 � 3

10 � 10

Commutative Property ofMultiplication (Order Property ofMultiplication) The property which

states that changing the order offactors does not change the product.

Example: 5 � 4 � 4 � 5

20 � 20

comparison bars Bars that represent thelarger amount, smaller amount, anddifference in a comparison problem.

In Volume 2, we use comparison barsfor multiplication.

cone A solid figure that has a circularbase and comes to a point called thevertex.

congruent figures Figures that have thesame size and shape.

Triangles A and B are congruent.

coordinates The numbers in an orderedpair that locate a point on a coordinategrid. The first number is the distanceacross and the second number is thedistance up.

coordinate grid A grid formed by twoperpendicular number lines in whichevery point is assigned an ordered pairof numbers.

cube A solid figure that has six squarefaces of equal size.

0 1 2 3 4 5

12345

0 1 2 3 4 5

12345 A

A B

7 7

56 7 7 7 7 7 7 7 7

smaller amount difference

larger amount

Glossary S3

The coordinates3 and 4 in theordered pair (3, 4)locate Point A onthe coordinate grid.

78294.EM01_001_014 3/30/06 12:51 PM Page S3

Index (Continued)

S4 Glossary

cup (c) A customary unit ofmeasurement used to measure capacity.

2 cups � 1 pint4 cups � 1 quart

16 cups � 1 gallon

cylinder A solid figure with twocongruent circular or elliptical facesand one curved surface.

data Pieces of information.

decimal A number with one or moredigits to the right of a decimal point.Examples: 1.23 and 0.3

decimal point The dot that separates thewhole number from the decimal part.

1.23

decimal point

decimeter (dm) A metric unit used tomeasure length

1 decimeter � 10 centimeters

degree (°) A unit for measuring anglesor temperature.

degrees Celsius (°C) The metric unit formeasuring temperature.

degrees Fahrenheit (°F) The customaryunit of temperature.

denominator The bottom number in afraction that shows the total number ofequal parts in the whole.Example: �

13

� denominator

diagonal A line segment that connectstwo corners of a figure and is not aside of the figure.

diameter A line segment that connectstwo point on a circle and also passesthrough the center of the circle. Theterm is also used to describe the lengthof such a line segment.

difference The result of subtraction orof comparing.

digit Any of the symbols 0, 1, 2, 3, 4, 5,6, 7, 8, 9.

dividend The number that is divided indivision.Examples: 4

12 � 3 � 4 3��1�2�

dividend dividend

division The mathematical operationthat separates an amount into smallerequal groups to find the number ofgroups or the number in each group.Example: 12 � 3 � 4 is a division

number sentence.

divisor The number that you divide by indivision.Example: 12 � 3 � 4 3��1�2�

divisor divisor

diameter

diagonal

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edge The line segment where two facesof a solid figure meet.

elapsed time The time that passesbetween the beginning and the end ofan activity.

endpoint The point at either end of aline segment or the beginning point ofa ray.

equation A mathematical sentence withan equals sign.Examples: 11 � 22 � 33

75 – 25 � 50

equilateral triangle A triangle whosesides are all the same length.

equivalent Equal, or naming the sameamount.

equivalent fractions Fractions thatname the same amount.Example: �

12

� and �24

�

equivalent fractions

estimate About how many or abouthow much.

even number A whole number that is amultiple of 2. The ones digit in an evennumber is 0, 2, 4, 6, or 8.

event In probability, a possible outcome.

expanded form A number written toshow the value of each of its digits. Examples:

347 � 300 � 40 � 7347 � 3 hundreds � 4 tens � 7 ones

expression A combination of numbers,variables, and/or operation signs. Anexpression does not have an equals sign.Examples: 4 � 7 a � 3

face A flat surface of a solid figure.

factors Numbers that are multiplied togive a product. Example: 4 � 5 � 20

factor factor product

flip To reflect a figure over a line. Thesize and shape of the figure remain the same.

foot (ft) A customary unit used tomeasure length.

1 foot � 12 inches

face

3 in. 3 in.

3 in.

endpointendpoint endpoint

edge

Glossary S5

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Index (Continued)

S6 Glossary

formula An equation with variables thatdescribes a rule. The formula for the area of a

rectangle is:A � l � wwhere A is the area, l is the length,and w is the width.

fraction A number that names part of awhole or part of a set.

front-end estimation A method ofestimating that keeps the largest placevalue in a number and drops the rest.Example: 527 → 500

� 673 → � 6001,100

The 5 in 527 is the “front end” numberThe 6 in 673 is the “front end” number

function table A table of ordered pairsthat shows a function.

gallon (gal) A customary unit used tomeasure capacity.

1 gallon � 4 quarts � 8 pints � 16 cups

gram (g) A metric unit of mass, about 1paper clip.

1,000 grams � 1 kilogram

greater than (�) A symbol used tocompare two numbers.Example: 6 � 5

6 is greater than 5.

group To combine numbers to form newtens, hundreds, thousands, and so on.

growing pattern A number orgeometric pattern that increases.Examples: 2, 4, 6, 8, l0…

1, 2, 5, 10, 17…

height A measurement of vertical length,or how tall something is.

horizontal Extending in two directions,left and right.

horizontal bar graph A bar graph withhorizontal bars.

hundredth One of the equal parts whena whole is divided into 100 equal parts.

one hundredth � � 0.011100


Number of Flowers

Kin

d o

f Fl

ow

er Rose

Zinnia

Tulip

0 1 2 3 4 5 6 7 8 9 10

Rule: add 2

Input Output

1 3

2 4

3 5

4 6

fraction13

23

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For every inputnumber, thereis only onepossible outputnumber.

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improper fraction A fraction in whichthe numerator is equal to or is greaterthan the denominator. Improperfractions are equal to or greater than 1.

�55

� and �83

� are improper fractions.

inch (in.) A customary unit used tomeasure length.

12 inches � 1 foot

isosceles triangle A triangle that has atleast two sides of the same length.

key A part of a map, graph, or chart thatexplains what symbols mean.

kilogram (kg) A metric unit of mass.

1 kilogram � 1,000 grams

kilometer (km) A metric unit of length.

1 kilometer � 1,000 meters

less than (�) A symbol used to comparenumbers.Example: 5 � 6

5 is less than 6.

line A straight path that goes on foreverin opposite directions.

line graph A graph that uses a straightline or a broken line to show changesin data.

line of symmetry A line on which afigure can be folded so that the twohalves match exactly.

line plot A way to show data using anumber line.

line segment A part of a line. A linesegment has two endpoints.

liter (L) A metric unit used to measurecapacity.

1 liter � 1,000 milliliters

1 2 3 4 5 6

X X X XX X

XX

X

Line of symmetry

Height of a Bean Plant

Weeks

Hei

gh

t (i

n in

ches

)

1

12345678

0 2 3 4 5 6 7 8

Glossary S7

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Index (Continued)

S8 Glossary

mass The amount of matter in an object.

mean (average) The sum of the valuesin a set of data divided by the numberof pieces of data in the set.Example: 3 � 5 � 4 � 8 � 20

20 � 4 � 5 5 is the mean

mental math A way to solve problemswithout using pencil and paper, or acalculator.

meter (m) A metric unit used tomeasure length.

1 meter � 100 centimeters

method A procedure, or way, of doingsomething.

mile (mi) A customary unit of length.

1 mile � 5,280 feet

milliliter (mL) A metric unit used tomeasure capacity.

1,000 milliliters � 1 liter

mixed number A whole number and afraction.1�

34

� is a mixed number.

mode The number that occurs mostoften in a set of data.In this set of numbers {3, 4, 5, 5, 5, 7, 8},

5 is the mode.

multiple A number that is the productof the given number and anothernumber.

multiplication A mathematicaloperation that combines equal groups.Example: 4 � 3 � 12


3 � 3 � 3 � 3 � 12

net A flat pattern that can be folded tomake a solid figure.

This net can be folded into arectangular prism.

number line A line on which numbersare assigned to lengths.

numerator The top number in a fractionthat shows the number of equal partscounted.

Example: �13

� numerator

obtuse angle An angle that measuresmore than 90° but less than 180°.

obtuse triangle A triangle with oneangle that measures more than 90°.

odd number A whole number that is nota multiple of 2. The ones digit in anodd number is 1, 3, 5, 7, or 9.

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opposite sides Sides that are acrossfrom each other; they do not meet at apoint.Example: Sides a and c are opposite.

ordered pair A pair of numbers such as (3, 4) in which one number isconsidered to be first and the othernumber second. They can name a pointon a coordinate grid.

ordinal numbers Numbers used to showorder or position.Example: first, second, fifth

ounce (oz) A customary unit used tomeasure weight.

16 ounces � 1 pound

parallel lines Two lines that areeverywhere the same distance apart.

parallelogram A quadrilateral withboth pairs of opposite sides parallel.

partner One of two numbers that add tomake a total.Example: 9 � 7 � 16 total

sum

partner partneraddend addend

perimeter The distance around theoutside of a figure.

perpendicular Two lines or linesegments that cross or meet to formright angles.

pictograph A graph that uses pictures orsymbols to represent data.

pint (pt) A customary unit used tomeasure capacity.

1 pint � 2 cups

place value The value assigned to theplace that a digit occupies in a number.

place value drawing A drawing thatrepresents a number. Hundreds arerepresented by boxes, tens by verticallines, and ones by small circles.

plane figure A closed figure that hastwo dimensions.

962

9

hundreds

6

tens

2

ones

Favorite Ice Cream Flavors

Peanut Butter Crunch

Cherry Vanilla

Chocolate

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Glossary S9

78294.EM01_001_014 3/30/06 12:51 PM Page S9

Index (Continued)

S10 Glossary

P.M. The time period between noon andmidnight.

pound (lb) A customary unit used tomeasure weight.

1 pound � 16 ounces

prism A solid figure with two parallelcongruent bases, and rectangles orparallelograms for faces. A prism isnamed by the shape of its bases.

hexagonal prism

probability The chance of an eventoccurring.

product The answer when you multiplynumbers.Example: 4 � 7 � 28


proof drawing A drawing used to showthat an answer is correct.

pyramid A solid figure with one baseand whose other faces are triangleswith a common vertex. A pyramid isnamed by the shape of its base.

quadrilateral A figure with four sides.

quart (qt) A customary unit used tomeasure capacity.

1 quart � 4 cups

quotient The answer when you dividenumbers.Examples: 5 quotient

35 � 7 � 5 7��3�5�

quotient

radius A line segment that connects thecenter of a circle to any point on thecircle. The term is also used to describethe length of such a line segment.

range The difference between thegreatest number and the least numberin a set of data.In this set of numbers {12, 15, 18, 19, 20},the range is 20 � 12 or 8

ray A part of a line that has oneendpoint and goes on forever in onedirection.

radius

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rectangle A parallelogram that has 4right angles.

rectangular prism A prism with sixrectangular faces.

rectangular pyramid A pyramid with arectangular base and four triangularfaces.

repeating pattern A pattern consistingof a group of numbers, letters, orfigures that repeat.Examples: 1, 2, 1, 2, …

A, B, C, A, B, C, …

rhombus A parallelogram withcongruent sides.

right angle An angle that measures 90°.

right triangle A triangle with one rightangle.

round To find about how many or howmuch by expressing a number to thenearest ten, hundred, thousand, and soon.

route The path taken to get to alocation.

row A horizontal group of cells in atable.

scale An arrangement of numbers inorder with equal intervals.

scalene triangle A triangle with sides ofthree different lengths.

Coin Toss

SamZoe

Heads Tails11 6

row9 10

Glossary S11

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Index (Continued)

S12 Glossary

shrinking pattern A number orgeometric pattern that decreases.Examples: 15, 12, 9, 6, 3,…

25, 20, 16, 13, 11,…

side (of a figure) A line segment thatmakes up a figure.

simplify To write an equivalent fractionwith a smaller numerator anddenominator.

slide To move a figure along a line in anydirection. The size and shape of the figureremain the same.

solid figure A figure that has threedimensions.

sphere A solid figure shaped like a ball.

square A rectangle with four sides of thesame length.

square number A product of a wholenumber and itself.Example: 4 � 4 � 16

square number

square pyramid A pyramid with asquare base and four triangular faces.

standard form The name of a numberwritten using digits.Example: 1,829

straight angle An angle that measures180°.

subtract To find the difference of twonumbers.Example: 18 – 11 � 7

subtraction A mathematical operationon a sum (total) and an addend, whichcan be called the difference.Example: 43 – 40 � 3

sum The answer when adding two ormore addends.Example: 37 � 52 � 89

addend addend sumpartner partner total

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survey A method of collectinginformation.

symmetry A figure has symmetry if itcan be folded along a line so that thetwo halves match exactly.

table An easy to read arrangement ofdata, usually in rows and columns.

tally marks Short line segments drawnin groups of 5. Each mark including theslanted marks stands for 1 unit.

tenth One of the equal parts when awhole is divided into ten equal parts.

thermometer A tool for measuringtemperature.

total The answer when adding two ormore addends. The sum of two or morenumbers.Example: 672 � 228 � 900

totalsum

trapezoid A quadrilateral with exactlyone pair of parallel sides.

triangular prism A solid figure with twotriangular faces and three rectangularfaces.Example:

triangular pyramid A pyramid whosebase is a triangle.

turn To rotate a figure around a point.The size and shape of the figureremains the same.one tenth � � 0.11

10

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Coin Toss

SamZoe

Heads Tails11 69 10

Glossary S13

partneraddend

partneraddend

78294.EM01_001_014 3/30/06 12:51 PM Page S13

Index (Continued)

S14 Glossary

ungroup To open up 1 in a given placeto make 10 of the next smaller placevalue in order to subtract.

unit fraction A fraction with anumerator of 1.

Venn diagram A diagram that usescircles to show the relationship amongsets of objects.

vertex A point where sides, rays, oredges meet.

vertical Extending in two directions, upand down.

vertical bar graph A bar graph withvertical bars.

weight The measure of how heavysomething is.

word form A name of a number writtenusing words instead of digits.Example: Nine hundred eighty-four

yard (yd) A customary unit used tomeasure length.

1 yard � 3 feet � 36 inches

Canned Goods at Turner’s Market

Canned Goods

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78294.EM01_001_014 3/31/06 2:52 PM Page S14

dr. karen c. fuson - iusd.org

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