Chapter 5 Resource Masters - Macmillan/McGraw-Hill

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4 5 6 7 8 9 10 ROV 18 17 16 15 14 13 12 11 10

Teacher’s Guide to Using 

Chapter 5 Resources ..........................................iv 

Chapter 5 Graphic Organizer ................................... 1 

Student Glossary .......................................................... 2 

Family Letter ................................................................ 4 

Family Letter Spanish ................................................. 5 

Chapter 5 Anticipation Guide .................................. 6 

Chapter 5 Game .......................................................... 7 

Lesson 5–1 Multiply by 3 

Reteach ........................................................................... 8 

Skills Practice ................................................................ 9 

Homework Practice ..................................................10 

Problem-Solving Practice ........................................11 

Enrich.............................................................................12 


Reteach .........................................................................13 

Skills Practice ..............................................................14 



Enrich.............................................................................17 

Lesson 5–3 Problem-Solving 

Strategy: Look for 

a Pattern 

Reteach .........................................................................18 



Enrich.............................................................................22 


Reteach .........................................................................23 




Enrich.............................................................................27 


Reteach .........................................................................28 




Enrich.............................................................................32 


Reteach .........................................................................33 




Enrich.............................................................................37 

Grade 3 Chapter 5 

Table of Contents 

iii 

Lesson 5–7 Problem-Solving 

Investigation: Choose 

a Strategy 

Reteach .........................................................................38 



Enrich.............................................................................42 

Lesson 5–8 Algebra: Associative 

Property 

Reteach .........................................................................43 




Enrich.............................................................................47 

Lesson 5–9 Algebra: Find a Rule 

Reteach .........................................................................48 




Enrich.............................................................................52 

Individual Progress Checklist .................................53 

Chapter Tests: 

Chapter Diagnostic Assessment ...........................54 

Chapter Pretest ..........................................................55 

Quizzes 1, 2, & 3 ........................................................56 

Quizzes 4, 5, & 6 ........................................................57 

Quizzes 7, 8, & 9 .....................................................58 

Mid-Chapter Review .................................................59 

Vocabulary Test ..........................................................60 

Oral Assessment ........................................................61 

Chapter Project Rubric .............................................63 

Foldables Rubric ........................................................64 

Test Form 1 .................................................................65 

Test Form 2A ...............................................................67 

Test Form 2B ...............................................................69 

Test Form 2C ...............................................................71 

Test Form 2D ..............................................................73 

Test Form 3 .................................................................75 

Extended-Response Test .........................................77 

Student Recording Sheet ....................................78 

Cumulative Standardized 

Test Practice ..............................................................79 

Answer Pages ...........................................................A1

Teacher’s Guide to Using the 

Chapter 5 Resource Masters 

The Chapter 5 Resource Masters includes the core materials needed for Chapter 5. These 

materials include worksheets, extensions, and assessment options. The answers for these 

pages appear at the back of this booklet. 

All of the materials found in this booklet are included for viewing and printing on the 

TeacherWorks Plus TM CD-ROM. 

Chapter Resources 

Graphic Organizer (page 1) This master 

is a tool designed to assist students with 

comprehension of grade-level concepts. While 

the content and layout of these tools vary, 

their goal is to assist students by providing 

a visual representation from which they can 

learn new concepts. 

Student Glossary (page 2) This master 

is a study tool that presents the key 

vocabulary terms from the chapter. You may 

suggest that students highlight or star the 

terms they do not understand. Give this list 

to students before beginning Lesson 5–1. 

Remind them to add these pages to their 

mathematics study notebooks. 

Anticipation Guide (page 6) This master 

is a survey designed for use before beginning 

the chapter. You can use this survey to 

highlight what students may or may not 

know about the concepts in the chapter. 

There is space for recording how well 

students answer the questions before they 

complete the chapter. You may find it helpful 

to interview students a second time, after 

completing the chapter, to determine their 

progress. 

Game (page 7) A game is provided to 

reinforce chapter concepts and may be used 

at appropriate times throughout the chapter. 

Resources for 

Computational Lessons 

Reteach Each lesson has an associated 

Reteach worksheet. In general, the Reteach 

worksheet focuses on the same lesson content 

but uses a different approach, learning style, 

or modality than that used in the Student 

iv 

Edition. The Reteach worksheet closes with 

computational practice of the concept. 

Skills Practice The Skills Practice 

worksheet for each lesson focuses on the 

computational aspect of the lesson. The 

Skills Practice worksheet may be helpful 

in providing additional practice of the skill 

taught in the lesson. 

Homework Practice The Homework 

Practice worksheet provides an opportunity 

for additional computational practice. The 

Homework Practice worksheet includes word 

problems that address the skill taught in the 

lesson. 

Problem-Solving Practice The Problem- 

Solving Practice worksheet presents 

additional reinforcement in solving word 

problems that apply both the concepts of the 

lesson and some review concepts. 

Enrich The Enrich worksheet presents 

activities that extend the concepts of the 

lesson. Some Enrich materials are designed 

to widen students’ perspectives on the 

mathematics they are learning. These 

worksheets are written for use with all 

levels of students. 

Resources for Problem-Solving Strategy 

and Problem-Solving Investigation 

Lessons In recognition of the importance 

of problem-solving strategies, worksheets 

for problem-solving lessons follow a slightly 

different format. For problem-solving lessons, 

a two-page Reteach worksheet offers a 

complete model for choosing a problemsolving 

strategy. For each Problem-Solving 

Strategy lesson, Reteach and Homework 

Practice worksheets offer reinforcement of 

the strategy taught in the Student Edition 

lesson. In contrast, the Problem-Solving

Investigation worksheets include a model 

strategy on the Reteach worksheets and 

provide problems requiring several alternate 

strategies on the Homework Practice and 

Skills Practice worksheets. 

Assessment Options The assessment 

masters in the Chapter 5 Resource Masters 

offer a wide variety of assessment tools 

for monitoring progress as well as final 

assessment. 

Individual Progress Checklist This 

checklist explains the chapter’s goals or 

objectives. Teachers can record whether 

a student’s mastery of each objective is 

beginning (B), developing (D), or mastered 

(M). The checklist includes space to record 

notes to parents as well as other pertinent 

observations. 

Chapter Diagnostic Assessment This onepage 

test assesses students’ grasp of skills 

that are needed for success in the chapter. 

Chapter Pretest This one-page quick 

check of the chapter’s concepts is useful 

for determining pacing. Performance on 

the pretest can help you determine which 

concepts can be covered quickly and which 

specific concepts may need additional time. 

Mid-Chapter Review This one-page 

chapter test provides an option to assess 

the first half of the chapter. It includes both 

multiple-choice and free-response questions. 

Quizzes Three free-response quizzes 

offer quick assessment opportunities at 

appropriate intervals in the chapter. 

Vocabulary Test This one-page test 

focuses on chapter vocabulary. It is suitable 

for all students. It includes a list of 

vocabulary words and questions to assess 

students’ knowledge of the words. 

Oral Assessment This two-page test 

consists of one page for teacher directions 

and questions and a second page for 

recording responses. Although this 

assessment is designed to be used with all 

students, the interview format focuses on 

assessing chapter content assimilated by 

ELL students. 

Chapter Project Rubric This one-page 

rubric is designed for use in assessing the 

chapter project. You may want to distribute 

copies of the rubric when you assign the 

project and use the rubric to record each 

student’s chapter project score. 

Foldables Rubric This one-page rubric 

is designed to assess the Foldables graphic 

organizer. The rubric is written to the 

students, telling them what you will be 

looking for as you evaluate their completed 

Foldables graphic organizer. 

Leveled Chapter Tests 

• Form 1 assesses basic chapter concepts 

through multiple-choice questions and is 

designed for use with on-level students. 

• Form 2A is designed for on-level students 

and is primarily for those who may have 

missed the Form 1 test. It may be used 

as a retest for students who received 

additional instruction following the 

Form 1 test. 

• Form 2B is designed for students with 

a below-level command of the English 

language. 

• Form 2C is a free-response test designed 

for on-level students. 

• Form 2D is written for students with 

a below-level command of the English 

language. 

• Form 3 is a free-response test written for 

above-level students. 

• Extended-Response Test is an extended 

response test for on-level students. 

Student Recording Sheet This one-page 

recording sheet is for the standardized test 

in the Student Edition. 

Cumulative Standardized Test Practice 

This three-page test, aimed at on-level 

students, offers multiple-choice questions 

and free-response questions. 

Answers 

The answers for the Anticipation Guide and 

Lesson Resources are provided as reduced 

pages with answers appearing in black. Full 

size line-up answer keys are provided for the 

Assessment Masters. 

v

Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. 

5 

Name Date 

Graphic Organizer 

Use this graphic organizer to take notes on Chapter 5: More 

Multiplication Facts. Fill in the missing information. 

Extend the Pattern Name the Pattern 

5, 10, 15, 20, , 

3, 6, 9, 12, , 

2, 4, 6, 8, , 

4, 8, 12, 16, , 

6, 12, 18, 24, , 

7, 14, 21, 28, , 

9, 18, 27, 36, , 

8, 16, 24, 32, , 

Grade 3 1 Chapter 5 

Chapter Resources

5 

Name Date 

This is an alphabetical list of new vocabulary terms you will learn 

in Chapter 5. As you study the chapter, complete each term’s 

definition or description. Remember to add the page number 

where you found the term. Add this page to your math study 

notebook to review vocabulary at the end of the chapter. 

array 

Student-Built Glossary 

Vocabulary Term 

Associative Property of 

Multiplication 

Commutative Property 

of Multiplication 

Found on 

Page Definition/Description/Example 


Copyright © Macmillan/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.


5 

factor 

Identity Property of 


pattern 

product 

Name Date 

Student-Built Glossary (continued) 



Name Date 

Dear Family, 

Today my 5 class started Chapter Chapter M 5: : More More Multiplication ultiplication F Facts. acts I 

will be learning to multiply by 3, 6, 7, 8, and 9. I will also be learning to 

use the associative and commutative properties of multiplication. Here 

are my vocabulary words and an activity that we can do together. 

Love, ______________________ 

Key Vocabulary 

Associative Property of Multipli cation The 

property that states that the grouping of the 

factors does not change the product. 

3 × (6 × 2) = (3 × 6) × 2 

factor A number that divides into a whole 

number evenly. Also a number that is multiplied 

by another number. 8 is a factor of 24. 

product The answer to a multiplication 

problem. It also refers to expressing a number as 

product of its factors. 

Books to Read 

Spaghetti and Meatballs for All! 

by Marilyn Burns 

Each Orange Has 8 Slices 

by Paul Giganti, Jr. 

Activity 

Place 81 paperclips in a bowl. 

Take 9 paperclips and put them 

into a small plastic bag. How 

many small plastic bags will you 

need for all 81 paperclips? What if 

you put 18 paperclips in to each 

bag? How many bags would you 

need then? 

2 × 2 = Boo Multiplication Stories 

by Loreen Leedy 

Grade Grade 3 4 4 Chapter Chapter 5 



Name Date 

Estimada familia: 

Hoy mi clase 5 comenzó el Capítulo Capítulo o 5: : Más Más operaciones cperaciones l m con on la a multiultiplicación.plicación Aprenderé a multiplicar por 3, 6, 7, 8 y 9 y también a usar la 

propiedad asociativa y la propiedad conmutativa de la multiplicación. A 

continuación, están mis palabras de vocabulario y una actividad que 

podemos hacer juntos. 

Cariños, ___________________ 

Vocabulario clave 

Propiedad asociativa de la 

multiplicación Propiedad que establece 

que la agrupación de los factores no altera 

el producto. 3 × (6 × 2) = (3 × 6) 

× 2 

Factor: Número que divide exactamente a 

otro número entero. También es un número 

multiplicado por otro número. 

8 es un factor de 24 

Producto: Respuesta a un problema 

de multiplicación. También se refiere a la 

expresión de un número como el producto 

de sus factores. 

Libros recomendados 

Spaghetti and Meatballs for All! 

de Marilyn Burns 

Each Orange Has 8 Slices 

de Paul Giganti, Jr. 

Actividad 

Coloquen 81 clips en un tazón. 

Separen 9 en una bolsita plástica. 

¿Cuántas bolsitas necesitarán 

para los 81 clips? ¿Qué pasaría si 

usaran bolsas plásticas más 

grandes donde cupieran 18 clips? 

¿Cuántas bolsas necesitarían 

entonces? 

2 × 2 = Boo Multiplication Stories 

de Loreen Leedy 

Grade Grade 3 3 5 5 Chapter Chapter 5 5 


5 

Name Date 

Anticipation Guide 

More Multiplication Facts 

STEP 1 Before you begin Chapter 5 

• Read each statement. 

• Decide whether you agree (A) or disagree (D) with the 

statement. 

• Write A or D in the first column OR if you are not sure whether 

you agree or disagree, write NS (not sure). 

STEP 1 

A, D, or NS Statement 

1. There is only way to multiply a number by 3. 

2. Organizing information in a table can help you to 

notice a pattern. 

3. 7 × 2 = 14 and 2 × 7 = 14 

4. You can use the doubles or near doubles strategy 

when one of the factors is odd. 

5. 9 × 8 = 72 

6. Looking for a pattern may be helpful in remembering 

the nines multiplication facts. 

7. The Associative Property of Multiplication states that 

the grouping of the factors does not change the 

product. 

8. Multiplication and addition are not helpful in 

extending a pattern. 

9. 9 × 9 = 99 

STEP 2 After you complete Chapter 5 

• Reread each statement and complete the last column by 

entering an A (agree) or a D (disagree). 

• Did any of your opinions about the statements change from the 

first column? 

• For those statements that you mark with a D, use a separate sheet 

of paper to explain why you disagree. Use examples, if possible. 

STEP 2 

A or D 




5 

You will need: 

56 index cards 

Pens 

Name Date 

Chapter 5 Game 

Multiplication Concentration 

Copy the following multiplication sentences on separate index 

cards. Make two sets of each fact. You will have 56 cards all 

together. 

4 × 4 = 16 4 × 9 = 36 5 × 8 = 40 6 × 8 = 48 7 × 9 = 63 8 × 10 = 80 

4 × 5 = 20 4 × 10 = 40 5 × 9 = 45 6 × 9 = 54 7 × 10 = 70 9 × 9 = 81 

4 × 6 = 24 5 × 5 = 30 5 × 10 = 50 6 × 10 = 60 8 × 8 = 64 9 × 10 = 90 

4 × 7 = 28 5 × 6 = 30 6 × 6 = 36 7 × 7 = 49 8 × 9 = 72 10 × 10 = 100 

4 × 8 = 32 5 × 7 = 35 6 × 7 = 42 7 × 8 = 56 

1. Shuffle and place the cards face down in rows and columns. 

2. Turn over 2 cards and say the multiplication sentences aloud. 

3. Keep the cards if the multiplication sentences match and take 

another turn. 

4. Turn the cards face down if the multiplication sentences do 

not match. Then it’s the next player’s turn. 

5. The player with the most cards wins. 

4 9 = 36 

6 6 = 36 



5–1 

Name Date 

Reteach 

Multiply by 3 

There are different ways to find answers for multiplication 

problems. One way is to use models to represent the problem. 

Find 3 × 4. 

Using Models Using Paper and Pencil 

Number of 

Groups 

Number in Each 

Group 

3NS2.2 

Total 

3 × 4 = 12 

3 groups of 4 cubes factor factor product 

Use models to find the total number. 

1. 2. 

3 groups of 5 = 4 groups of 3 = 

3. 4 × 5 = 4. 

3 groups of 7 = 

5. 3 × 6 = 6. 8 × 3 = 

7. 3 groups of 3 = 8. 4 groups of 3 = 





5–1 

Multiply. 

Name Date 

Skills Practice 

Multiply by 3 

1. 3 × 10 = 2. 5 × 3 = 

3. 3 × 8 = 4. 6 × 3 = 

5. 7 × 3 = 6. 3 × 9 = 

7. 2 × 3 = 8. 1 × 3 = 

9. 0 × 3 = 10. 3 × 7 = 

11. 8 × 3 = 12. 3 × 6 = 

13. 3 × 5 = 14. 4 × 3 = 

15. 3 × 4 = 16. 3 × 8 = 

ALGEBRA Complete each table. 

17. 

Solve. 

Rule: multiply by 3 

Input 

3 

6 

1 

Output 

30 

0 


18. 


Input 

9 

7 

Output 

19. Jay has 3 bags of fruit. Each bag has 8 pieces of fruit. How 

many pieces of fruit does Jay have altogether? 

20. Heather has 3 bags of pretzels. Each bag has 6 pretzels. How 

many pretzels does Heather have altogether? 

12 

6 

24 

3NS2.2 


5–1 

Multiply. 

Name Date 

Homework Practice 

Multiply by 3 

1. 3 × 3 = 2. 3 × 5 = 

3. 5 × 3 = 4. 9 × 3 = 

5. 4 × 3 = 6. 10 × 3 = 

7. 8 × 3 = 8. 3 × 7 = 

9. 6 × 3 = 10. 1 × 3 = 

Solve. 

11. The parking lot has 3 rows of cars. There are 6 cars in each 

row. How many cars are in the parking lot? 

12. Mary has 3 dimes in her pocket. Each dime equals 

10 pennies. If she traded her dimes for pennies, how many 

pennies would she have? 

Multiply. (Lesson 4–9) 

13. 0 × 3 = 14. 1 × 5 = 

15. 1 × 6 = 16. 0 × 9 = 

17. 0 × 1 = 18. 2 × 0 = 

19. 8 × 1 = 20. 1 × 0 = 

21. 1 × 4 = 22. 2 × 1 = 

23. 5 × 0 = 24. 0 × 1 = 

3NS2.2 




5–1 

Solve. 

Name Date 

Problem-Solving Practice 

Multiply by 3 

1. Sean and Dave are playing with toy racecars. Sean has his 

cars lined up in 3 rows. He has 5 cars in each row. How 

many cars does he have in all? 

2. Dave has 4 rows of cars lined up. He has 3 cars in each row. 

How many cars does Dave have in all? 

3. The boys are sharing some special cars. They have 2 rows of 

special cars with 3 in each row. How many special cars do 

they have in all? 

4. Dave’s mom said that she would buy them more special cars. 

These cars cost $3 each. If she buys the boys 3 more, how 

much will she have to spend? 

5. The boys used their building blocks to create a wall for the 

cars to drive through. They plan to stack the blocks 3 across 

and 9 up. How many blocks do they need to build the wall? 

6. After they finish the wall, Dave and Sean each have 3 extra 

blocks. Two of these blocks are broken. How many extra 

blocks do they have left that are not broken? 

3NS2.2 



5–1 

Name Date 

Enrich 

The Birthday Party 

Karlie, Keri, and Kristie are triplets. They are having a 

birthday party. Read each problem. Draw a picture for each 

number sentence. Use a separate sheet of paper if you 

need more room. Then write a number sentence that helps 

answer questions 1–4. 

1. Each girl wants to invite six different friends to the party. How 

many friends will be invited to the party? 

2. The girls’ dad is making a jewelry box for each girl. Each box 

has four sides, a bottom, and a lid that opens. How many 

sides for the jewelry boxes will he make? 

3. Their aunt is knitting sweaters for the girls. She is buying 

eight flowered buttons to put on each sweater. How many 

buttons does she need to buy? 

4. The girls are going to be 9 years old. They will blow out the 

candles on their cake together. If their mom wants to buy 

one set of nine candles for each girl to put on the cake, how 

many candles does she need to buy? 

3NS2.2 




5–2 

Name Date 

Reteach 

Multiply by 6 

You can use facts that you already know to help you multiply by 6. 

Find 7 × 6 by doubling 7 × 3. 

3NS2.2 

7 groups of 6 = 7 groups of 3 plus 7 groups of 3 

7 × 6 = 7 × 3 + 7 × 3 

= 21 + 21 = 42 

Write a multiplication sentence for the picture. 

1. 2. 3. 

Multiply. 

= + 

4. 6 × 3 = 5. 6 × 5 = 6. 6 × 6 = 

7. 6 × 8 = 8. 6 × 1 = 9. 6 × 2 = 

10. 9 × 6 = 11. 6 × 7 = 12. 6 × 4 = 

13. 3 × 9 = 14. 3 × 3 = 15. 7 × 3 = 

16. 3 × 5 = 17. 3 × 8 = 18. 6 × 3 = 



5–2 

Multiply. 

Name Date 


Multiply by 6 

1. 6 × 5 = 2. 6 × 7 = 

3. 9 × 6 = 4. 3 × 6 = 

5. 6 × 6 = 6. 7 × 6 = 

7. 1 × 6 = 8. 6 × 2 = 

9. 8 × 6 = 10. 10 × 6 = 

11. 3 × 6 = 12. 6 × 4 = 

13. 5 × 6 = 14. 6 × 3 = 

15. 6 × 8 = 16. 6 × 7 = 

17. 4 × 6 = 18. 6 × 9 = 

ALGEBRA Find each missing number. 

19. 5 × = 30 20. 9 × = 54 

21. 8 × = 24 22. 6 × = 42 

23. 6 × = 48 24. 9 × = 27 

ALGEBRA Find each rule. 

25. Rule: Multiply by 

Rule: Multiply by 

Input 

6 

7 

8 

9 

Output 

36 

42 

48 

54 



3NS2.2 

Output 


Input 

6 

7 

8 

48 

56 

64 



5–2 

Multiply. 

Name Date 


Multiply by 6 

1. 6 × 4 = 2. 3 × 6 = 

3. 6 × 8 = 4. 4 × 6 = 

5. 6 × 0 = 6. 6 × 1 = 

7. 6 × 9 = 8. 9 × 6 = 

9. 5 × 6 = 10. 7 × 6 = 

Solve. 

11. Brad’s rabbit has 6 whiskers on both sides of its face. How 

many whiskers does the rabbit have on its face? 

12. Jan has 4 insects in a jar. Each insect has 6 legs. How many 

legs in all? 


13. 3 × 9 = 14. 3 × 7 = 

15. 6 × 3 = 16. 5 × 3 = 

17. 4 × 3 = 18. 8 × 3 = 

19. 0 × 3 = 20. 7 × 3 = 

21. 3 × 2 = 22. 3 × 4 = 

23. 3 × 8 = 24. 9 × 3 = 

3NS2.2 



5–2 

Solve. 

Name Date 


Multiply by 6 

1. Cindy and Mandy went to the beach. They each found 

6 starfish. How many starfish do they have in all? 

2. Each of the 6 starfish has 5 arms. The girls counted them all. 

How many starfish arms did the girls count? 

3. The girls made a sandcastle with 3 waterways leading to 

each of their 6 towers. How many waterways did they dig 

altogether? 

4. The girls each carried 6 pails with them to the beach. They 

found out that they really did not need so many pails, so they 

let a group of children use 4 of their pails. How many pails 

do the girls still have left to use? 

5. Cindy has 6 dimes that she can spend on stickers. Each 

sticker costs 5¢. 

Does she have enough money to buy 6 stickers? Explain. 

6. Write a problem that can be solved by multiplying by 6. 

3NS2.2 




5–2 

Name Date 

Enrich 

Multiply by 6 

Find the missing factor for each problem. Draw an array 

or a picture that matches the problem. Then use words to 

write a number sentence for each drawing. 

Find the Factors Show the Problem Write It in Words 

1. 6 × = 18 

2. 6 × = 30 

3. 2 × = 12 

4. 24 = × 6 

5. × = 36 

3NS2.2 



5–3 

Name Date 

Reteach 

Look for a Pattern 

Problem-Solving Strategy 

3MR1.1, 3AF2.2 

Liz created a castle with pink towers and blue flags. On the first tower, she has 

2 flags. The second tower has 4 flags, and the third tower has 8. If she keeps the 

pattern up, how many flags are on the fourth tower? 

Step 1 

Understand 

Step 2 

Plan 

Step 3 

Solve the problem. 

Step 4 

Check 

Think: What is 

added, subtracted 

or multiplied? 

What do you know? 

There are 2 flags on the first tower. 

There are 4 flags on the second tower. 

There are 8 flags on the third tower. 

What do you need to find out? 

How many flags will be on the fourth tower? 

Organize the data in a table. What are your 

columns? The towers 

What is in the row under each column? The 

number of flags 

Tower 1 Tower 2 Tower 3 Tower 4 

What is done to 2 to get 4 ? 2 was added to get 4 OR 

2 was multiplied to get 4. 

What was done to 4 to get 8 ? 4 was multiplied by 2. 

What was done to both the first and the second 

number? They were both multiplied by 2. 

Repeat the steps for tower 3 to check your rule. Then 

repeat for the fourth tower. Multiply 8 by 2. 16 flags 

will be on the fourth tower. 

Look back at your answer. Does it make sense ? Why ? 


? 



5–3 

Name Date 

Practice by following the steps. 

Fred is putting pictures in a scrapbook. He uses a pattern of 

groups of space and sports pictures. Each group has 1 space 

picture and 3 sports pictures. If the pattern continues, how many 

sports pictures will he use in all if there are a total of 24 pictures? 

Step 1 

Understand 

Step 2 

Plan 

Step 3 

Solve 

Step 4 

Check 

Reteach 

Problem -Solving Strategy (continued) 

You know: There is 1 space picture in each group. There are 3 

sports pictures in each group. 

You need to find out: 

How many will be used? 

Organize the data in a table. What are your columns? The 

groups. There are 4 pictures in each group and 24 pictures in all. 

4 × = 24. You need columns. 

What is in the row under each column? The number of space 

and sports pictures in each group. 

Look for the pattern. Since the same group repeats, 

the number of sports pictures by 6. 

Multiply 3 by 6. 

3MR1.1, 3AF2.2 

Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 

1 space 1 space 1 space 1 space 1 space 1 space 

3 sports 

3 sports 

3 sports 

3 sports 

3 sports 

6 groups of 3 sports pictures equal sports pictures. 

3 sports 



5–3 

Name Date 



Solve. Use the look for a pattern strategy. 

1. A dancer practices 3 days in a row 

and then takes one day off to rest. 

She has a show in two weeks. If 

she practices on the first 3 days, 

and takes the 4th day off, how 

many times will she practice in 

14 days? 

3. The marching band lines up in 

rows. The first row has 2 people. 

The second row has 4 people. 

The third row has 6 people. 

If this pattern continues, how 

many people will be in the fifth 

row? 

Mixed Strategy Review 

5. Ken takes piano lessons. The 1st 

week, he practices 20 minutes 

each day. The 2nd week, he 

practices 40 minutes each day. The 

3rd week, he practices 1 hour each 

day. If this pattern continues, how 

many minutes will he practice each 

day in the 5th week? 

3MR1.1, 3AF2.2 

2. The concert hall offers specials on 

tickets. When you buy 5 tickets, 

you get 1 other ticket free. When 

you buy 10 tickets, you get 2 other 

tickets free. Lyddie got 4 tickets 

free. How many tickets did she 

buy? 

4. The Portsmouth Players perform 

2 daytime shows and 3 evening 

shows per week. Their current 

play will run for 30 shows. How 

many of the shows will be daytime 

shows? 

6. A theater seat in the orchestra costs 

$32. A balcony seat costs $14. How 

much more does an orchestra seat 

cost than a balcony seat? 




5–3 

Solve. 

Name Date 



1. Every home on Main Street has a dog and other pets. 

The first house has 1 dog and 1 cat. The second house 

has 1 dog and 2 cats. The third house has 1 dog and 

3 rabbits. The fourth house has 1 dog and 4 angel fish. If the 

pattern continues, the fifth house has 1 dog and how many 

hamsters? 

2. Ann is a pet babysitter. She gets paid to help the families 

on Main Street with their pets every day. The first week she 

earned $2. The second week she earned $4. The third week 

she earned $6. The fourth, $8. What did she earn by the 

seventh week? 

3. Ann decided to set up a pet parade. She had the pet owners 

walk in rows with their pets. In the first row she put 

1 owner with 1 pet. The second row had 2 owners with 

1 pet each. The third row had 1 pet owner and 2 pets. The 

fourth row had 2 pet owners with 2 pets each. The fifth row 

had 1 pet owner with 3 pets. If the pattern continues, what 

did the sixth row have? 


4. 3 × 6 = 5. 4 × 6 = 

6. 6 × 6 = 7. 7 × 6 = 

3MR1.1, 3AF2.2 



5–3 

Carmen 

Zack 

Jenna 

April 

Carlos 

Name Date 

Enrich 

Favorite Numbers 

36 80 24 30 63 

Read each clue. If the answer is “yes,” draw an “O” in the 

box. If the answer is “no,” draw an “X” in the box. Then fill 

in the correct answers below. 

Carmen’s favorite number is more than 1 × 6 × 8 but less than 8 × 8. 

Zack’s favorite number is the product of each of these multiplication 

facts 8 × 3, 6 × 4, or 2 × 12. 

Carlos’ favorite number would belong in the patterns 5, 10, 15 . . . 

and 6, 12, 18 . . . 

3MR1.1, 3AF2.2 

Jenna’s favorite number is a multiple of 10 that is greater than 5 × 8. 

April’s favorite number is the product of two equal factors that when added 

together equal twelve. 

Carmen’s favorite number is . Zack’s favorite number is . Jenna’s 

favorite number is . April’s favorite number is . Carlos’ favorite 

number is . 

Grade 3 22 Chapter 5


5–4 

Name Date 

Reteach 

Multiply by 7 

You can add on to a known fact to find a new fact. 

Find 7 × 3 by finding (6 × 3) + (1 × 3). 

= + 

3NS2.2 

7 groups of 3 = 6 groups of 3 plus 1 group of 3 

7 × 3 = 6 × 3 + 1 × 3 

= 18 + 3 = 21 


1. 2. 3. 

Find each product . 

4. 3 × 7 = 5. 5 × 7 = 6. 7 × 7 = 

7. 8 × 7 = 8. 7 × 6 = 9. 7 × 9 = 

10. 9 × 7 = 11. 4 × 7 = 12. 7 × 1 = 

13. 6 × 7 = 14. 3 × 7 = 15. 0 × 7 = 

16. 7 × 4 = 17. 1 × 7 = 18. 2 × 7 = 



5–4 

Name Date 


Multiply by 7 

Write multiplication sentences. 

1. How many train cars? 2. How many fingers? 

Multiply. 

3NS2.2 

3. 7 4. 7 5. 7 6. 7 7. 5 8. 2 

____ × 3 ____ × 6 

____ × 9 

____ × 7 

____ × 7 

____ × 7 

9. 7 × 4 = 10. 7 × 5 = 11. 7 × 1 = 

ALGEBRA Complete the table. 

12. 13. 

Rule: Multiply by 7 Rule: 

Solve. 

Input Output 

7 

35 

42 

56 

Input Output 

14. Jason read about trains for 2 hours each day for 1 week. How many hours 

did Jason read? 


3 

7 

Multiply by 7 

35 

63 



5–4 

Multiply. 

Name Date 


Multiply by 7 

1. 7 × 3 = 2. 5 × 7 = 

3. 6 × 7 = 4. 7 × 7 = 

5. 7 × 8 = 6. 9 × 7 = 

7. 4 × 7 = 8. 7 × 6 = 

9. 7 × 10 = 10. 7 × 1 = 

11. 7 × 0 = 12. 7 × 5 = 

13. 7 × 4 = 14. 7 × 9 = 


15. 8 × = 56 16. 7 × = 35 

17. × 7 = 14 18. × 7 = 49 

Solve. Use the look for a pattern strategy. (Lesson 5–3) 

19. Fred buys and sells sports cards. Week 1, he bought 10 cards 

and sold 2. Week 2, he bought 10 more and sold 2, giving 

him 16. Week 3, he bought 10 more and sold 2, giving him 

24. If the pattern continued, how many cards did he have by 

the end of Week 4? 

20. Fred collected football, basketball, and baseball cards. He 

has a total of 50 cards, with an equal number of football 

and basketball cards. He has 20 baseball cards. How many 

football cards does he have? 

3NS2.2 



5–4 

Solve. 

Name Date 


Multiply by 7 

1. The Martins will buy 2 new tires for 

each of their 7 bicycles. How many 

new tires will they buy? 

3. Each house on Alpine Street 

has 7 front windows. There are 

3 houses on each side of the 

street. How many front windows 

are there in all? 

5. Nell bought 3 pairs of white socks 

and 4 pairs of black socks. Each 

pair cost $6. Then she bought a 

$5.75 hat. She got back $12.25 in 

change. How much did Nell give 

to the cashier to pay for the socks 

and hat ? Show your work. 

3NS2.2 

2. It takes Cally 3 minutes to paint 

each slat on a fence. There are 

7 slats in each section of the fence. 

How long will it take Cally to paint 

each section of the fence? 

4. Mario will go on vacation for 

8 weeks this summer. For how 

many days will Mario be on 

vacation? 

6. There are an equal number of 

cars and bicycles in the garage. If 

there are 42 tires in all, how many 

bicycles and cars are in the garage? 

Explain. 




5–4 

Name Date 

Enrich 

Lucky Seven Store 

The Lucky Seven Store sells every item in the store for 7 cents each. 

1. Alvin wants to buy 3 bags of marbles and 2 pencils. How 

much will they cost? Write two number sentences to show 

how much for each. 

cents 

cents 

Write one number sentence to show how much the items 

will cost in all. 

cents 

2. Clare bought 7 buttons, a bottle of glitter, and a stuffed toy. 

How much did they cost? Write three number sentences to 

show how much for each. 

cents 

cents 

cents 


cost in all. 

cents 

3. How many items could be purchased with a one dollar bill? 

items 

4. How many items could be purchased with a five dollar bill? 

items 

3NS2.2 



5–5 

Name Date 

Reteach 

Multiply by 8 

You can use facts that you already know to help you 

multiply by 8. 



6 × 8 = 6 × 4 + 6 × 4 

= 24 + 24 = 48 

Write a multiplication sentence for each picture. 

1. 2. 

Multiply. 

= + 

3. 2 × 8 = 4. 0 × 8 = 5. 8 × 5 = 

6. 8 × 6 = 7. 8 × 1 = 8. 8 × 7 = 

9. 5 × 8 = 10. 8 × 4 = 11. 3 × 8 = 

3NS2.2 




5–5 

Multiply. 

Name Date 


Multiply by 8 

1. 7 × 8 = 2. 5 × 8 = 

3. 8 × 7 = 4. 8 × 8 = 

5. 9 × 8 = 6. 8 × 3 = 

7. 4 × 8 = 8. 6 × 8 = 

9. 8 × 10 = 10. 8 × 1 = 

11. 8 × 0 = 12. 8 × 5 = 

13. 8 × 4 = 14. 8 × 9 = 

15. 2 × 8 = 16. 9 × 8 = 


17. × 8 = 64 18. × 6 = 48 

19. × 5 = 40 20. × 8 = 24 

21. × 8 = 32 22. × 8 = 56 

23. × 8 = 64 24. × 8 = 48 

25. × 8 = 0 26. × 9 = 72 

Solve. 

27. Justin is going to a baseball game with 8 other boys. The 

tickets cost $5. How much will it cost for all 9 boys to watch 

the game? 

28. Mike worked 8 hours washing cars for Mr. Smith. Mr. Smith 

paid him $4 an hour. How much did Mike earn? 

3NS2.2 



5–5 

Multiply. 

Name Date 


Multiply by 8 

1. 8 × 3 = 2. 5 × 8 = 

3. 6 × 8 = 4. 7 × 8 = 

5. 8 × 8 = 6. 9 × 8 = 

7. 4 × 8 = 8. 8 × 6 = 

9. 8 × 10 = 10. 8 × 1 = 

11. 8 × 0 = 12. 8 × 5 = 

13. 8 × 4 = 14. 8 × 9 = 


15. 8 × = 64 16. 7 × = 56 

17. × 8 = 24 18. × 8 = 64 


19. 7 × 5 = 20. 4 × 7 = 

21. 10 × 7 = 22. 7 × 7 = 

23. 7 × 8 = 24. 9 × 7 = 

25. 2 × 7 = 26. 7 × 6 = 

Solve. (Lesson 5–3) 

3NS2.2 

27. Fred has collected a total of 80 cards. A display of Fred’s cards includes 

2 rows of football cards with 15 in each row. In front of the football cards 

are 3 rows of baseball cards with 10 in each row. In front of the baseball 

cards are 4 rows of basketball cards. If the pattern continues, how many 

basketball cards are in each of the 4 rows? 




5–5 

Solve. 

Name Date 


Multiply by 8 

1. Find the total number of dolphins if there are 8 groups of 

dolphins with 5 dolphins in each group. 

2. A dolphin has 4 fins. How many total fins do 8 dolphins 

have? 

3. Eight dolphins are swimming around a tour boat. Each 

dolphin swims around the boat 8 times. How many times did 

all the dolphins swim around the boat? 

4. The 8 tourists on the boat were able to touch 4 dolphins 

each. What was the total number of times a dolphin got 

touched? 

5. Using their tail fins, 7 dolphins jumped in the air 8 times. 

What was the total number of jumps the dolphins made? 

6. Eight tourists each took 3 photos of the dolphins. How many 

dolphin photos were taken in all? 

3NS2.2 



5–5 

Name Date 

Enrich 

Roll of the Number Cube Times 8 

Four friends are playing a game. Each gets to roll a pair of 

number cubes. After each roll, they multiply the number on the 

cubes by 8. They are trying to get to 80 without going over. Each 

person gets two chances to roll. Look at what each person got on 

two rolls. 

1. Carlos 

2. Melanie 

3. Eric 

4. Marie 

5. How much did each person get? (Hint: Find the value of each 

roll for each person. Add the total that each person got.) 

Carlos Eric 

Melanie Marie 

6. Who won? 

7. What is a faster way to find out who won without finding 

each value, adding each person’s rolls, and comparing them? 

3NS2.2 




5–6 

Name Date 

Reteach 

Multiply by 9 

Here is a strategy you can use when multiplying by 9. 

You can multiply the number by 10 and then subtract the 

number to find a new fact. 

Find 9 × 7. 

3NS2.2 

9 groups of 7 = 10 groups of 7 minus 1 groups of 7 

9 × 7 = 10 × 7 - 1 × 7 

Multiply. 

= - 

= 70 - 7 = 63 

1. 9 2. 9 3. 3 4. 9 5. 9 6. 6 

____ × 4 ____ × 5 

____ × 9 

____ × 7 

____ × 8 

____ × 9 

7. 9 × 2 = 8. 5 × 9 = 9. 9 × 4 = 

10. 6 × 9 = 11. 9 × 3 = 12. 9 × 1 = 

13. 9 × 9 = 14. 9 × 0 = 15. 9 × 8 = 

16. 2 × 9 = 17. 8 × 9 = 18. 3 × 9 = 



5–6 

Multiply. 

Name Date 


Multiply by 9 

3NS2.2 

1. 9 2. 9 3. 4 4. 9 5. 9 6. 9 

____ × 3 ____ × 8 

____ × 9 

____ × 1 

____ × 7 

____ × 5 

7. 9 8. 5 9. 9 10. 9 11. 9 12. 8 

____ × 2 ____ × 9 

____ × 0 

____ × 9 

____ × 6 

____ × 9 

13. 2 × 9 = 14. 4 × 9 = 15. 9 × 6 = 

16. 8 × 9 = 17. 9 × 1 = 18. 7 × 9 = 

19. 3 × 9 = 20. 9 × 9 = 21. 9 × 0 = 

22. 9 × 1 = 23. 7 × 9 = 24. 5 × 9 = 

25. 2 × 9 = 26. 0 × 9 = 27. 9 × 4 = 

28. 8 × 6 = 29. 3 × 8 = 30. 6 × 7 = 

31. 6 × 5 = 32. 7 × 3 = 33. 5 × 7 = 

34. 9 × 3 = 35. 8 × 7 = 36. 9 × 6 = 

Solve. 

37. Jordan saw 9 airplanes fly over 

his house every day last week. 

How many airplanes did Jordan 

see last week? 

38. The Sports Cap Company sent 

3 caps to each of the 9 starters on 

a baseball team. How many caps 

did the company send? 




5–6 

Multiply. 

Name Date 


Multiply by 9 

1. 9 × 3 = 2. 5 × 9 = 

3. 6 × 9 = 4. 7 × 9 = 

5. 9 × 8 = 6. 9 × 9 = 

7. 4 × 9 = 8. 9 × 6 = 

9. 9 × 10 = 10. 9 × 1 = 

11. 9 × 0 = 12. 9 × 5 = 

13. 9 × 4 = 14. 8 × 9 = 


15. 9 × = 72 16. 9 × = 36 

17. × 9 = 45 18. × 6 = 54 


19. 8 × 5 = 20. 8 × 7 = 

21. 10 × 8 = 22. 7 × 8 = 

23. 7 × 8 = 24. 9 × 8 = 

25. 2 × 8 = 26. 8 × 6 = 

27. 8 × 10 = 28. 8 × 1 = 


29. 

Factor 4 9 9 9 

Factor 9 

Product 45 63 81 

3NS2.2 



5–6 

Solve 

Name Date 


Multiply by 9 

1. Jose spends $9 on lunch each 

day. How much does he spend for 

lunch in 2 days? 

3. On Mr. Dugan’s farm, 9 cows can 

be milked in an hour. Mr. Dugan 

says that 45 cows will be milked in 

5 hours. Is he correct? Explain. 

5. For the school talent contest, 

9 singers will perform for 

3 minutes each. Then 5 dancers 

will perform for 4 minutes each. 

How many minutes will it take for 

the singers and dancers to perform 

in all? 

3NS2.2 

2. Carmen’s parrot eats 9 crackers a 

day. How many crackers will it eat 

in 4 days? 

4. The So Rich cookie factory can 

bake 9 chocolate chip cookies 

a minute. Can the factory fill an 

order for 80 cookies in 9 minutes? 

Explain. 

6. Ty works 9 hours a day and earns 

$6 an hour. Cal works 6 hours a 

day and earns $9 an hour. If they 

both work 5 days per week, who 

earns more money? 

Who works longer? Explain. 



5–6 

Name Date 

Enrich 

Find the Products for the Nines 

Write the products for the 9s. Find each product in the picture. 

Use a blue crayon or colored pencil to shade or color all the 

numbers that make up the products of the fact families for the 

9s. Shade all other numbers with the colors of your choice. 

9 × 1 = 9 × 6 = 9 × 2 = 

9 × 7 = 9 × 3 = 9 × 8 = 

9 × 4 = 9 × 9 = 9 × 5 = 

9 × 10 = 

5 

17 

13 

71 

27 

37 

10 

36 

64 55 

18 

72 

90 

What do you notice about the products of the numbers 1 – 10 

multiplied by 9? (Hint: look for a pattern.) 

54 

38 

91 

81 

9 

If you add the digits of each product you found, what is the sum of each? For 

example, what is the sum of the digits in 18? 

45 

63 


34 

73 

21 

29 

19 

8 

47 

3NS2.2 


5–7 

Name Date 

Reteach 

Choose a Strategy 

Problem–Solving Investigation 

Juan has pieces of wood. The first piece of wood is 8 inches. The 

second piece of wood is 16 inches. The third piece of wood is 

24 inches. If this pattern continues, what will be the length of 

the twelfth piece of wood? 

Step 1 

Understand 

Step 2 

Plan 

• Logical Reasoning 

• Draw a Picture or 

Diagram 

• Make a Graph 

• Act It Out 

• Make a Table or 

List 

• Find a Pattern 

• Guess and Check 

• Write an Equation 

• Work Backward 

• Solve a Simpler 

Problem 

Be sure you understand the problem. 

What facts do you know? 

3MR1.1 

• The first piece of wood is inches. 

• The second piece of wood is inches. 

• The third piece of wood is inches. 

What do you need to find? 

• You need to find the length of 

Make a plan. 

Choose a strategy. 

You can find the pattern. 

You can also draw a picture. Show 12 pieces of wood. 

Use the pattern, and write the length of each piece 

next to the piece of wood. 


. 



5–7 

Name Date 

Reteach 

Step 3 

Solve Plan 1 

Step 4 

Check 

Solve. 

Problem–Solving Investigation (continued) 

Plan 2 

Carry out your plan. 

Find the pattern. 

8 16 24 The pattern is add 8. 

+8 +8 

3MR1.1 

Draw a picture of 12 pieces of wood. Write the length 

next to each piece. 

1 

7 

8 

56 

2 

8 

16 

64 


3 

9 

24 

72 

4 

10 

32 

80 

5 

11 

40 

88 

The twelfth piece of wood is inches. 

Is the solution reasonable? 

Reread the problem. 

1. Jim has 5 packs of cards. There are 

15 cards in each pack. He gives 3 

of his packs away. How many cards 

does he have left ? 

How can you check your answer ? 

6 

12 

48 

96 

2. Winnie is making a quilt. The first 

section has 2 pieces of fabric. 

The second section has 5 pieces 

of fabric. The third section has 

8 pieces of fabric. If this pattern 

continues, how many pieces of 

fabric will be in the eighth section 

of the quilt ? 


5–7 

Name Date 


Problem-Solving Investigation 

Choose a strategy to solve the problem. 

1. On Park Day, volunteers plant trees 

in the park. The first tree is 2 feet 

tall. The second tree is 4 feet tall. 

The third tree is 6 feet tall. Suppose 

this pattern continues. What will be 

the height of the fifth tree? 

3. Jenny takes a photo of the town 

square. She makes a square frame 

for the photo. Each of the 4 sides 

of the frame is 9 inches long. How 

many inches around is the frame? 


5. This year, a town sells tickets 

to the picnic to 252 adults and 

518 children. Last year, there were 

695 people at the picnic. How 

many more people are there this 

year than last year ? 

7. Write a problem that you could 

solve by drawing a picture or by 

finding a pattern. Share it with 

others. 

3MR1.1 

2. There are 8 rows of trees in the 

park. Each row has 8 trees. How 

many trees are there in all? 

4. Some volunteers are building 

picnic tables. Each table uses 

5 pieces of wood for the top, 

2 pieces of wood for the sides, 

and 6 pieces of wood for the rest 

of the table. How many pieces of 

wood are needed to make 

4 picnic tables? 

6. There are three groups of students 

making murals for the train station. 

Each group has 6 students. How 

many students are there in all? 




5–7 

Name Date 



Solve. Use any strategy. 

1. Bob rode 2 miles on his bike for 9 days. What is the total 

number of miles he rode? 

2. Two toads are near the path. Together, they have 6 dark 

spots on them. The larger one has 2 times as many spots as 

the smaller one. How many spots does each one have? 

3. Mandy has $5. Becky has $5 more than Mandy. Sue has 

2 times as much as Becky. How much money do the girls 

have together? 

4. 36 students were standing in the lunch line. The principal 

gave the first girl a star. Then, he gave every sixth person in 

back of the girl a star. How many people got stars? 


5. 9 × 6 = 6. 9 × 10 = 

7. 9 × 1 = 8. 9 × 0 = 

9. 9 × 7 = 10. 9 × 4 = 

11. 8 × 9 = 12. 9 × 9 = 

3MR1.1 



5–7 

Name Date 

Enrich 

Unlock the Pyramids 

Find the missing numbers in the patterns. Then multiply 

them together to unlock the top number of the pyramid. 

Under each pyramid, write multiplication sentence to show 

how you unlocked the pyramid. 

1. 

8 10 

4 6 

3. 4. 

5. Create your own pyramid for a friend to unlock. 


2. 

3MR1.1 



5–8 

Name Date 

Reteach 

Algebra: Associative Property 

3AF1.5 

You can use the properties of multiplication to multiply 3 numbers. 

Find 3 × 2 × 5. 

The Commutative Property of 


When multiplying, the order of the 


3 × 2 × 5 = 30 

2 × 5 × 3 = 30 

5 × 2 × 3 = 30 


You can use the 

Commutative 

Property to 

switch the order 

of the numbers 

3, 2, and 5. 

The Associative Property of 


When multiplying, the grouping of the 


3 × 2 × 5 = 30 

3 × (2 × 5) = 30 

(3 × 2) × 5 = 30 

You can use 

the Associative 

Property to 

group two 

factors. 

1. 5 × 3 × 2 = 2. 2 × 2 × 6 = 3. 7 × 4 × 1 = 

4. 3 × 2 × 3 = 5. 5 × 4 × 2 = 6. 7 × 8 × 0 = 

7. 2 × 7 × 2 = 8. 3 × 6 × 2 = 9. 8 × 7 × 1 = 

10. 3 × 4 × 2 = 11. 6 × 3 × 3 = 12. 6 × 2 × 3 = 

13. 8 × 9 × 0 = 14. 6 × 5 × 0 = 15. 9 × 1 × 5 = 

Find each missing number. 

16. 5 × 2 × = 80 17. × 2 × 6 = 24 

18. 1 × 7 × 3 = 19. × 2 × 5 = 20 



5–8 

Find each product. 

Name Date 



1. 2 × 2 × 6 = 2. 1 × 8 × 4 = 

3. 9 × 3 × 2 = 4. 3 × 3 × 1 = 

5. 5 × 2 × 4 = 6. 9 × 1 × 0 = 

7. 6 × 3 × 1 = 8. 8 × 3 × 2 = 

9. 4 × × 4 = 32 10. 5 × × 1 = 45 

11. × 6 × 2 = 12 12. × 6 × 1 = 12 

13. 3 × × 4 = 24 14. 6 × 9 × = 0 

15. 1 × × 3 = 15 16. 5 × × 3 = 60 

Solve. 

17. Tony and his friends had a pizza party. They bought 2 pizzas, 

each cut into 8 slices. Tony put 3 slices of banana pepper on 

each piece. How many slices of banana peppers did he use? 

18. Tony also bought 3 packs of soda in cans. Each pack held 

6 cans. How many cans of soda did Tony buy? 

19. Which of the following does not belong with the other three? 

(1 × 3) × 2 = 1 × (3 × 2) (6 × 3) × 2 = 6 × (3 × 2) 

2 × (6 × 1) = (2 × 6) × 1 5 × (3 × 1) = (5 × 5) × 2 

3AF1.5 




5–8 


Name Date 



1. 1 × 2 × 3 = 2. 5 × 2 × 4 = 

3. 8 × 2 × 2 = 4. 3 × 5 × 1 = 

5. 7 × 2 × 1 = 6. 8 × 8 × 0 = 

7. 3 × 3 × 7 = 8. 4 × 3 × 2 = 


9. 2 × × 2 = 4 10. 3 × × 1 = 12 

11. × 4 × 2 = 56 12. × 2 × 3 = 30 


13. Angie collects pairs of earrings. She hangs them on an earring 

tree. On the first row she hung 9 pairs, on the second row 

she hung 7 pairs, and on the third row she hung 5 pairs. 

If she continued this pattern, how many pairs would Angie 

hang on the fourth row? How many pairs of earrings does 

she have in all four rows? 

14. Fred made a display with a deck of playing cards. In the first 

row he used 6 cards. In the second row he used 12 cards. In 

the third row he used 18. In the fourth row, 24. If the pattern 

keeps up, how many cards will be in the sixth row? 

3AF1.5 



5–8 

Solve. 

Name Date 



1. Mallory and her 4 friends are setting up a lemonade stand. 

They each brought 2 bags of lemons. Each bag has 4 lemons. 

How many lemons do the girls have altogether? 

2. Mallory set up 2 tables with 3 containers of lemonade 

on each. Each container has 8 ice cubes. Write a number 

sentence to find the number of ice cubes she used. 

3. Two of Mallory’s friends were each serving three customers at 

each table. Write a number sentence to show the number of 

customers the girls were serving. 

4. Every hour, 5 people stopped for lemonade and spent $2 

each. After 4 hours, how much had the girls earned? 

5. At the end of the day, Mallory’s 4 friends each had two 

$5-bills. How much did Mallory’s friends earn altogether? 

3AF1.5 




5–8 

Name Date 

Enrich 


Help the leprechaun find his pot of gold. Start at the leprechaun. 

Find his path by multiplying numbers as you go. When all the 

numbers are in the correct path, the product is 45. Shade the 

path the leprechaun should follow. 

5 

5 

4 

2 

1 

3 

1 

45 


3 

5 

6 

2 

3AF1.5 


5–9 

Name Date 

Reteach 

Algebra: Find a Rule 

A rule tells you what to do. This works in math too. 

To build a boxcar, Bob needs to put 4 wheels on the corners 

of a wooden box. If he wanted to build 4 boxcars, how many 

wheels would he need? 

Step 1 Find a pattern. 

You know that 1 boxcar = 4 wheels. 

So, 2 boxcars = 8 wheels. 

The pattern or rule is to multiply by 4. 

Step 2 Extend the pattern. 

3 boxcars = 3 × 4 or 12 wheels. 

3 × 4 = 12 

4 boxcars = 4 × 4 = 16 wheels 

So, Bob needs 16 wheels. 

Practice. 

1. For every 2 wheels that Bob bought, the man in the store 

gave him 2 free wheels. When Bob bought 16 wheels, how 

many did he get free? 

2. Write the rule for each table. Then, complete the table. 

Input 

3 

9 

Rule: 

Output 

6 

10 

7 14 

18 

Input 

4 

5 

7 

Rule: 

Output 

12 

15 

24 


Input 

5 

5 

7 

Rule: 

Output 

25 

30 

35 

3AF2.2 


5–9 

Name Date 



Write the rule for each table. Then complete the table. 

1. 2. 3. 

4. 5. 6. 

7. 8. 9. 

Find a rule. Then extend the rule to solve. 

10. On Monday, there were 5 flowers blooming in the garden. 

On Tuesday, there were 10 flowers blooming. There were 15 

by Wednesday. By Friday, how many flowers were blooming? 

3AF2.2 



5–9 

Name Date 




1. 2. 3. 

Rule: 

Rule: 

Input 

3 

6 

9 

Output 

15 

20 

30 

45 

Input 

4. 5. 

Rule: 

Input 

2 

5 

8 

Output 

21 

35 

56 


4 

7 

Output 

3AF2.2 


24 

30 

48 

Input 

4 

9 

10 

Rule: 

6. 8 × 2 × 0 = 7. 3 × 4 × 1 = 

Output 

54 

81 

Input 

8. 2 × 5 × 2 = 9. 2 × × 2 = 16 

10. Sal wants to make oatmeal for himself and his brother. The 

directions say to add 2 cups of boiling water to the oatmeal 

for 1 serving. Both Sal and his brother want double servings. 

How many cups of boiling water will Sal need to measure? 

3 

5 

7 

Rule: 

Output 

24 

32 

56 



5–9 

Name Date 




1. There are 24 crayons in 3 boxes. There are 32 crayons in 

4 boxes. How many crayons are in 5 boxes? 

2. There are 10 strawberries in 2 boxes and 15 strawberries in 

3 boxes. How many strawberries are in 4 boxes? 

3. A farmer grows carrots. Each row has 5 carrots. How many 

carrots are there in a garden with 7 rows? a garden with 

8 rows? a garden with 9 rows? 

4. After 6 weeks, Russ saved $60. By the end of the next week, 

he had $70. How much did he save by the third week? 

5. The amusement park sold ride tickets in packs of 5, 10, 15, 

20 tickets. What would a pack of 10 tickets cost if 20 tickets 

cost $8? 

6. A recipe calls for 2 onions for one batch. Two batches need 

4 onions. How many onions are needed for four batches? 

3AF2.2 



5–9 

Name Date 

Enrich 

What’s My Rule? 

Find and extend the rule for each table. Then write a multiplication 

sentence that tells what completes each table. 


Input 0 1 2 3 

Output 0 2 4 6 

2. Rule Multiply by 

Input 1 2 3 4 

Output 8 16 24 32 


Input 1 2 3 4 

Output 7 14 21 28 


Input 0 1 2 3 



Input 4 5 6 7 

Output 36 45 54 63 

3AF2.2 




5 

Name Date 

B D M Goal Progress 

Notes 

Individual Progress Checklist 

explore using the multiplication table to multiply 

multiply by 3 

multiply by 6 

multiply by 7 

multiply by 8 

multiply by 9 

use the Associative Property of Multiplication 

use the Commutative Property of Multiplication 

find a rule and extend a pattern 

use the Look for a Pattern strategy to solve 

multiplication problems 


Assessment

5 

Name Date 

Diagnostic Assessment 

Draw an array for each fact. Write the product. 

1. 3 × 4 2. 1 × 5 

3. 8 × 2 4. 4 × 5 

Write a number sentence for each picture. 

5. 

6. 

7. 

Solve. 

8. Yolanda wants to buy 2 pencils at 25¢ each. She has 1 quarter 

and 1 dime. Does she have enough to buy 2 pencils? 

9. Last evening Mrs. Rogers put 10 corn muffins on the kitchen 

counter to cool. This morning, there were only 6 corn muffins 

left. How many were taken? 

Identify and extend the pattern. 

10. 10, 15, 20, 25, 30, , 

11. 3, 6, 9, 12, 15, , 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 



5 

Multiply. 

Name Date 

Chapter Pretest 

1. 2 × 3 = 2. 5 × 6 = 

3. 7 × 4 = 4. 4 × 8 = 

5. 9 × 6 = 6. 8 × 3 = 

7. (3 × 4) × 3 = 8. 6 × (2 × 5) = 

Solve using the Commutative or Associative Property 

of Multiplication. 

9. Three students are carrying backpacks. Each backpack holds 

one pencil case. Each pencil case can hold 10 pencils. How 

many pencils are the students carrying? 

10. Carla’s mother bought 6 cases of milk. Each case holds 

8 cartons of milk. How many cartons of milk did Carla’s 

mother buy? 

11. Mitchell has a lot of toy cars to put away. He has 3 empty 

shelves in his room. Each shelf holds 7 toy cars. How many 

cars can he put away? 

12. Maria earns $2 each time she takes out the recycling to the 

curb for pickup. There are 3 kinds of recycling: paper, plastic 

and glass. If each kind of recycling is picked up once a week, 

how much money will Maria earn at the end of 4 weeks? 

Find the rule. Extend the pattern to answer the question. 

13. Kim notices that her tomato plant is growing every day. The 

plant started at 6 inches and grew to 8 inches on the second 

day. On the third day, the plant was 10 inches. How tall will 

the plant be on the fourth day? 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

Assessment

5 

Multiply. 

1. 3 × 6 

2. 7 × 3 

3. 6 × 8 

4. 9 × 6 

5. 4 × 3 

Name Date 

6. Complete the table. 

Solve. 

Quiz 1 (Lessons 5–1 through 5–3) 


Input 

3 

6 

Output 

7. John has 3 packs of gum. Each pack has 6 pieces of gum. 

How many pieces of gum does John have altogether? 

8. Anwar is collecting seashells at the beach. If the pattern 

continues, how many seashells will he collect on day 4? 

Day 5? 

Day 1 2 3 4 5 

Shells 6 12 18 ? ? 

30 

0 


1. 

2. 

3. 

4. 

5. 

7. 

8. 



5 

Multiply. 

1. 7 × 4 

2. 5 × 7 

3. 6 × 8 

4. 7 × 7 

5. 9 × 8 

6. 6 × 7 

7. 8 × 8 

8. 9 × 2 

Solve. 

Name Date 


9. Nine of Tammy’s friends each gave her 3 flowers. How many 

flowers was Tammy given? 

10. Later, Tammy gave away one flower each to 9 other friends. 

How many flowers did she give away? 

11. Tammy put 6 flowers in each of 3 vases. How many flowers 

did Tammy put in vases? 

12. Tammy added 3 more flowers to each of the vases. How 

many total flowers did Tammy add to the vases? 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

Assessment

5 


1. 5 × 2 × 2 

2. 1 × 3 × 9 

3. 4 × 2 × 7 

4. 6 × 2 × 1 

Name Date 



5. 3 × 3 × = 45 

6. × 1 × 7 = 56 

7. 4 × 5 × 2 = 

8. 3 × × 7 = 42 

Solve. 

9. James puts 4 books on the first shelf. He put 8 books on the 

second shelf and 12 books on the third shelf. If the pattern 

continues, how many books will be on the fourth and fifth 

shelves? 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 



5 

Name Date 

Mid-Chapter Review 

1. What is the missing number in the problem below? 

6 × = 24 

A. 5 B. 4 C. 3 D. 2 

2. 7 boys bought 5 apples each. How many apples do the boys 

have altogether? 

F. 35 G. 40 H. 45 J. 46 

3. A class is building a tall ship. They need 2 pieces of paper for 

the first sail, 3 pieces for the second, and 4 for the third. How 

many pieces of paper will they need for the fifth sail? 

A. 2 B. 4 C. 5 D. 6 

4. How many sticks are shown by an array of 2 rows with 

7 sticks in each row? 

F. 20 G. 14 H. 7 J. 2 

5. What will you count by if you are using repeated addition to 

count the pencils in 8 packs with 5 pencils each? 

A. by eights B. by twos 

C. by fives D. by threes 

6. To solve a problem using a pattern, how can you organize 

the data? 

7. If you want to solve the problem 6 × 7, how can you double 

a known fact to find the answer? 

8. Write a real-world problem that can be solved by multiplying 

by 3. 

9. How can you use a known fact to find the 

answer for 5 × 3? 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

Assessment

5 

Name Date 

Vocabulary Test 

Match each word to its definition. Write your answers on 

the lines provided. 

1. Associative property of 


2. Commutative Property of 


A. a number that divides into a whole 

number evenly. It is also known 

as a number that is multiplied by 

another number. 

B. If you multiply a number by 1, the 

product is the same as the given 

number. 

3. factor C. a sequence of numbers, figures, 

or symbols that follows a rule or 

design 

4. Identity Property of 


D. the answer to a multiplication 

problem; It also refers to expressing 

a number as product of its factors. 

5. pattern E. the property that states that the 

grouping of the factors does not 

change the product 

6. product F. the property that states that the 

order in which two numbers are 

multiplied does not change the 

product 




5 

Name Date 

Oral Assessment 

Put 3 paperclips, 4 erasers, and 2 pencils on the table. 

Read each question aloud to the student. Then write the student’s answers on 

the lines below the question. 

1. If you multiply the amount of paperclips by the amount of erasers what do 

you get? 

2. Multiply that product by the amount of pencils. What is the product? 

3. If you change the order and first multiply the number of pencils by the 

number of erasers, and then that product by the number of paperclips, 

would the final product be the same? 

4. Tell how you got your answer. 

5. There were 2 car races on Saturday and 4 on Sunday. If there were 8 cars 

racing in each race, how many cars raced over 2 days? 


Assessment

5 

Name Date 

Oral Assessment (continued) 

6. If there were 10 cars racing in each race, how many cars would have raced 

over 2 days? 


8. If there was one additional race on Friday, where 10 cars raced, how many 

cars would have raced over the 3 days? 





5 

Name Date 

Chapter Project Rubric 

Score Explanation 

3 Student successfully completed the 

chapter project. 

Student demonstrated appropriate use 

of chapter information in completing the 


2 Student completed the chapter project 

with partial success. 

Student partially demonstrated appropriate 

use of chapter information in completing 

the chapter project. 

1 Student did not complete the chapter 

project or completed it with little success. 

Student demonstrated very little 

appropriate use of chapter information in 

completing the chapter project. 

0 Student did not complete the chapter 

project. 

Student demonstrated inappropriate use 

of chapter information in completing the 



Assessment

5 

Addition 

Name Date 

Chapter Foldables Rubric 

Four-Door Book Foldables 

Score Explanation 

3 Student properly assembled Foldables graphic organizer 

according to instructions. 

Student recorded information related to the chapter in the 

manner directed by the Foldables graphic organizer. 

Student used the Foldables graphic organizer as a study guide 

and organizational tool. 

2 Student exhibited partial understanding of proper Foldables 

graphic organizer assembly. 

Student recorded most but not all information related to 

the chapter in the manner directed by the Foldables graphic 

organizer. 

Student demonstrated partial use of the Foldables graphic 

organizer as a study guide and organizational tool. 

1 Student showed little understanding of proper Foldables graphic 

organizer assembly. 

Student recorded only some information related to the chapter in 

the manner directed by the Foldables graphic organizer. 

Student demonstrated little use of the Foldables graphic 

organizer as a study guide and organizational tool. 

0 Student did not assemble Foldables graphic organizer according 

to instructions. 

Student recorded little or no information related to the chapter in 

the manner directed by the Foldables graphic organizer. 

Student did not use the Foldables graphic organizer as a study 

guide and organizational tool. 




5 

Name Date 

Read each question carefully. Write your answer on the line 

provided. 

Multiply. 

1. 6 × 4 

A. 10 B. 18 C. 24 D. 30 

2. 9 × 9 

F. 64 G. 72 H. 81 J. 82 

3. 5 × 8 

A. 13 B. 20 C. 40 D. 80 

4. Lindsey plans to bake 3 batches of raisin muffins. Each batch 

will make 9 muffins. How many raisins will she need to make 

sure that each muffin has 3 raisins? 

F. 100 G. 81 H. 27 J. 18 

5. Tara bought tickets for two rides on the merry-go-round for 

herself and her two sisters. A ticket for one ride costs $1. If 

she paid for the tickets with a $10-bill, how much change 

should she get? 

A. $2.00 B. $4.00 C. $6.00 D. $8.00 

6. An airplane has 8 rows of 4 seats each. If passengers are 

allowed to bring on no more than 2 bags, what is the 

greatest number of bags allowed on the plane? 

F. 24 bags G. 32 bags H. 64 bags J. 78 bags 

Find the missing number. 

7. 2 × 3 × 7 = 

Chapter Test, Form 1 

A. 14 B. 21 C. 38 D. 42 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

Assessment

5 

8. 5 × 8 × 10 = 

Name Date 

F. 400 G. 360 H. 200 J. 130 

9. (2 × ) × 7 = 56 

A. 14 B. 8 C. 7 D. 4 

10. × (2 × 3) = 36 

F. 6 G. 7 H. 8 J. 9 

11. ( 7 × )× 6 = 42 

Solve. 

Chapter Test, Form 1 (continued) 

A. 1 B. 7 C. 13 D. 21 

12. Kyle plans to eat 4 slices of pizza. Each slice has 7 pieces of 

pepperoni on it. How many pieces of pepperoni will Kyle eat? 

F. 11 pieces G. 14 pieces H. 28 pieces J. 35 pieces 

13. Charles earns $5 an hour. He works 2 hours each day for 

5 days. How much money does he earn? 

A. $10 B. $25 C. $30 D. $50 

14. At a movie theater, the cost of an adult ticket is $6. The cost 

of a child ticket is $2. Mrs. Lopez buys 2 adult tickets and 

1 child ticket. How much does she spend? 

F. $14 G. $12 H. $10 J. $8 


8. 

9. 

10. 

11. 

12. 

13. 

14.


5 

Name Date 


provided. 

Multiply. 

1. 8 × 3 

A. 5 B. 11 C. 16 D. 24 

2. 6 × 9 

F. 15 G. 24 H. 35 J. 54 

3. 7 × 5 

A. 12 B. 21 C. 35 D. 40 

4. Bonita plans to bake 2 batches of chocolate chip cookies. 

Each batch will make 10 cookies. How many chocolate chips 

will she need to make sure that each cookie has 4 chips? 

F. 8 G. 20 H. 40 J. 80 

5. Joyce bought tickets for three rides on the ferris wheel for 

herself and her brother. A ticket for 1 ride costs $1. She paid 

for the tickets with a $10-bill. How much change did she get? 

A. $8 B. $6 C. $4 D. $3 

6. A train has 9 rows of 5 seats each. If passengers are allowed 

to bring on no more than 2 bags, what is the greatest 

number of bags allowed on the train? 

F. 45 bags H. 90 bags 

G. 64 bags J. 100 bags 


7. 3 × 2 × 5 = 

Chapter Test, Form 2A 

A. 5 B. 10 C. 15 D. 30 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

Assessment

5 

8. 4 × 1 × 5 = 

Name Date 

F. 30 G. 20 H. 10 J. 9 

9. (3 × ) × 6 = 36 

Solve. 

Chapter Test, Form 2A (continued) 

A. 1 B. 2 C. 6 D. 7 

10. Dara plans to eat 3 slices of pizza. Each slice has 5 olives on 

it. How many olives will Dara eat? 

F. 3 G. 8 H. 11 J. 15 

11. Rosie earns $4 an hour. She works 2 hours each day for 

5 days. How much money does she earn? 

A. $80 B. $60 C. $40 D. $20 

12. At the concert hall, the cost of an adult ticket is $8. The cost 

of a child ticket is $3. Mr. Ambler buys 2 adult tickets and 

2 child tickets. How much does he spend? 

F. $22 G. $19 H. $14 J. $11 


8. 

9. 

10. 

11. 

12. 



5 

Name Date 


provided. 

Multiply. 

1. 4 × 3 

A. 7 B. 12 C. 13 

2. 8 × 4 

F. 32 G. 22 H. 12 

3. 6 × 9 

A. 15 B. 48 C. 54 

4. 7 × 5 

F. 25 G. 35 H. 45 

5. Jorge bought tickets for 4 rides on the roller coaster for 

himself and his brother. A ticket for 1 ride costs $1. If he paid 

for the tickets with a $10-bill, how much change should he 

get? 

A. $1 B. $2 C. $3 

6. An airplane has 7 rows with 3 seats in each row. If 

passengers are allowed to bring on no more than 2 bags, 

what is the greatest number of bags allowed on the plane? 

F. 12 G. 21 H. 42 


7. 4 × 2 × 6 = 

Chapter Test, Form 2B 

A. 14 B. 28 C. 48 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

Assessment

5 

8. 2 × 5 × 7 = 

Name Date 

F. 70 G. 57 H. 17 

9. (4 × ) × 3 = 24 

Solve. 

A. 1 B. 2 C. 3 

10. × (2 × 2) = 20 

F. 2 G. 4 H. 5 

11. (5 × ) × 9 = 45 

Chapter Test, Form 2B (continued) 

A. 1 B. 2 C. 3 

12. Alejandro earns $6 an hour. He works 2 hours a day for 

4 days. How much money does he earn? 

F. $18 G. $24 H. $48 

13. At the carnival, the cost of an adult ticket is $5. The cost of a 

child ticket is $3. Mr. Chung buys 2 adult tickets and 3 child 

tickets. How much does he spend? 

A. $19 B. $10 C. $9 

14. Kelly earns $5 an hour babysitting. She babysits 9 hours a 

week. How much money will she earn in a week? 

F. $45 G. $50 H. $54 


8. 

9. 

10. 

11. 

12. 

13. 

14. 



5 

Name Date 

Read each question carefully. Write your answer 

on the line provided. 

Multiply. 

1. 4 × 7 

2. 9 × 3 

3. 8 × 6 

4. 7 × 7 

5. 3 × 8 

Write a number sentence for each situation. Then 

solve. 

6. Christy plans to bake 5 batches of blueberry 

muffins. Each batch will make 8 muffins. How 

many blueberries will she need to make sure that 

each muffin has 10 blueberries? 

7. Grace bought tickets for 2 rides on the Tilt-a-Whirl 

for herself and her three sisters. A tickets for one 

ride costs $1. If she paid for the tickets with a 

$10-bill, how much change should she get? 

8. A plane has 7 rows of 3 seats each. If passengers 

are allowed to bring on no more than 2 bags, 

what is the greatest number of bags allowed on 

the plane? 

Compare. Use >,

5 

Name Date 


11. × (2 × 4) = 72 

12. (8 × ) × 2 = 16 

13. 9 × 2 × 4 = 

14. 6 × 5 × 2 = 

15. (2 × 3) × = 54 

Solve. 

Chapter Test, Form 2C (continued) 

16. Sean plans to eat 5 slices of pizza. Each slice has 

7 pieces of mushroom on it. How many pieces of 

mushroom will Sean eat? 

17. Pete earns $4 an hour. He works 2 hours each day 

for 6 days. How much money does he earn? 

18. At the concert hall, the cost of an adult ticket is $8. 

The cost of a child ticket is $3. Mr. Jackson buys 

3 adult tickets and 2 child tickets. How much does 

he spend? 

19. Eva drove 6 miles to the store and then 11 miles 

to see a friend. Later, she returned the same way. 

How many miles did she drive? 

20. The drama club went on a trip to see a play. The 

group traveled in 2 cars of 4 people each, and 

3 vans of 6 people each. How many people went 

on the trip? 


11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 



5 

Name Date 

Read each question carefully. Write you answer 


Multiply. 

1. 6 × 6 

2. 9 × 7 

3. 8 × 3 

4. 5 × 9 

5. 4 × 8 

6. Marcia will bake 1 batch of oatmeal raisin muffins. 

Each batch will make 10 muffins. How many 

raisins will she need so that each muffin has 8 

raisins? 

7. Pedro bought tickets for 2 rides on the roller 

coaster for himself and his two brothers. A ticket 

for one ride costs $1. If he paid with a $10-bill, 

how much change did he get? 

8. A bus has 10 rows of 2 seats each. If passengers 

are not allowed to bring on more than 2 bags, 

what is the greatest number of bags allowed on 

the bus? 

Compare. Use >,

5 

Name Date 

Find the number missing. 

11. × (2 × 5) = 90 

12. (2 × ) × 7 = 56 

13. 3 × 9 × 1 = 

14. 9 × 2 × 3 = 

15. (2 × ) × 5 = 40 

Solve. 

Chapter Test, Form 2D (continued) 

16. Tony will eat 3 slices of pizza. Each slice has 

4 hot peppers on it. How many hot peppers will 

Tony eat? 

17. Lucia makes $5 an hour babysitting. She babysits 

3 hours each day for 2 days. How much money 

does she make? 

18. At the movie theater, an adult ticket costs $5. A 

child’s ticket cost $2. Mr. Ramirez buys 2 adult 

tickets and 4 child tickets. How much money does 

he spend? 

19. Dana drove 3 miles to the store and then she 

drove 8 miles to see a friend. Later, she drove 

back the same way. How many miles did 

she drive? 

20. The soccer club went on a trip to see a soccer 

match. The group traveled to the match in 3 cars 

of 3 people each, and in 2 vans of 7 people each. 

How many people went on the trip? 


11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 



5 

Name Date 

Read each question carefully. Write your answer 


Multiply. 

1. 9 × 6 

2. 9 × 9 

3. 7 × 8 

4. 8 × 8 

5. 4 × 8 × 2 

6. 9 × 3 × 2 

7. Mary plans to bake 2 batches of chocolate-chip 

walnut cookies. Each batch will make 10 cookies. 

How many chocolate chips will she need to make 

sure that each cookie has 4 chocolate chips? How 

many walnuts will she need to make sure each 

cookie has 5 walnuts? 

8. Charley purchased tickets for 2 rides on the 

carnival’s newest and scariest roller coaster, for 

himself and his three friends. A ticket for one ride 

costs $1. If he paid for the tickets with a $10-bill, 

how much change should he get? 

9. A plane has 10 rows of seats with 3 seats in each 

row. If passengers are allowed to bring on no 

more than 2 bags, what is the greatest number of 

bags allowed on the plane? 

Complete, using >,

5 

Name Date 

Determine the missing number. 

13. (4 × ) × 3 = 24 

14. × (4 × 3) = 36 

15. (3 × ) × 3 = 27 

Solve. 

Chapter Test, Form 3 (continued) 

16. Tony will eat 4 slices of pizza. Each slice has 

4 black olives and 6 slices of onion on it. How 

many slices of onion will Tony eat? 

17. Lara earns $2 an hour stuffing envelopes. She 

works 4 hours each day for 5 days. How much 

money does she earn? 

18. At the ballpark, an adult ticket costs $9. A child’s 

ticket cost $6. Mr. Jameson buys 3 adult tickets 

and 2 child tickets. How much does he spend? 

19. Alan drove 8 miles to the store and then 5 miles 

to see a friend and then 3 miles to the ballpark. 

Later, he returned the same way. How many miles 

did he drive? 

20. The music club went on a trip to see a jazz 

concert in the next town. The group traveled in 

4 cars of 3 people each, and 2 vans of 8 people 

each. How many people went on the trip? 


13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 



5 

Name Date 

Chapter Extended-Response Test 

Demonstrate your knowledge by giving a clear, concise 

solution to each problem. Be sure to include all relevant 

drawings and justify your answers. You may show your 

solution in more than one way or investigate beyond the 

requirements of the problem. If necessary, record your 

answer on another piece of paper. 

1. a. How can you use skip counting or draw an array to help 

multiply a number by 3? Give an example of each. 

b. How can you draw a picture to help solve a multiplication 

problem? 

c. Write a real-world problem in which 3 is the factor and 

then solve the problem. 

2. Use the look for a pattern strategy to solve the following 

problem. Explain each step. 

Luke is setting up chairs for the music show. The first row has 

6 chairs. The second row has 9 chairs and the third row has 

12 chairs. How many chairs will be in the fifth row? 


Assessment

5 

Name Date 

Use this recording sheet with pages 246–247 of the Student Edition. 

Read each question. Then fill in the correct answer. 

1. A B C D 

2. F G H J 

3. A B C D 

4. F G H J 

5. A B C D 

6. F G H J 

7. A B C D 

8. F G H J 

9. A B C D 

10. F G H J 

Student Recording Sheet 

Grade 3 78 Chapter 5


5 

Test Example 

Name Date 


At the corner grocery store, Davis is in charge of unpacking 

3 boxes. Each box has 5 bottles. How many bottles is Davis 

unpacking? 

A. 3 B. 5 C. 15 D. 20 

Read the Question 

You need to find the total number of cans Davis is unpacking. 

Solve the Question 

Use what you know about changing 

the order of the factors. Changing the 

order of the factors does not 

change the product. 

You know that 3 × 5 = 15. 

So, 5 × 3 = 15. 

The answer is C. 

Choose the best answer. 

1. For the school band concert, chairs were set in 7 rows of 

7 seats. How many seats are in all? 

A. 36 B. 49 C. 56 D. 64 

2. Each package of crayons has 8 crayons. How many crayons 

are in 6 packages? 

F. 30 G. 36 H. 48 J. 54 

3. What number makes this number sentence true? 

9 × = 27 

A. 3 B. 4 C. 5 D. 6 


1. 

2. 

3. 

Assessment

5 

Name Date 

Cumulative Standardized Test 

Practice (continued) 

4. What multiplication sentence describes the array shown 

below? 

F. 4 × 4 G. 3 × 5 

H. 2 × 5 J. 3 × 4 

5. If 4 × 2 × 5 = 40, then what is 2 × 4 × 5? 

A. 32 B. 40 C. 45 D. 48 

6. A container of milk costs about $3. About 

how much will 6 containers of milk cost? 

F. $12 G. $15 

H. $18 J. $24 

7. The Applegate School bought 1,360 pencils. They gave out 

756 to students. How many pencils are left? 

A. 604 B. 614 C. 741 D. 906 

8. Carlos bought 4 packages of cinnamon muffins. Each package 

has 5 muffins. Which number sentence shows how to find 

the number of muffins in all? 

F. 4 × 5 = G. 4 + 5 = 

H. 5 - 4 = J. 20 - 5 = 

9. Complete the number sentence below. 

× 7 = 0 

A. 3 B. 2 C. 1 D. 0 

10. What is 7,658 rounded to the nearest hundred? 

MILK 

F. 8,000 G. 7,700 H. 7,600 J. 7,660 


$3.00 

4. 

5. 

6. 

7. 

8. 

9. 

10. 



5 

Name Date 

Write your answer on the line provided. 


11. 3 × ( × 4) = 12 

12. 6 × 5 × = 60 

13. × 3 × 7 = 63 

14. 6 × 3 × 2 = 

Solve. 

Cumulative Standardized Test 

Practice (continued) 

15. Mason planted corn in the garden. He planted 

3 seeds in the first row, 6 seeds in the second, and 

9 seeds in the third row. If this pattern continued, 

how many seeds did he plant in the seventh row? 

16. Jillian is wrapping gifts for the holiday. For each gift, 

she used 1 yard of wrapping paper and 2 yards of 

ribbon. How many yards of wrapping paper and 

ribbon does she need to wrap 9 gifts? 


11. 

12. 

13. 

14. 

15. 

16. 

Assessment

Chapter 5 Assessment Answer Key 

Page 77, Extended-Response Test 

Scoring Rubric 

Level Specific Criteria 

4 The student demonstrates a thorough understanding of the 

mathematics concepts and/or procedures embodied in the task. The 

student has responded correctly to the task, used mathematically 

sound procedures, and provided clear and complete explanations 

and interpretations. The response may contain minor flaws that do 

not detract from the demonstration of a thorough understanding. 

3 The student demonstrates an understanding of the mathematics 

concepts and/or procedures embodied in the task. The student’s 

response to the task is essentially correct with the mathematical 

procedures used and the explanations and interpretations provided 

demonstrating an essential but less than thorough understanding. 

The response may contain minor errors that reflect inattentive 

execution of the mathematical procedures or indications of some 

misunderstanding of the underlying mathematics concepts and/or 

procedures. 

2 The student has demonstrated only a partial understanding of 

the mathematics concepts and/or procedures embodied in the 

task. Although the student may have used the correct approach to 

obtaining a solution or may have provided a correct solution, the 

student’s work lacks an essential understanding of the underlying 

mathematical concepts. The response contains errors related 

to misunderstanding important aspects of the task, misuse of 

mathematical procedures, or faulty interpretations of results. 

1 The student has demonstrated a very limited understanding of the 


student’s response to the task is incomplete and exhibits many flaws. 

Although the student has addressed some of the conditions of the 

task, the student reached an inadequate conclusion and/or provided 

reasoning that was faulty or incomplete. The response exhibits many 

errors or may be incomplete. 

0 The student has provided a completely incorrect solution or 

uninterpretable response, or no response at all. 






Sample Answers 

In addition to the scoring rubric found on page 82, the following sample 

answers may be used as guidance in evaluating open-ended assessment items. 

1. a. Answers will vary. Sample answer: 

You can use skip counting to 

multiply a number by 3 by 

adding 3 to the number over 

and over again. For example: 

to find 3 × 4 you can count 3 

jumps of four (4, 8, 12) . You can 

also draw an array to multiply 

by 3. For example: to find 6 × 3 

you can count 3 rows of 6. 

b. You can draw a picture to help 

solve a multiplication problem. 

For example: If you know there 

are 3 children and each child 

is wearing two gloves, you can 

draw a picture to find out how 

many gloves there are in all. 

c. Samantha goes to the pet store. 

There are black cats, white cats, 

spotted cats and brown cats. 

She notices that there are 3 of 

each color. How many cats are 

there altogether? 

Answer: 12 

2. Answers may vary slightly. Sample 

answer: 

Step 1: 

I know that there will be 6 chairs in 

the first row. 


the second row. 

I know that there will be 12 chairs 

in the third row. 

I need to find how many chairs will 

be in the fifth row. 

Step 2: 

My plan is to organize the data in a 

table and then look for a pattern. 

Step 3: 

I will first put the information in a 

table. 

1 st 2 nd 3 rd 4 th 5 th 

6 9 12 15 18 

I will then look for a pattern. I 

see that the pattern is +3, so I 

complete the chart. 

So, there will be 18 chairs in the 

fifth row. 

Step 4: 

I will check my work. 

I look back at the problem 

6 + 3 = 9 

9 + 3 = 12 

12 + 3 = 15 

15 + 4 = 18 

There are 18 chairs in the fifth row. 

So, I know I am correct. 


Assessment


Name Date 

Anticipation Guide 

More Multiplication Facts 

5 

Name Date 

Graphic Organizer 

5 

Answers (Graphic Organizer and Anticipation Guide) 

STEP 1 Before you begin Chapter 5 

• Read each statement. 


Use this graphic organizer to take notes on Chapter 5: More 

Multiplication Facts. Fill in the missing information. 

• Decide whether you agree (A) or disagree (D) with the 

statement. 

Extend the Pattern Name the Pattern 

• Write A or D in the first column OR if you are not sure whether 

you agree or disagree, write NS (not sure). 

25 25 30 30 + 5 or × 5 

5, 10, 15, 20, , 

15 18 + 3 or × 3 

3, 6, 9, 12, , 

STEP 2 

A or D 

D 

A 

A 

D 

A 

A 


AA 

DD 

DD 

STEP 1 

A, D, or NS Statement 

1. There is only way to multiply a number by 3. 

2. Organizing information in a table can help you to 

notice a pattern. 

3. 7 × 2 = 14 and 2 × 7 = 14 

4. You can use the doubles or near doubles strategy 

when one of the factors is odd. 

5. 9 × 8 = 72 

6. Looking for a pattern may be helpful in remembering 

the nines multiplication facts. 

7. The Associative Property of Multiplication states that 

the grouping of the factors does not change the 

product. 

8. Multiplication and addition are not helpful in 

extending a pattern. 

9. 9 × 9 = 99 

10 12 12 + 2 or × 2 

2, 4, 6, 8, , 

20 24 24 + 4 or × 4 

30 36 + 6 or × 6 

4, 8, 12, 16, , 

6, 12, 18, 24, , 

35 42 + + 7 or × × 7 

45 54 + 9 or × 9 

Grade 3 A1 Chapter 5 

7, 14, 21, 28, , 

9, 18, 27, 36, , 

+ 8 or × 8 

40 48 

8, 16, 24, 32, , 

STEP 2 After you complete Chapter 5 

• Reread each statement and complete the last column by 

entering an A (agree) or a D (disagree). 

• Did any of your opinions about the statements change from the 

first column? 

• For those statements that you mark with a D, use a separate sheet 

of paper to explain why you disagree. Use examples, if possible. 



Answers

Name Date 


Multiply by 3 

5–1 

Name Date 

3NS2.2 

3NS2.2 

Reteach 

Multiply by 3 

5–1 


Multiply. 

30 15 

24 18 

21 27 

6 3 

0 21 

24 24 

18 

15 12 

12 24 

There are different ways to find answers for multiplication 

problems. One way is to use models to represent the problem. 

1. 3 × 10 = 2. 5 × 3 = 

3. 3 × 8 = 4. 6 × 3 = 

Find 3 × 4. 

5. 7 × 3 = 6. 3 × 9 = 

Using Models Using Paper and Pencil 

7. 2 × 3 = 8. 1 × 3 = 

Total 

9. 0 × 3 = 10. 3 × 7 = 

Number in Each 

Group 

Number of 

Groups 

Answers (Lesson 5 –1) 

11. 8 × 3 = 12. 3 × 6 = 

3 × 4 = 12 

13. 3 × 5 = 14. 4 × 3 = 

15. 3 × 4 = 16. 3 × 8 = 

3 groups of 4 cubes factor factor product 

ALGEBRA Complete each table. 

Use models to find the total number. 

1. 2. 



18. 


17. 

Output 

Input 

Output 

Input 

12 

4 

9 

18 

3 

27 

9 

6 

6 

2 8 

30 

24 

0 

10 

0 

21 

7 

3 

1 

Solve. 

19. Jay has 3 bags of fruit. Each bag has 8 pieces of fruit. How 

many pieces of fruit does Jay have altogether? 

24 pieces of fruit 


15 12 

3 groups of 5 = 4 groups of 3 = 

3. 4 × 5 = 4. 

20 

21 

3 groups of 7 = 

5. 3 × 6 = 6. 8 × 3 = 

20. Heather has 3 bags of pretzels. Each bag has 6 pretzels. How 

many pretzels does Heather have altogether? 


18 pretzels pretzels 

18 24 

99 1 21 2 

6 2 72 7 






Name Date 

3NS2.2 


Multiply by 3 

5–1 

Name Date 

3NS2.2 


Multiply by 3 

5–1 


Solve. 

Multiply. 

1. Sean and Dave are playing with toy racecars. Sean has his 

cars lined up in 3 rows. He has 5 cars in each row. How 

1. 3 × 3 = 2. 3 × 5 = 

3. 5 × 3 = 4. 9 × 3 = 

many cars does he have in all? 

15 15 cars 

9 1 51 5 

15 15 

27 

12 12 

30 

24 24 

21 

18 3 

5. 4 × 3 = 6. 10 × 3 = 

7. 8 × 3 = 8. 3 × 7 = 


2. Dave has 4 rows of cars lined up. He has 3 cars in each row. 

How many cars does Dave have in all? 

9. 6 × 3 = 10. 1 × 3 = 

12 12 cars 

Solve. 

3. The boys are sharing some special cars. They have 2 rows of 

special cars with 3 in each row. How many special cars do 

11. The parking lot has 3 rows of cars. There are 6 cars in each 

row. How many cars are in the parking lot? 

they have in all? 

18 cars cars 

6 6 cars 


12. Mary has 3 dimes in her pocket. Each dime equals 

10 pennies. If she traded her dimes for pennies, how many 

4. Dave’s mom said that she would buy them more special cars. 

These cars cost $3 each. If she buys the boys 3 more, how 

much will she have to spend? 

$9 

5. The boys used their building blocks to create a wall for the 

cars to drive through. They plan to stack the blocks 3 across 

and 9 up. How many blocks do they need to build the wall? 

27 blocks 

6. After they finish the wall, Dave and Sean each have 3 extra 

blocks. Two of these blocks are broken. How many extra 

blocks do they have left that are not broken? 


pennies would she have? 

30 pennies 


13. 0 × 3 = 14. 1 × 5 = 

15. 1 × 6 = 16. 0 × 9 = 

17. 0 × 1 = 18. 2 × 0 = 

19. 8 × 1 = 20. 1 × 0 = 

4 blocks 

0 5 

6 0 

0 0 

8 00 

4 2 

0 00 

21. 1 × 4 = 22. 2 × 1 = 

23. 5 × 0 = 24. 0 × 1 = 



Answers

Name Date 

3NS2.2 

Reteach 

Multiply by 6 

5–2 

Name Date 

3NS2.2 

Enrich 

The Birthday Party 

5–1 


You can use facts that you already know to help you multiply by 6. 


Answers (Lessons 5 –1 and 5 –2) 

= ++ 

Karlie, Keri, and Kristie are triplets. They are having a 

birthday party. Read each problem. Draw a picture for each 

number sentence. Use a separate sheet of paper if you 

need more room. Then write a number sentence that helps 

answer questions 1–4. 


7 × 6 = 7 × 3 + 7 × 3 

= 21 + 21 = 42 

Pictures should accurately 

reflect reflect sentence 

1. Each girl wants to invite six different friends to the party. How 

many friends will be invited to the party? 



3 × × 6 = = 18 friends friends 

1. 2. 3. 

4 × 6 = 24 2 × 6 = 12 3 × 6 = 18 

Multiply. 

18 30 36 

48 48 

6 12 

54 54 

42 24 

27 9 21 

15 24 18 

4. 6 × 3 = 5. 6 × 5 = 6. 6 × 6 = 

7. 6 × 8 = 8. 6 × 1 = 9. 6 × 2 = 

10. 9 × 6 = 11. 6 × 7 = 12. 6 × 4 = 


2. The girls’ dad is making a jewelry box for each girl. Each box 

has four sides, a bottom, and a lid that opens. How many 

sides for the jewelry boxes will he make? 

3 × × 4 = = 12 sides 

3. Their aunt is knitting sweaters for the girls. She is buying 

eight flowered buttons to put on each sweater. How many 

buttons does she need to buy? 

3 × 8 = 24 buttons 

13. 3 × 9 = 14. 3 × 3 = 15. 7 × 3 = 

4. The girls are going to be 9 years old. They will blow out the 

candles on their cake together. If their mom wants to buy 

one set of nine candles for each girl to put on the cake, how 

many candles does she need to buy? 

16. 3 × 5 = 17. 3 × 8 = 18. 6 × 3 = 

9 × 3 = 27 candles 





Name Date 

3NS2.2 


Multiply by 6 

5–2 

Name Date 

3NS2.2 


Multiply by 6 

5–2 


Multiply. 

Multiply. 

24 24 

18 

48 24 

0 66 

54 54 

54 

30 30 

42 

1. 6 × 4 = 2. 3 × 6 = 

1. 6 × 5 = 2. 6 × 7 = 

3. 6 × 8 = 4. 4 × 6 = 

3. 9 × 6 = 4. 3 × 6 = 

5. 6 × 0 = 6. 6 × 1 = 

5. 6 × 6 = 6. 7 × 6 = 

7. 6 × 9 = 8. 9 × 6 = 

7. 1 × 6 = 8. 6 × 2 = 

9. 5 × 6 = 10. 7 × 6 = 

9. 8 × 6 = 10. 10 × 6 = 


11. 3 × 6 = 12. 6 × 4 = 

Solve. 

13. 5 × 6 = 14. 6 × 3 = 

15. 6 × 8 = 16. 6 × 7 = 

11. Brad’s rabbit has 6 whiskers on both sides of its face. How 

many whiskers does the rabbit have on its face? 

30 30 

42 

54 54 

18 

36 36 

42 

6 12 12 

48 60 

18 24 

30 18 

48 42 

24 54 

17. 4 × 6 = 18. 6 × 9 = 

12 whiskers 



12. Jan has 4 insects in a jar. Each insect has 6 legs. How many 

legs in all? 

24 legs 


27 21 

18 15 

12 12 

24 

00 2 12 1 

6 1 21 2 

24 24 

27 

13. 3 × 9 = 14. 3 × 7 = 

15. 6 × 3 = 16. 5 × 3 = 

17. 4 × 3 = 18. 8 × 3 = 

19. 0 × 3 = 20. 7 × 3 = 

21. 3 × 2 = 22. 3 × 4 = 


19. 5 × = 30 20. 9 × = 54 

21. 8 × = 24 22. 6 × = 42 

23. 6 × = 48 24. 9 × = 27 

66 6 

33 77 

88 3 

6 26. Rule: Multiply by 8 

ALGEBRA Find each rule. 




Output 

Input 

Output 

Input 

48 

6 

36 

6 

56 

7 

42 

7 

64 

8 

48 

8 

23. 3 × 8 = 24. 9 × 3 = 

54 

9 



Answers

Name Date 

Enrich 

Multiply by 6 

5–2 

Name Date 

3NS2.2 

3NS2.2 


Multiply by 6 

5–2 


Find the missing factor for each problem. Draw an array 

or a picture that matches the problem. Then use words to 

write a number sentence for each drawing. 

Solve. 

1. Cindy and Mandy went to the beach. They each found 

6 starfish. How many starfish do they have in all? 

Find the Factors Show the Problem Write It in Words 

12 starfish 

6 groups of 3 

equals 18 


drawing should 

accurately represent 

6 groups with 

3 items in each group 

2. Each of the 6 starfish has 5 arms. The girls counted them all. 

How many starfish arms did the girls count? 

1. 6 × 33 = 18 

30 30 arms arms 

6 groups of 5 

equals 30 

drawing should should 


6 groups with 


3. The girls made a sandcastle with 3 waterways leading to 

each of their 6 towers. How many waterways did they dig 

altogether? 

2. 6 × 55 = 30 

18 waterways 

2 groups of 6 

equals 12 



2 groups with 



3. 2 × 6 = 12 

6 groups of 4 

equal 24, or 

4 groups of 6 

equals 24 



24 items in groups of 

6 with 4 items in each 

group or 4 groups with 


4. 24 = 4 × 6 

6 groups of 6 

equals 36 



36 in groups of 6 


4. The girls each carried 6 pails with them to the beach. They 

found out that they really did not need so many pails, so they 

let a group of children use 4 of their pails. How many pails 

do the girls still have left to use? 

8 pails 

5. Cindy has 6 dimes that she can spend on stickers. Each 

sticker costs 5¢. 

Does she have enough money to buy 6 stickers? Explain. 

yes, the stickers will cost 30¢ and Cindy has has 60¢ 

6. Write a problem that can be solved by multiplying by 6. 

5. 66 × 6 = 36 

Sample answer: Mandy bought 6 pieces of fruit fruit that cost 

7¢ each. How much did she pay for her fruit? 42¢ 





Name Date 

Reteach 

Problem -Solving Strategy (continued) 

5–3 

Name Date 

3MR1.1, 3AF2.2 

3MR1.1, 3AF2.2 

Reteach 


5–3 


Practice by following the steps. 

Look for a Pattern 

Fred is putting pictures in a scrapbook. He uses a pattern of 

groups of space and sports pictures. Each group has 1 space 

picture and 3 sports pictures. If the pattern continues, how many 

sports pictures will he use in all if there are a total of 24 pictures? 

Liz created a castle with pink towers and blue flags. On the first tower, she has 

2 flags. The second tower has 4 flags, and the third tower has 8. If she keeps the 

pattern up, how many flags are on the fourth tower? 

What do you know? 

There are 2 flags on the first tower. 

Step 1 

Understand 


You know: There is 1 space picture in each group. There are 3 

sports pictures in each group. There There are are a a total total of of 24 24 

pictures. 

You need to find out: 

Step 1 

Understand 

There are 4 flags on the second tower. 

There are 8 flags on the third tower. 

sports pictures 

How many will be used? 

Organize the data in a table. What are your columns? The 

groups. There are 4 pictures in each group and 24 pictures in all. 

4 × 6 = 24. You need 6 columns. 

What do you need to find out? 

How many flags will be on the fourth tower? 

Step 2 

Plan 

Organize the data in a table. What are your 

columns? The towers 

Step 2 

Plan 


What is in the row under each column? The number of space 

and sports pictures in each group. 

What is in the row under each column? The 

number of flags 

Group 1 Group 2 Group 3 Group 4 Group 5 Group 6 

1 space 1 space 1 space 1 space 1 space 1 space 

3 sports 3 sports 3 sports 3 sports 3 sports 3 sports 

Look for the pattern. Since the same group repeats, 

multiply multiply the number of sports pictures by 6. 

Step 3 

Solve 

Multiply 3 by 6. 

Step 4 

Check 

6 groups of 3 sports pictures equal 18 sports pictures. 


Tower 1 Tower 2 Tower 3 Tower 4 

? 

What is done to 2 to get 4 ? 2 was added to get 4 OR 

2 was multiplied to get 4. 

Step 3 

Solve the problem. 

What was done to 4 to get 8 ? 4 was multiplied by 2. 

What was done to both the first and the second 

number? They were both multiplied by 2. 

Think: What is 

added, subtracted 

or multiplied? 

Repeat the steps for tower 3 to check your rule. Then 

repeat for the fourth tower. Multiply 8 by 2. 16 flags 

will be on the fourth tower. 

Look back at your answer. Does it make sense ? Why ? 

Step 4 

Check 



Answers

Name Date 



5–3 

Name Date 

3MR1.1, 3AF2.2 

3MR1.1, 3AF2.2 



5–3 


Solve. 

Solve. Use the look for a pattern strategy. 

1. Every home on Main Street has a dog and other pets. 

The first house has 1 dog and 1 cat. The second house 

has 1 dog and 2 cats. The third house has 1 dog and 

3 rabbits. The fourth house has 1 dog and 4 angel fish. If the 

pattern continues, the fifth house has 1 dog and how many 

hamsters? 

2. The concert hall offers specials on 

tickets. When you buy 5 tickets, 

you get 1 other ticket free. When 

you buy 10 tickets, you get 2 other 

tickets free. Lyddie got 4 tickets 

free. How many tickets did she 

1. A dancer practices 3 days in a row 

and then takes one day off to rest. 

She has a show in two weeks. If 

she practices on the first 3 days, 

and takes the 4th day off, how 

many times will she practice in 


5 hamsters 

buy? 

14 days? 

11 times 20 20 tickets 

2. Ann is a pet babysitter. She gets paid to help the families 

on Main Street with their pets every day. The first week she 

earned $2. The second week she earned $4. The third week 

she earned $6. The fourth, $8. What did she earn by the 

seventh week? 

$14 

4. The Portsmouth Players perform 

2 daytime shows and 3 evening 

shows per week. Their current 

play will run for 30 shows. How 

many of the shows will be daytime 

3. Ann decided to set up a pet parade. She had the pet owners 

walk in rows with their pets. In the first row she put 

1 owner with 1 pet. The second row had 2 owners with 

1 pet each. The third row had 1 pet owner and 2 pets. The 

fourth row had 2 pet owners with 2 pets each. The fifth row 

had 1 pet owner with 3 pets. If the pattern continues, what 


shows? 

3. The marching band lines up in 

rows. The first row has 2 people. 

The second row has 4 people. 

The third row has 6 people. 

If this pattern continues, how 

many people will be in the fifth 

did the sixth row have? 

3 pet owners with 3 pets each 



12 shows 

row? 

10 people 


6. A theater seat in the orchestra costs 

$32. A balcony seat costs $14. How 

much more does an orchestra seat 

cost than a balcony seat? 

$18 

5. Ken takes piano lessons. The 1st 

week, he practices 20 minutes 

each day. The 2nd week, he 

practices 40 minutes each day. The 

3rd week, he practices 1 hour each 

day. If this pattern continues, how 

many minutes will he practice each 

18 18 

24 

36 42 

4. 3 × 6 = 5. 4 × 6 = 

day in the 5th week? 

1 hour 40 minutes 

6. 6 × 6 = 7. 7 × 6 = 





Name Date 

3NS2.2 

Reteach 

Multiply by 7 

5–4 

Name Date 

3MR1.1, 3AF2.2 

Enrich 

Favorite Numbers 

5–3 


You can add on to a known fact to find a new fact. 

36 80 24 30 63 

Find 7 × 3 by finding (6 × 3) +(1 × 3). 


= + 

Carmen x x x x O 

Zack x x O x x 

Jenna x O x x x 

April O x x x x 

Carlos x x x O x 

7 groups of 3 = 6 groups of 3 plus 1 group of 3 

7 × 3 = 6 × 3 + 1 × 3 

= 18 + 3 = 21 

Read each clue. If the answer is “yes,” draw an “O” in the 

box. If the answer is “no,” draw an “X” in the box. Then fill 

in the correct answers below. 


Carmen’s favorite number is more than 1 × 6 × 8 but less than 8 × 8. 

1. 2. 3. 


4. 3 × 7 = 21 5. 5 × 7 = 35 6. 7 × 7 = 49 

7. 8 × 7 = 56 8. 7 × 6 = 42 9. 7 × 9 = 63 

10. 9 × 7 = 63 11. 4 × 7 = 28 12. 7 × 1 = 7 

13. 6 × 7 = 42 14. 3 × 7 = 21 15. 0 × 7 = 0 

16. 7 × 4 = 28 17. 1 × 7 = 7 18. 2 × 7 = 14 


Zack’s favorite number is the product of each of these multiplication 

facts 8 × 3, 6 × 4, or 2 × 12. 

Carlos’ favorite number would belong in the patterns 5, 10, 15 . . . 

and 6, 12, 18 . . . 

7 × 4 = 28 7 7 × 6 6 = 42 42 7 × 8 = 56 

Jenna’s favorite number is a multiple of 10 that is greater than 5 × 8. 

April’s favorite number is the product of two equal factors that when added 

together equal twelve. 

Carmen’s favorite number is 63 . Zack’s favorite number is 24 . Jenna’s 

favorite number is 80 . April’s favorite number is 36 . Carlos’ favorite 

number is 30 . 



Answers

Name Date 

3NS2.2 


Multiply by 7 

5–4 

Name Date 

3NS2.2 


Multiply by 7 

5–4 


Multiply. 

Write multiplication sentences. 

21 35 

42 49 

56 63 

28 42 

70 77 

0 35 

28 63 

1. 7 × 3 = 2. 5 × 7 = 

1. How many train cars? 2. How many fingers? 

3. 6 × 7 = 4. 7 × 7 = 

5. 7 × 8 = 6. 9 × 7 = 

7. 4 × 7 = 8. 7 × 6 = 

9. 7 × 10 = 10. 7 × 1 = 


7 × × 3 = = 21 train cars 7 × 5 = 35 fingers 

11. 7 × 0 = 12. 7 × 5 = 

13. 7 × 4 = 14. 7 × 9 = 

Multiply. 


15. 8 × = 56 16. 7 × = 35 

17. × 7 = 14 18. × 7 = 49 

7 5 

2 7 

3. 7 4. 7 5. 7 6. 7 7. 5 8. 2 

____ × 3 ____ × 6 ____ × 9 

____ × 7 

____ × 7 ____ × 7 

21 42 63 49 35 14 

28 35 7 


9. 7 × 4 = 10. 7 × 5 = 11. 7 × 1 = 

Solve. Use the look for a pattern strategy. (Lesson 5–3) 

19. Fred buys and sells sports cards. Week 1, he bought 10 cards 

and sold 2. Week 2, he bought 10 more and sold 2, giving 

him 16. Week 3, he bought 10 more and sold 2, giving him 

24. If the pattern continued, how many cards did he have by 

the end of Week 4? 

32 cards 

20. Fred collected football, basketball, and baseball cards. He 

has a total of 50 cards, with an equal number of football 

and basketball cards. He has 20 baseball cards. How many 



Rule: Multiply by 7 

Input Input Output 

12. 13. 

Rule: Multiply by 7 

21 

21 

3 

35 

5 

49 49 

7 

63 

9 

Input Output 

5 

35 

6 

42 

7 49 

49 

56 

8 

Solve. 

football cards does he have? 

15 15 cards cards 

14. Jason read about trains for 2 hours each day for 1 week. How many hours 

did Jason read? 

14 hours; 7 × 2 = 14 





Name Date 

3NS2.2 

Enrich 

Lucky Seven Store 

5–4 

Name Date 

3NS2.2 


Multiply by 7 

5–4 


Solve. 

2. It takes Cally 3 minutes to paint 

each slat on a fence. There are 

7 slats in each section of the fence. 

How long will it take Cally to paint 

each section of the fence? 

21 minutes minutes 

1. The Martins will buy 2 new tires for 

each of their 7 bicycles. How many 

new tires will they buy? 

14 new tires tires 


The Lucky Seven Store sells every item in the store for 7 cents each. 

1. Alvin wants to buy 3 bags of marbles and 2 pencils. How 

much will they cost? Write two number sentences to show 

how much for each. 

cents 

3 × 7 = 21 

4. Mario will go on vacation for 

8 weeks this summer. For how 

many days will Mario be on 

cents 

2 × 7 = 14 

3. Each house on Alpine Street 

has 7 front windows. There are 

3 houses on each side of the 

street. How many front windows 

vacation? 

56 days days 



will cost in all. 

are there in all? 

42 windows 

cents 

5 × 7 = 35 

2. Clare bought 7 buttons, a bottle of glitter, and a stuffed toy. 

How much did they cost? Write three number sentences to 

show how much for each. 

7 × 7 = 49 

cents 

7 × 1 = 7 

cents 

7 × 1 = 7 

cents 


cost in all. 

cents 

9 × 7 = 63 


6. There are an equal number of 

cars and bicycles in the garage. If 

there are 42 tires in all, how many 

bicycles and cars are in the garage? 

Explain. 

7 7 bicycles bicycles and 7 cars; 

7 × 2 bicycle tires = 14; 

5. Nell bought 3 pairs of white socks 

and 4 pairs of black socks. Each 

pair cost $6. Then she bought a 

$5.75 hat. She got back $12.25 in 

change. How much did Nell give 

to the cashier to pay for the socks 

and hat ? Show your work. 

7 × 4 car tires = 28; 14 + 28 

= 42 tires in all. 

$60; (3 (3 + 4) 4) × 6 = $42 

for the socks; $42 + 5.75 

= $47.75 for all; $47.75 + 

$12.25 = $60. 

3. How many items could be purchased with a one dollar bill? 

14 items 

4. How many items could be purchased with a five dollar bill? 

71 items 



Answers

Name Date 


Multiply by 8 

5–5 

Name Date 

3NS2.2 

3NS2.2 

Reteach 

Multiply by 8 

5–5 


Multiply. 

56 40 

56 64 

72 24 

32 48 

80 80 

8 

0 40 

32 72 

16 72 

You can use facts that you already know to help you 

multiply by 8. 

1. 7 × 8 = 2. 5 × 8 = 

3. 8 × 7 = 4. 8 × 8 = 


5. 9 × 8 = 6. 8 × 3 = 

7. 4 × 8 = 8. 6 × 8 = 

9. 8 × 10 = 10. 8 × 1 = 


= + 

11. 8 × 0 = 12. 8 × 5 = 

13. 8 × 4 = 14. 8 × 9 = 

15. 2 × 8 = 16. 9 × 8 = 



6 × 8 = 6 × 4 + 6 × 4 

= 24 + 24 = 48 

17. × 8 = 64 18. × 6 = 48 


19. × 5 = 40 20. × 8 = 24 

21. × 8 = 32 22. × 8 = 56 

23. × 8 = 64 24. × 8 = 48 

25. × 8 = 0 26. × 9 = 72 

8 88 

8 3 

4 7 

8 6 

0 8 

Write a multiplication sentence for each picture. 

Solve. 

27. Justin is going to a baseball game with 8 other boys. The 

tickets cost $5. How much will it cost for all 9 boys to watch 

the game? 

$45 

28. Mike worked 8 hours washing cars for Mr. Smith. Mr. Smith 

paid him $4 an hour. How much did Mike earn? 


1. 2. 

1 × × 8 = = 8 3 3 × 8 8 = 24 

Multiply. 

16 0 40 40 

3. 2 × 8 = 4. 0 × 8 = 5. 8 × 5 = 

48 8 56 

6. 8 × 6 = 7. 8 × 1 = 8. 8 × 7 = 

40 3 23 2 2 42 4 

$32 

9. 5 × 8 = 10. 8 × 4 = 11. 3 × 8 = 





Name Date 

3NS2.2 


Multiply by 8 

5–5 

Name Date 

3NS2.2 


Multiply by 8 

5–5 


Solve. 

Multiply. 

1. Find the total number of dolphins if there are 8 groups of 

dolphins with 5 dolphins in each group. 

1. 8 × 3 = 2. 5 × 8 = 

40 dolphins 

3. 6 × 8 = 4. 7 × 8 = 

5. 8 × 8 = 6. 9 × 8 = 

2. A dolphin has 4 fins. How many total fins do 8 dolphins 

have? 

7. 4 × 8 = 8. 8 × 6 = 

9. 8 × 10 = 10. 8 × 1 = 


32 32 fins 

2 42 4 4 04 0 

48 48 

56 

64 64 

72 72 

32 32 

48 48 

80 8 

0 4 04 0 

32 72 

11. 8 × 0 = 12. 8 × 5 = 

13. 8 × 4 = 14. 8 × 9 = 

3. Eight dolphins are swimming around a tour boat. Each 

dolphin swims around the boat 8 times. How many times did 


all the dolphins swim around the boat? 

64 laps around the boat 

15. 8 × = 64 16. 7 × = 56 

17. × 8 = 24 18. × 8 = 64 

88 88 

3 8 


4. The 8 tourists on the boat were able to touch 4 dolphins 

each. What was the total number of times a dolphin got 

touched? 

32 touches 

5. Using their tail fins, 7 dolphins jumped in the air 8 times. 

What was the total number of jumps the dolphins made? 

56 jumps 

6. Eight tourists each took 3 photos of the dolphins. How many 

dolphin photos were taken in all? 

24 photos 



35 28 

70 49 

5 65 6 6 36 3 

1 41 4 4 24 2 

19. 7 × 5 = 20. 4 × 7 = 

21. 10 × 7 = 22. 7 × 7 = 

23. 7 × 8 = 24. 9 × 7 = 

25. 2 × 7 = 26. 7 × 6 = 


27. Fred has collected a total of 80 cards. A display of Fred’s cards includes 

2 rows of football cards with 15 in each row. In front of the football cards 

are 3 rows of baseball cards with 10 in each row. In front of the baseball 

cards are 4 rows of basketball cards. If the pattern continues, how many 

basketball cards are in each of the 4 rows? 

5 5 cards 



Answers

Name Date 

Name Date 

3NS2.2 

Reteach 

Multiply by 9 

5–6 

3NS2.2 

Enrich 

Roll of the Number Cube Times 8 

5–5 


Here is a strategy you can use when multiplying by 9. 

You can multiply the number by 10 and then subtract the 

number to find a new fact. 

Four friends are playing a game. Each gets to roll a pair of 

number cubes. After each roll, they multiply the number on the 

cubes by 8. They are trying to get to 80 without going over. Each 

person gets two chances to roll. Look at what each person got on 

two rolls. 


Find 9 × 7. 

1. Carlos 

2. Melanie 

= - 

3. Eric 

9 groups of 7 = 10 groups of 7 minus 1 groups of 7 

9 × 7 = 10 × 7 - 1 × 7 

= 70 - 7 = 63 


Multiply. 

1. 9 2. 9 3. 3 4. 9 5. 9 6. 6 

____ × 4 ____ × 5 ____ × 9 ____ × 7 ____ × 8 

____ × 9 

36 45 27 63 72 54 

7. 9 × 2 = 18 8. 5 × 9 = 45 9. 9 × 4 = 36 

10. 6 × 9 = 54 11. 9 × 3 = 

27 

12. 9 × 1 = 

9 

81 

13. 9 × 9 = 14. 9 × 0 = 

0 

15. 9 × 8 = 

72 


4. Marie 

5. How much did each person get? (Hint: Find the value of each 

roll for each person. Add the total that each person got.) 

Carlos 48 and 40; 88 Eric 48 48 and 32; 80 

Melanie 

56 and 64; 120 

Marie 56 and 16; 72 

Eric 

6. Who won? 

7. What is a faster way to find out who won without finding 

each value, adding each person’s rolls, and comparing them? 

16. 2 × 9 = 

18 

17. 8 × 9 = 

72 

18. 3 × 9 = 

27 

Total the number on the four cubes for each each person 

and multiply by 8; see who is closest to 8 × 10 





Name Date 

3NS2.2 


Multiply by 9 

5–6 

Name Date 

3NS2.2 


Multiply by 9 

5–6 


Multiply. 

1. 9 × 3 = 27 2. 5 × 9 = 45 

3. 6 × 9 = 54 4. 7 × 9 = 63 

5. 9 × 8 = 72 6. 9 × 9 = 81 

7. 4 × 9 = 36 8. 9 × 6 = 54 

9. 9 × 10 = 

90 

10. 9 × 1 = 

9 

11. 9 × 0 = 

0 

12. 9 × 5 = 

45 45 

13. 9 × 4 = 

36 

14. 8 × 9 = 

72 

Multiply. 

1. 9 2. 9 3. 4 4. 9 5. 9 6. 9 

____ × 3 ____ × 8 

____ × 9 

____ × 1 

____ × 7 

____ × 5 

27 72 72 36 9 63 45 

7. 9 8. 5 9. 9 10. 9 11. 9 12. 8 

____ × 2 ____ × 9 

____ × 0 

____ × 9 

____ × 6 

____ × 9 

18 45 0 81 54 72 


13. 2 × 9 = 18 14. 4 × 9 = 36 15. 9 × 6 = 54 

16. 8 × 9 = 

72 

17. 9 × 1 = 9 18. 7 × 9 = 63 


15. 9 × 8 = 72 16. 9 × 

4 

= 36 

17. 5 × 9 = 45 18. 

9 

× 6 = 54 

19. 3 × 9 = 27 20. 9 × 9 = 81 21. 9 × 0 = 0 

22. 9 × 1 = 9 23. 7 × 9 = 63 24. 5 × 9 = 45 


19. 8 × 5 = 

40 

20. 8 × 7 = 56 

21. 10 × 8 = 

80 

22. 7 × 8 = 56 

23. 7 × 8 = 

56 

24. 9 × 8 = 72 

25. 2 × 8 = 16 26. 8 × 6 = 

48 

27. 8 × 10 = 80 28. 8 × 1 = 

88 


25. 2 × 9 = 18 26. 0 × 9 = 0 27. 9 × 4 = 36 


Factor 4 9 9 9 

Factor 9 

55 7 9 

Product 36 45 45 63 81 

29. 


28. 8 × 6 = 48 29. 3 × 8 = 24 30. 6 × 7 = 42 

31. 6 × 5 = 30 32. 7 × 3 = 21 33. 5 × 7 = 35 

34. 9 × 3 = 27 35. 8 × 7 = 56 36. 9 × 6 = 54 

Solve. 

37. Jordan saw 9 airplanes fly over 38. The Sports Cap Company sent 

his house every day last week. 

3 caps to each of the 9 starters on 

How many airplanes did Jordan a baseball team. How many caps 

see last week? 

did the company send? 

63 airplanes; 7 × 9 = 63 27 caps; 9 × 3 = 27 



Answers

Name Date 

Enrich 

Find the Products for the Nines 

5–6 

Name Date 

3NS2.2 

3NS2.2 


Multiply by 9 

5–6 


Write the products for the 9s. Find each product in the picture. 

Use a blue crayon or colored pencil to shade or color all the 

numbers that make up the products of the fact families for the 

9s. Shade all other numbers with the colors of your choice. 

Solve 

2. Carmen’s parrot eats 9 crackers a 

day. How many crackers will it eat 

in 4 days? 

1. Jose spends $9 on lunch each 

day. How much does he spend for 

lunch in 2 days? 

9 × 1 = 9 9 × 6 = 54 9 × 2 = 18 

36 

$18 $18 

9 × 7 = 63 9 × 3 = 27 9 × 8 = 72 


9 × 4 = 36 9 × 9 = 81 9 × 5 = 45 

90 

9 × 10 = 

4. The So Rich cookie factory can 

bake 9 chocolate chip cookies 

a minute. Can the factory fill an 

order for 80 cookies in 9 minutes? 

Explain. 

3. On Mr. Dugan’s farm, 9 cows can 

be milked in an hour. Mr. Dugan 

says that 45 cows will be milked in 

5 hours. Is he correct? Explain. 

Yes; 9 cows × 5 hours = 

8 

73 

64 55 

18 

72 

90 

81 45 

63 

54 

9 

13 

Yes; Yes; 9 cookies × 

9 minutes = 81 cookies 

in 9 minutes; 81 > 80 

45 cows milked 


36 

19 

5 

71 

29 

17 

47 

34 

91 

37 

27 

10 

21 

38 

What do you notice about the products of the numbers 1 – 10 

multiplied by 9? (Hint: look for a pattern.) 

The digit in the tens place is 0 - 9, and the digit ones 

place is 9 - 0, they are in reverse order. 

If you add the digits of each product you found, what is the sum of each? For 

example, what is the sum of the digits in 18? 


6. Ty works 9 hours a day and earns 

$6 an hour. Cal works 6 hours a 

day and earns $9 an hour. If they 

both work 5 days per week, who 

earns more money? 

They both earn the same 

amount. 

5. For the school talent contest, 

9 singers will perform for 

3 minutes each. Then 5 dancers 

will perform for 4 minutes each. 

How many minutes will it take for 

the singers and dancers to perform 

in all? 

Who works longer? Explain. 

47 minutes 

Ty; Ty works 9 hours × 5 days 

= 45 hours; Cal works 6 hours 

× 5 days = 30 hours; 45 hours 

- 30 hours = 15 hours longer. 

9 





Name Date 

3MR1.1 

Reteach 

Problem–Solving Investigation (continued) 

5–7 

Name Date 

3MR1.1 

Reteach 

Problem–Solving Investigation 

5–7 


Carry out your plan. 

Find the pattern. 

8 16 24 The pattern is add 8. 

Step 3 

Solve Plan 1 

Choose a Strategy 

+8 +8 

Draw a picture of 12 pieces of wood. Write the length 

next to each piece. 

Plan 2 

Juan has pieces of wood. The first piece of wood is 8 inches. The 

second piece of wood is 16 inches. The third piece of wood is 

24 inches. If this pattern continues, what will be the length of 

the twelfth piece of wood? 

6 

5 

4 

3 

2 

1 

Be sure you understand the problem. 


48 

40 

32 

24 

16 

8 

Step 1 

Understand 

What facts do you know? 

12 

11 

10 

9 

8 

7 

96 

88 

80 

72 

64 

56 

The twelfth piece of wood is 

96 

inches. 

• The first piece of wood is 88 inches. 

• The second piece of wood is 16 inches. 

• The third piece of wood is 24 inches. 

Is the solution reasonable? 

Step 4 

Check 

What do you need to find? 


Reread the problem. 

• You need to find the length of 

the twelfth piece piece of wood 

How can you check your answer ? 

See students’ work; Possible answer: 

repeated addition: 8 + 8 + 8 + 8 + 8 + 8 + 8 

+ 8 + 8 + 8 + 8 + 8 = 96 

Solve. 

2. Winnie is making a quilt. The first 

section has 2 pieces of fabric. 

The second section has 5 pieces 

of fabric. The third section has 

8 pieces of fabric. If this pattern 

continues, how many pieces of 

fabric will be in the eighth section 

of the quilt ? 

1. Jim has 5 packs of cards. There are 

15 cards in each pack. He gives 3 

of his packs away. How many cards 

does he have left ? 

30 cards cards 


. 

Make a plan. 

Choose a strategy. 

You can find the pattern. 

You can also draw a picture. Show 12 pieces of wood. 

Use the pattern, and write the length of each piece 

next to the piece of wood. 

23 pieces of fabric 

Step 2 

Plan 

• Logical Reasoning 

• Draw a Picture or 

Diagram 

• Make a Graph 

• Act It Out 

• Make a Table or 

List 

• Find a Pattern 

• Guess and Check 

• Write an Equation 

• Work Backward 

• Solve a Simpler 

Problem 



Answers

Name Date 



5–7 

Name Date 

3MR1.1 

3MR1.1 



5–7 


Solve. Use any strategy. 

Choose a strategy to solve the problem. 

1. Bob rode 2 miles on his bike for 9 days. What is the total 

number of miles he rode? 

18 18 miles 

2. There are 8 rows of trees in the 

park. Each row has 8 trees. How 

many trees are there in all? 

64 trees 

2. Two toads are near the path. Together, they have 6 dark 

spots on them. The larger one has 2 times as many spots as 

the smaller one. How many spots does each one have? 

1. On Park Day, volunteers plant trees 

in the park. The first tree is 2 feet 

tall. The second tree is 4 feet tall. 

The third tree is 6 feet tall. Suppose 

this pattern continues. What will be 

the height of the fifth tree? 


10 10 feet 

large large -4; -4; small -2 

3. Mandy has $5. Becky has $5 more than Mandy. Sue has 

2 times as much as Becky. How much money do the girls 

have together? 

$35 

4. Some volunteers are building 

picnic tables. Each table uses 

5 pieces of wood for the top, 

2 pieces of wood for the sides, 

and 6 pieces of wood for the rest 

of the table. How many pieces of 

wood are needed to make 

3. Jenny takes a photo of the town 

square. She makes a square frame 

for the photo. Each of the 4 sides 

of the frame is 9 inches long. How 

many inches around is the frame? 

36 inches 

4. 36 students were standing in the lunch line. The principal 

gave the first girl a star. Then, he gave every sixth person in 

back of the girl a star. How many people got stars? 


6 people 


54 90 

99 0 

6 36 3 3 63 6 

72 81 

5. 9 × 6 = 6. 9 × 10 = 

7. 9 × 1 = 8. 9 × 0 = 

9. 9 × 7 = 10. 9 × 4 = 


4 picnic tables? 

52 pieces pieces of wood 


6. There are three groups of students 

making murals for the train station. 

Each group has 6 students. How 

many students are there in all? 

18 students 

5. This year, a town sells tickets 

to the picnic to 252 adults and 

518 children. Last year, there were 

695 people at the picnic. How 

many more people are there this 

year than last year ? 

75 more people 

11. 8 × 9 = 12. 9 × 9 = 

7. Write a problem that you could 

solve by drawing a picture or by 

finding a pattern. Share it with 

others. 

See students’ work 





Name Date 

3AF1.5 

Reteach 


5–8 

Name Date 

3MR1.1 

Enrich 

Unlock the Pyramids 

5–7 


You can use the properties of multiplication to multiply 3 numbers. 

Find 3 × 2 × 5. 

Find the missing numbers in the patterns. Then multiply 

them together to unlock the top number of the pyramid. 

Under each pyramid, write multiplication sentence to show 

how you unlocked the pyramid. 


2. 

1. 

18 18 

24 

33 66 

4 6 

22 

The Associative Property of 


The Commutative Property of 


12 

8 10 

When multiplying, the grouping of the 


When multiplying, the order of the 


2 × 12 = 24 3 × 6 6 = 18 

You can use 

the Associative 

Property to 

group two 

factors. 

3 × 2 × 5 = 30 

3 × (2 × 5) = 30 

(3 × 2) × 5 = 30 

You can use the 

Commutative 

Property to 

switch the order 

of the numbers 

3, 2, and 5. 

3 × 2 × 5 = 30 

2 × 5 × 3 = 30 

5 × 2 × 3 = 30 


3. 4. 


30 24 28 

18 40 0 

28 28 

36 56 

24 24 

54 36 

0 00 45 

1. 5 × 3 × 2 = 2. 2 × 2 × 6 = 3. 7 × 4 × 1 = 

4. 3 × 2 × 3 = 5. 5 × 4 × 2 = 6. 7 × 8 × 0 = 

7. 2 × 7 × 2 = 8. 3 × 6 × 2 = 9. 8 × 7 × 1 = 

10. 3 × 4 × 2 = 11. 6 × 3 × 3 = 12. 6 × 2 × 3 = 

13. 8 × 9 × 0 = 14. 6 × 5 × 0 = 15. 9 × 1 × 5 = 



32 

4 88 

100 

5 

20 20 

5 × 20 = 100 4 4 × × 8 = 32 

5. Create your own pyramid for a friend to unlock. 

16. 5 × 2 × = 80 17. × 2 × 6 = 24 

18. 1 × 7 × 3 = 19. × 2 × 5 = 20 

8 22 

21 2 



Answers

Name Date 



5–8 

Name Date 

3AF1.5 

3AF1.5 



5–8 



6 4 04 0 

32 15 


1. 1 × 2 × 3 = 2. 5 × 2 × 4 = 

1. 2 × 2 × 6 = 2. 1 × 8 × 4 = 

3. 8 × 2 × 2 = 4. 3 × 5 × 1 = 

3. 9 × 3 × 2 = 4. 3 × 3 × 1 = 

14 0 

63 24 

5. 7 × 2 × 1 = 6. 8 × 8 × 0 = 

5. 5 × 2 × 4 = 6. 9 × 1 × 0 = 

7. 3 × 3 × 7 = 8. 4 × 3 × 2 = 

7. 6 × 3 × 1 = 8. 8 × 3 × 2 = 

9. 4 × × 4 = 32 10. 5 × × 1 = 45 


9. 2 × × 2 = 4 10. 3 × × 1 = 12 

11 4 

11. × 6 × 2 = 12 12. × 6 × 1 = 12 

11. × 4 × 2 = 56 12. × 2 × 3 = 30 

7 5 

13. 3 × × 4 = 24 14. 6 × 9 × = 0 

24 32 

54 9 

40 0 

18 48 

2 99 

1 22 

2 0 

5 4 


15. 1 × × 3 = 15 16. 5 × × 3 = 60 



Solve. 

13. Angie collects pairs of earrings. She hangs them on an earring 

tree. On the first row she hung 9 pairs, on the second row 

she hung 7 pairs, and on the third row she hung 5 pairs. 

If she continued this pattern, how many pairs would Angie 

hang on the fourth row? How many pairs of earrings does 

she have in all four rows? 

3 3 pairs 

24 pairs 

14. Fred made a display with a deck of playing cards. In the first 

row he used 6 cards. In the second row he used 12 cards. In 

the third row he used 18. In the fourth row, 24. If the pattern 

keeps up, how many cards will be in the sixth row? 


17. Tony and his friends had a pizza party. They bought 2 pizzas, 

each cut into 8 slices. Tony put 3 slices of banana pepper on 

each piece. How many slices of banana peppers did he use? 

48 slices slices 

18. Tony also bought 3 packs of soda in cans. Each pack held 

6 cans. How many cans of soda did Tony buy? 

18 18 cans 

19. Which of the following does not belong with the other three? 

(1 × 3) × 2 = 1 × (3 × 2) (6 × 3) × 2 = 6 × (3 × 2) 

2 × (6 × 1) = (2 × 6) × 1 5 × (3 × 1) = (5 × 5) × 2 

5 × (3 (3 × 1) 1) = (5 (5 × 5) 5) × 2 

36 36 cards cards 





Name Date 

5–8 

Name Date 

3AF1.5 

Enrich 


3AF1.5 



5–8 


Help the leprechaun find his pot of gold. Start at the leprechaun. 

Find his path by multiplying numbers as you go. When all the 

numbers are in the correct path, the product is 45. Shade the 

path the leprechaun should follow. 

Solve. 

1. Mallory and her 4 friends are setting up a lemonade stand. 

They each brought 2 bags of lemons. Each bag has 4 lemons. 

How many lemons do the girls have altogether? 

40 lemons 


1 

2. Mallory set up 2 tables with 3 containers of lemonade 

on each. Each container has 8 ice cubes. Write a number 

sentence to find the number of ice cubes she used. 

(2 (2 × 3) 3) × 8 = 48 ice cubes cubes 

6 

5 

3 

2 

3. Two of Mallory’s friends were each serving three customers at 

each table. Write a number sentence to show the number of 

customers the girls were serving. 


2 

3 

5 

2 × 2 × 3 = 12 customers customers 

5 

4 

1 

45 


4. Every hour, 5 people stopped for lemonade and spent $2 

each. After 4 hours, how much had the girls earned? 

$40 $40 

5. At the end of the day, Mallory’s 4 friends each had two 

$5-bills. How much did Mallory’s friends earn altogether? 

$40 $40 



Answers

Name Date 



5–9 

Name Date 

3AF2.2 

3AF2.2 

Reteach 


5–9 



A rule tells you what to do. This works in math too. 

x 9 

3. 

x 2 

2. 

x 4 

1. 

To build a boxcar, Bob needs to put 4 wheels on the corners 

of a wooden box. If he wanted to build 4 boxcars, how many 

wheels would he need? 

7 

5 

6 

Step 1 Find a pattern. 

72 

14 


8 

You know that 1 boxcar = 4 wheels. 

So, 2 boxcars = 8 wheels. 

6. x 2 

x 6 

5. 

x 3 

4. 

The pattern or rule is to multiply by 4. 

Step 2 Extend the pattern. 

42 

30 

3 boxcars = 3 × 4 or 12 wheels. 

1 

8 

18 

24 

3 × 4 = 12 

4 boxcars = 4 × 4 = 16 wheels 


48 

9. x 2 

8. x 10 

7. x 4 

18 

9 

90 

30 

40 

8 


10. On Monday, there were 5 flowers blooming in the garden. 

On Tuesday, there were 10 flowers blooming. There were 15 

by Wednesday. By Friday, how many flowers were blooming? 


So, Bob needs 16 wheels. 

Practice. 

1. For every 2 wheels that Bob bought, the man in the store 

gave him 2 free wheels. When Bob bought 16 wheels, how 

many did he get free? 

8 wheels wheels 

2. Write the rule for each table. Then, complete the table. 

x 5 

Rule: 

x 3 

Rule: 

x 2 

Rule: 

Output 

Input 

Output 

Input 

Output 

Input 

25 

5 

12 

4 

6 

3 

25 flowers flowers 

30 

6 

15 

5 

10 

5 

25 

21 

7 

35 

5 

7 

24 

8 

7 14 

9 18 





Name Date 

Name Date 

3AF2.2 



5–9 

3AF2.2 



5–9 




1. There are 24 crayons in 3 boxes. There are 32 crayons in 

4 boxes. How many crayons are in 5 boxes? 

× 8 

Rule: 

40 crayons 

Output 

Input 

24 

3 

32 

4 

2. There are 10 strawberries in 2 boxes and 15 strawberries in 

3 boxes. How many strawberries are in 4 boxes? 

40 

5 

56 

7 

1. 2. 3. 

Rule: × × 5 

Rule: × 6 

Input Output Output 

Input Output 

3 15 15 

4 24 

4 20 

5 30 

6 30 

7 42 

9 45 

8 48 


20 20 strawberries 

strawberries 

3. A farmer grows carrots. Each row has 5 carrots. How many 

carrots are there in a garden with 7 rows? a garden with 

× 9 

Rule: Rule: 

4. 5. 

Rule: × 7 

Output 

Input 

Output 

Input 

8 rows? a garden with 9 rows? 

35 carrots; 40 carrots; 45 carrots 

36 

4 

14 

2 

54 

6 

21 

3 



4. After 6 weeks, Russ saved $60. By the end of the next week, 

he had $70. How much did he save by the third week? 

81 

9 

35 

5 

90 

10 

56 

8 

$30 

5. The amusement park sold ride tickets in packs of 5, 10, 15, 

20 tickets. What would a pack of 10 tickets cost if 20 tickets 


cost $8? 

0 1 21 2 

$4 

6. 8 × 2 × 0 = 7. 3 × 4 × 1 = 

8. 2 × 5 × 2 = 9. 2 × × 2 = 16 

20 4 

6. A recipe calls for 2 onions for one batch. Two batches need 

4 onions. How many onions are needed for four batches? 

8 8 onions onions 

10. Sal wants to make oatmeal for himself and his brother. The 

directions say to add 2 cups of boiling water to the oatmeal 

for 1 serving. Both Sal and his brother want double servings. 

How many cups of boiling water will Sal need to measure? 

8 cups cups 



Answers

Name Date 

Name Date 

Vocabulary Test 

5 

3AF2.2 

Enrich 

What’s My Rule? 

5–9 

Match each word to its definition. Write your answers on 

the lines provided. 

Find and extend the rule for each table. Then write a multiplication 

sentence that tells what completes each table. 

Answers (Lesson 5 –9 and Vocabulary Test) 

A. a number that divides into a whole 

number evenly. It is also known 

as a number that is multiplied by 

another number. 

1. Associative property of 

Multiplication E 


Input 0 1 2 3 


2 × 4 = 8 

2. Commutative Property of 

B. If you multiply a number by 1, the 

Multiplication F 

product is the same as the given 

number. 

3. factor A 

C. a sequence of numbers, figures, 

or symbols that follows a rule or 

design 

4. Identity Property of 

D. the answer to a multiplication 

Multiplication B 

problem; It also refers to expressing 

a number as product of its factors. 

5. pattern CC 

E. the property that states that the 

grouping of the factors does not 

change the product 

6. product D 

F. the property that states that the 

order in which two numbers are 

multiplied does not change the 

product 

Multiply by 2 


Input 1 2 3 4 

Output 8 16 24 32 

8 × 5 = 40 

Multiply by 8 


Input 1 2 3 4 

Output 7 14 21 28 




Input 0 1 2 3 



Input 4 5 6 7 

Output 36 45 54 63 


7 × 5 = 35 

Multiply by 7 

3 × 4 = 12 

Multiply by 3 

9 × 8 = 72 

Multiply by 9 





Name Date 

Oral Assessment (continued) 

5 

Name Date 

Oral Assessment 

5 

6. If there were 10 cars racing in each race, how many cars would have raced 

over 2 days? 

Put 3 paperclips, 4 erasers, and 2 pencils on the table. 

60 cars 

Read each question aloud to the student. Then write the student’s answers on 

the lines below the question. 


1. If you multiply the amount of paperclips by the amount of erasers what do 

you get? 

Answers (Oral Assessment) 

Sample answer : I know there are 6 races. S0, 6 × 10 = 60. 

Assessment 

12 

8. If there was one additional race on Friday, where 10 cars raced, how many 

cars would have raced over the 3 days? 

2. Multiply that product by the amount of pencils. What is the product? 

24 

70 cars 




Sample answer : There are 7 races with 10 cars in each. 7 × 10 = 70 

3. If you change the order and first multiply the number of pencils by the 

number of erasers, and then that product by the number of paperclips, 

would the final product be the same? 

Yes; 24 


Sample answer : I multiplied 2 × 4 and got 8. Then I multiplied 8 × 3. 

5. There were 2 car races on Saturday and 4 on Sunday. If there were 8 cars 

racing in each race, how many cars raced over 2 days? 

48 cars 



Answers


Diagnostic Assessment Chapter Pretest Quiz 1 (5–1 through 5–3) 

Page 54 Page 55 Page 56 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12 

5 

16 

20 

3 × 4 = 12 

3 × 5 = 15 

6 × 2 = 12 

no 

4 corn 

muffins 

count by 

5s; 35, 40 

count by 

3s; 18, 21 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

13. 

6 

30 

28 

32 

54 

24 

36 

60 

30 

48 

21 

24 

12 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

18 

21 

48 

54 

12 


Input 

3 

6 

10 

0 

18 

24; 30 

Output 

9 

18 

30 

0 




Quiz 2 (5–4 through 5–6) Quiz 3 (5–7 through 5–9) Mid-Chapter Review 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

28 

35 

48 

49 

72 

42 

64 

18 

27 

9 

18 

9 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

20 

27 

56 

12 

5 

8 

40 

2 

16, 20 


1. 

2. 

3. 

4. 

5. 

6. 

3 × 7 to get 42 

7. 

8. 

9. 

B 

F 

D 

G 

C 

You can 

organize 

data in a 

table. 

Double the 

answer to 

Check student 

problem to include 

multiplying by 3. 

The known fact 

is 3 × 5. 

Answers


Chapter Test, Form 1 Chapter Test, Form 2A 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

C 

H 

C 

G 

B 

H 

D 

8. 

9. 

10. 

11. 

12. 

13. 

14. 

F 

D 

F 

A 

H 

D 

F 

(continued on the next page) 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

D 

J 

C 

J 

C 

H 

D 




Chapter Test, Form 2A Chapter Test, Form 2B 


8. 

9. 

10. 

11. 

12. 

G 

B 

J 

C 

F 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

B 

F 

C 

G 

B 

H 

C 


8. 

9. 

10. 

11. 

12. 

13. 

14. 

F 

B 

H 

A 

H 

A 

F 

Answers


Chapter Test, Form 2C Chapter Test, Form 2D 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

28 

27 

48 

49 

24 

1 × 8 × 10; 

80 blueberries 

2 × 4= 8; 

10 - 8 = $2 

7 × 3 × 2 

42 bags 

< 

= 

11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

9 

1 

72 

60 

9 

35 

$48 

$30 

34 

26 

(continued on the next page) 


1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

36 

63 

24 

45 

32 

80 raisins 

$4 

40 bags 

< 

= 




Chapter Test, Form 2D Chapter Test, Form 3 


11. 

12. 

13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

9 

4 

27 

54 

4 

12 

$30 

$18 

22 miles 

23 people 

1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

12. 

54 

81 

56 

64 

64 

54 54 

80 chocolate 

chips, 

100 walnuts 

$2 

60 bags 

> 

< 

= 


13. 

14. 

15. 

16. 

17. 

18. 

19. 

20. 

2 

3 

3 

24 slices 

$40 

$39 

32 miles 

28 people 

Answers



Scoring Rubric 

Level Specific Criteria 

4 The student demonstrates a thorough understanding of the mathematics 

concepts and/or procedures embodied in the task. The student has 

responded correctly to the task, used mathematically sound procedures, and 

provided clear and complete explanations and interpretations. The response 

may contain minor flaws that do not detract from the demonstration of a 

thorough understanding. 

3 The student demonstrates an understanding of the mathematics concepts 

and/or procedures embodied in the task. The student’s response to the 

task is essentially correct with the mathematical procedures used and 

the explanations and interpretations provided demonstrating an essential 

but less than thorough understanding. The response may contain minor 

errors that reflect inattentive execution of the mathematical procedures 

or indications of some misunderstanding of the underlying mathematics 

concepts and/or procedures. 

2 The student has demonstrated only a partial understanding of the 

mathematics concepts and/or procedures embodied in the task. Although 

the student may have used the correct approach to obtaining a solution or 

may have provided a correct solution, the student’s work lacks an essential 

understanding of the underlying mathematical concepts. The response 

contains errors related to misunderstanding important aspects of the task, 

misuse of mathematical procedures, or faulty interpretations of results. 

1 The student has demonstrated a very limited understanding of the 


student’s response to the task is incomplete and exhibits many flaws. 

Although the student has addressed some of the conditions of the task, 

the student reached an inadequate conclusion and/or provided reasoning 

that was faulty or incomplete. The response exhibits many errors or may be 

incomplete. 

0 The student has provided a completely incorrect solution or 

uninterpretable response, or no response at all. 






Sample Answers 

In addition to the scoring rubric found on page A32, the following sample 

answers may be used as guidance in evaluating open-ended assessment items. 

1. a. Answers will vary. Sample answer: 

You can use skip counting to 

multiply a number by 3 by adding 

3 to the number over and over 

again. For example: to find 3 × 

4 you can count 3 jumps of four 

(4, 8, 12) . You can also draw 

an array to multiply by 3. For 

example: to find 6 × 3 you can 

count 3 rows of 6. 

b. You can draw a picture to help 

solve a multiplication problem. 

For example: If you know there 

are 3 children and each child 

is wearing two gloves, you can 

draw a picture to find out how 

many gloves there are in all. 

c. Samantha goes to the pet store. 

There are black cats, white cats, 

spotted cats and brown cats. 

She notices that there are 3 of 

each color. How many cats are 

there altogether? 

Answer: 12 

2. Answers may vary slightly. Sample 

answer: 

Step 1: 


the first row. 


the second row. 

I know that there will be 12 chairs 

in the third row. 

I need to find how many chairs will 

be in the fifth row. 

Step 2: 

My plan is to organize the data in a 

table and then look for a pattern. 

Step 3: 

I will first put the information in a 

table. 

1st 2nd 3rd 4th 5th 

6 9 12 15 18 

I will then look for a pattern. I 

see that the pattern is +3, so I 

complete the chart. 

So, there will be 18 chairs in the 

fifth row. 

Step 4: 

I will check my work. 

I look back at the problem 

6 + 3 = 9 

9 + 3 = 12 

12 + 3 = 15 

15 + 4 = 18 

There are 18 chairs in the fifth row. 

So, I know I am correct. 


Answers




1. 

2. 

3. 

B 

H 

A 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

J 

B 

H 

A 

F 

D 

G 


11. 

12. 

13. 

14. 

15. 

16. 

1 

2 

3 

36 

21 21 

9 yards or 

wrapping 

paper and 

18 yards of 

ribbon

Chapter 5 Resource Masters - Macmillan/McGraw-Hill

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