197A Chapter 4

About the MathProfessional Development

LESSON AT A GLANCE

Interactive Student Edition

Personal Math Trainer

Math on the Spot

Animated Math Models

iTools: Counters

iTools: Number Lines

HMH Mega Math

F C R Focus:Common Core State Standards3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement

quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

Also 3.OA.A.1, 3.OA.C.7

MATHEMATICAL PRACTICESMP1 Make sense of problems and persevere in solving them. MP4 Model with mathematics.MP7 Look for and make use of structure.

F C R Coherence:Standards Across the GradesBefore2.OA.A.1

Grade 33.OA.A.3

After4.OA.A.2

Multiply with 5 and 10

LESSON 4.2

Teaching for DepthThis lesson presents different ways to represent multiplication with the factors 5 and 10. Different strategies, such as making jumps on a number line and skip counting by 5s or 10s, help students develop a deeper understanding of multiplication.

In this lesson, students further explore the concept of multiplication by finding unknown factors given the product and one factor or a picture and one factor.

The goals are to make multiplying by 5 or 10 flexible and fast and to deepen understanding of what multiplying by 5 or 10 means through visual representation, exploring strategies, and solving problems in context.

Professional Development Videos

FOCUS COHERENCE RIGOR

Learning ObjectiveUse skip counting, a number line, or a bar model to multiply with the factors 5 and 10.

Language ObjectiveStudents explain to a partner how you multiply with 5 and 10.

Materials MathBoard

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your OwnLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 189J.

ENGAGE1

Lesson 4.2 197B

Daily RoutinesCommon Core

7 7 7 7 77 7 7 77

777 7 7

7

Books Read2 3 4 510

Fluency BuilderMaterials Multiplication Table (see eTeacher Resources)

Multiplication Table and Patterns Have students practice multiplication facts for 2 and 4. Give students copies of a blank multiplication table.

• Review how to fill in the table by pointing out that the numbers on the top and side are the factors and that the products are written in the boxes where the rows and columns meet.

• Have students complete the rows for 2 and 4.

• After students complete the rows, discuss any patterns they see.

Problem of the Day 4.2Hiro made a line plot to show the number of books read by the students in his class. How many people read more than 3 books?

Vocabulary multiple

Interactive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can you multiply with 5 and 10?

Making ConnectionsInvite students to tell you what they know about prairie dogs.

What is a prairie? a grassy, flat area What is a prairie dog? a small, furry animal Where do prairie dogs live? in the ground in grassy plains areas, or prairies How do prairie dogs live, alone or in groups? In groups, in the same burrows, and they have many burrows in one area

Learning ActivityWhat is the problem the students are trying to solve? Connect the story to the problem.

• How many burrows is Pedro looking at? 6 burrows

• Are the same number of prairie dogs in each burrow? yes

• How many prairie dogs are in each burrow? 10 prairie dogs

• What operation combines equal groups? multiplication

Literacy and MathematicsChoose one or more of the following activities.

• Ask students to read the question aloud and then restate it in their own words.

• Invite students to write a story about homes of other animals. Suggest that the number of animals in each home be the same so that students can multiply to find the total number of animals.

5

How can you multiply with 5 and 10?

EXPLORE2

0 5 10 15 20 25 30 35 40 5045

Unlock the ProblemUnlock the Problem

MATHEMATICAL PRACTICES 1MathTalk MATHEMATICAL PRACTICES 1MathTalk

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Chapter 4 197

Use skip counting.

Skip count by 5s until you say 6 numbers.

5, _, _, _, _, _

6 × 5 = _

So, Marcel needs _ strings in all.

Marcel is making 6 toy banjos. He needs 5 strings for each banjo. How many stringsdoes he need in all?

Multiply with 5 and 10Essential Question How can you multiply with 5 and 10?

Lesson 4.2

• How many banjos is Marcel

making? __• How many strings does each

banjo have? __

Example 1 Use a number line.

Each string is 10 inches long. How many inches of string will Marcel use for each banjo?

Think: 1 jump = 10 inches

• Draw 5 jumps for the 5 strings. Jump 10 spaces at a time for the length of each string.

• You land on 10,_, _, _, and _. 5 × 10 = _

The numbers 10, 20, 30, 40, and 50 are multiples of 10.

So, Marcel will use _ inches of string for each banjo.

A multiple of 10 is any product that has 10 as one of its factors.

Operations and Algebraic Thinking—3.OA.A.3 Also 3.OA.A.1, 3.OA.C.7

MATHEMATICAL PRACTICESMP1, MP4, MP7

Analyze What do you notice about the multiples of 10?

50403020

50

10 15 20 25 30

30

6 banjos

5 strings

30

50

Possible answer: the ones digit in the multiples of 10 is zero.

Name

5. How are all of the products in Exercise 4 alike?

7 10 10 2

6 60 70 1

3 5 0 5

0 9 5 25

4 10 10 2

7 20 90 9

6 5 7 5

1 5 8 40

1. 5 3 5

3 5 30

5 3 5

3 5 35

2. 3 5 70

10 3 5

10 3 5

3 5 40

3. 5 3 5

5 3 5

3 5 45

3 5 15

4. 3 5 20

10 3 5

3 5 10

10 3 5

Unknown Numbers

Use the numbers in each oval to complete four different number sentences. Use each number in the oval only once.

Lesson 4.2Enrich

Possible answers are shown. 8

51

5

20

90

2

9

10

57

0

255

0

10

5

5

606

10

2

707

1

10

3

9

4

7

6

40

Possible answer: they are all even. The ones digit is always 0.

4-8 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

Multiply with 5 and 10

You can use an array to multiply with 5.

Find the product. 5 3 4

Step 1 Make an array to show 5 3 4.Show 5 rows of 4 tiles.

Step 2 Count the tiles.5 rows of 4 tiles 5 20 tiles

So, 5 3 4 5 20.

You can use doubles to multiply with 10.

Find the product. 6 3 10

Think: 5 1 5 5 10

Multiply with 5. 6 3 5 5 30

Then double the product. 30 1 30 5 60

So, 6 3 10 5 60.

Find the product.

1. 2 3 5 5 2. 10 3 2 5 3. 5 3 5 5 4. 5 3 1 5

5. 10 3 1 5 6. 10 3 5 5 7. 3 3 5 5 8. 10 3 7 5

9. 10 3 4

_

40

10. 6 3 5

_

30

11. 9 3 5

_

45

12. 10 3 3

_

30

13. 5 3 2

_

10

14. 10 3 6

_

60

15. 8 3 5

_

40

16. 10 3 8

_

80

Lesson 4.2Reteach

70

5

15

25

50

20

10

10

4-7 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

DifferentiatedInstruction1

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197 Chapter 4

Enrich 4.2Reteach 4.2

Unlock the ProblemMATHEMATICAL PRACTICES

Be sure students understand what the numbers in the problem represent. MP2 Reason abstractly and quantitatively. • If there were 5 instruments with 6 strings

each, how would the skip counting be different? Possible answer: I would count by 6s instead of by 5s.

Example 1Help students see that each jump represents one string. Have them count aloud as they make each jump.A counting number is a whole number that can be used to count a set of objects (1, 2, 3, and so on). Explain that a multiple is a number that is the product of a given number and a counting number. Give examples of multiples of 5: 5, 10, 15, 20, 25; and multiples of 10: 10, 20, 30, 40, 50.• Why are multiples of 10 also multiples of 5?

Since 5 is a factor of 10, 10 is a multiple of 5. So, every multiple of 10 is also a multiple of 5.

MP3 Construct viable arguments and critique the reasoning of others.• When you multiply with 10, you can multiply

with 5 and then double the product. Explain how you would find the product 6 × 10 using this strategy. Possible answer: I would multiply 6 × 5 = 30. Then I can double 30. Since 30 + 30 = 60, the product 6 × 10 = 60.

MathTalk Use Math Talk to focus on students’

understanding that multiples of 10 always have 0 in the ones place.

ELL Strategy: Elicit Prior KnowledgeRemind students of previous learning by having them use a number line to skip count aloud by 2s, while they draw the jumps from 0–12.• Have students count the number of jumps it

took to get to 12.

• How many jumps by 2s did it take to reach 12 on the number line? 6

• Model the multiplication equation, 2 × 6 = 12.

• Have students follow the steps to skip count by 4s.

LESSON 4.23.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

COMMON ERRORS

COMMON ERRORS

EXPLAIN3

Quick Check

If

Rt I RR1

2

3

Quick Check

If

Rt I 1

2

3

Then

0 5 10 15 20 25 30 35 40

10¢ 10¢ 10¢

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MathTalk MATHEMATICAL PRACTICES 3

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198

Example 2 Use a bar model.

Marcel bought 3 packages of strings. Each package cost 10¢. How much did the packages cost in all?

So, the packages of strings cost _ in all.

Share and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and ShowShare and Show MATHBOARDMATHBOARDMATHBOARDMATHBOARDMATHMATHMATHMATHBOARDBOARDBOARDBOARD

1. How can you use this number line to find 8 × 5?

2. 2 × 5 = _ 3. _ = 6 × 10 4. _ = 5 × 5 5. 10 × 7 = _

Find the product.

6. 10 × 4

_

7. 5 × 6

_

8. 10 × 0

_

9. 5 × 3

_

10. 7 × 5

_

11. 5 ×10

_

12. 4 × 5

_

13. 9 ×10

_

THINK

1 unit → 10¢

3 units → _ × _

RECORD

_ × _ = _

MODEL

Apply How can knowing 4 × 5 help you find 4 × 10?

Possible answer: start at 0, make 8 jumps of 5 spaces each. 5, 10, 15, 20, 25, 30, 35, 40,

so 8 × 5 = 40.

Possible explanation: if you know 4 × 5 = 20, you can double 20 to fi nd the product of 4 and 10; 20 + 20 = 40, so 4 × 10 = 40.

10 702560

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35

30

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Advanced LearnersAdvanced LearnersAdvanced Learners

Lesson 4.2 198

Error Students may write incorrect products for multiplications with 5 because they skip counted incorrectly.

Example In Exercise 7, students may write 6 × 5 = 35, instead of 6 × 5 = 30.Springboard to Learning Remind students to keep track of the number of times they skip count. The other factor tells them how many times to skip count.

Example 2Ask students to point to the bar model and say aloud what each section represents. Make sure students understand that each section represents one package of string. Then discuss what the total length of the bar represents.

Share and Show MATHBOARDMATHBOARDMBOARDMMMMBOARDBOARDBOARDBOARDMATHATHABOARDMMMMAAAATHATHATHTHTHATHATHATHAATHAAAATHAAATHATHTHTHATHATHAAATHATHATHAAATHABOARDBOARDBOARDBOARD

The first problem connects the learner to the learning model. Have students use the MathBoard to explain their thinking.

MathTalk Use Math Talk to reinforce the

doubles strategy students learned in the previous lesson. Students should recognize that the same reasoning that allows them to use doubles when multiplying with 4 can be used when multiplying with 10. • Explain how knowing 7 × 3 can help you find

7 × 6. If you know 7 × 3 = 21, you can double 21 to find the product of 7 and 6; 21 + 21 = 42, so 7 × 6 = 42.

Use the checked excercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

a student misses the checked excercises

Differentiate Instruction with • Reteach 4.2 • Personal Math Trainer 3.OA.A.3 • RtI Tier 1 Activity (online)

VisualIndividual

Materials Analog Clockface (see eTeacher Resources)

• Ask students how each minute is shown on the clock. short lines between the numbers and at the numbers

• How many spaces are there between 12 and 1 on the clock? 5 spaces How many minutes does this represent? 5 minutes

• How many spaces are there between 12 and 2 on the clock? 10 spaces How many minutes does this represent? 10 minutes

• Have students write the related multiplication facts for each number on the clock using a factor of 5. 1 × 5 = 5, 2 × 5 = 10, 3 × 5 = 15, etc.

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Chapter 4 • Lesson 2 199

Name

On Your OwnOn Your Own

Find the product.

14. 5 × 1 = _

18. 10 × 0 = _

15. _ = 10 × 2

19. 10 × 5 = _

16. _ = 4 × 5

20. _ = 1 × 5

17. 10 × 10 = _

21. _ = 5 × 9

22. 3 × 4

_

23. 5 × 0

_

24. 4 × 8

_

25. 10 × 5

_

MATHEMATICALPRACTICE 7 Identify Relationships Algebra Use the pictures

to find the unknown numbers.

MATHEMATICALPRACTICE 4 Use a Diagram Complete the bar model to solve.

3 × _ = _ _ × 3 = _

______ ______

26. 27.

28. Marcel played 5 songs on the banjo. If each song lasted 8 minutes, how long did he play?

29. There are 6 banjo players. If each player needs 10 sheets of music, how many sheets of music are needed?

30. DEEPER Chris has 5 stacks of DVDs on a shelf. Each stack has 10 DVDs. If Chris adds 2 more identical stacks of DVDs to the shelves, how many DVDs will Chris have?

31. DEEPER Mark is making 10 kites. He uses 5 yards of ribbon for each kite. He has already made 2 of the kites. How many yards of ribbon will Mark need to make the rest of the kites?

50 5

20

45

5

0

20 100

012 5032

155 3010

40 minutes

70 DVDs

60 sheets of music

40 yards

199 Chapter 4

On Your OwnIf students complete the checked excercises correctly, they may continue with the On Your Own section. MP7 Look for and make use of structure. Exercises 26 and 27 require students to interpret pictures to find unknown factors in multiplication sentences.MP4 Model with mathematics. Exercises 28 and 29 require students to label a bar model and use it to answer the question.MP3 Construct viable arguments and critique the reasoning of others. Discuss different strategies that can be used to find unknown factors. Write × 5 = 25 on the board. Tell students that one strategy they can use to find the unknown factor in this problem is to find how many 5s are in 25. Have students use this strategy by starting at 0, counting on by 5s to 25, and keeping track of how many 5s are counted.

ELABORATE4

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESDEVALUATE5 Formative

Assessment

Stringed Instruments

Guitar 6

5

8

4

Banjo

Mandolin

Violin

Instrument Strings

MATHEMATICAL PRACTICES M

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200

Use the table for 32–34.

32. John and his dad own 7 banjos. They want to replace the strings on all of them. How many strings should they buy? Write a multiplication sentence to solve.

33. DEEPER Mr. Lemke has 5 guitars, 4 banjos, and 2 mandolins. What is the total number of strings on Mr. Lemke’s instruments?

34. SMARTER The orchestra has 5 violins and 3 guitars that need new strings. What is the total number of strings that need to be replaced? Explain.

35. WRITE Math What’s the Error? Mr. James has 3 banjos. Mr. Lewis has 5 times the number of banjos Mr. James has. Riley says Mr. Lewis has 12 banjos. Describe her error.

36. SMARTER Circle the number that makes the multiplication sentence true.

5 × 789

= 45

7 × 5 = 35; 35 strings

66 strings

Possible answer: Riley multiplied 4 × 3

38 strings; possible explanation: the violins will need

instead of 5 × 3. Mr. Lewis has 15 banjos.

5 × 4 = 20 strings; the guitars will need 3 × 6 = 18 strings.

Then add 20 + 18 = 38.

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

SMARTER

Lesson 4.2 200

Students read the book and determine how to use multiplication to find the total number of objects in each collection.

Students complete purple Activity Card 7 by using randomly generated factors to practice multiplication facts for 1, 2, 4, and 5.

Students complete blue Activity Card 7 by using nickels to practice counting by fives.

LiteratureCollections Times Four

ActivitiesFactor Spin

ActivitiesLine ’Em Up

Essential QuestionUsing the Language ObjectiveReflect Have students explain to a partner to answer the Essential Question. How can you multiply with 5 and 10? Possible answers: skip count; use a number line; use a bar model; draw a picture

Math Journal WRITE MathMichelle bought some pinwheels for a dollar and paid in dimes. How many dimes did she use? Explain.

MATHEMATICAL PRACTICES

MP1 Make sense of problems and persevere in solving them. Have students read the first problem and discuss how they will solve it. You may need to remind them to use the data in the table.

DEEPER

Exercise 33 requires students to organize their work so they can find the numbers they need to answer the question.

SMARTER

This item gives students a menu of three numbers from which to choose the missing factor. Students must demonstrate a knowledge of multiplying with 5 to make the multiplication sentence true.

Math on the Spot Video TutorUse this video to help students model and solve this type of Think Smarter problem.

Problem Solving • Applications

Cross-Curricular

Problem SolvingProblem Solving

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Multiply with 5 and 10

Find the product.

17. Ginger takes 10 nickels to buy some pencils at the school store. How many cents does Ginger have to spend?

_______

18. The gym at Evergreen School has three basketball courts. There are 5 players on each of the courts. How many players are there?

_______

Chapter 4 201

9. 5 × 6

_

10. 10 × 7

_

11. 5 × 3

_

12. 10 × 4

_

13. 5 × 0

_

14. 10 × 8

_

15. 5 × 2

_

16. 10 × 6

_

5. 1× 10 = ______ 6. ______ = 4 × 5 7. 5× 10 = ______ 8. 7× 5 = ______

1. 5× 7 = ______ 2. 5× 1 = ______ 3. 2 × 10 = ______ 4. ______ = 8 × 5

COMMON CORE STANDARD—3.OA.A.3 Represent and solve problems involving multiplication and division.

Lesson 4.2Practice and Homework

70 15 40

0 80 10 60

35 5 20 40

50 cents

Check students’ work.

15 players

10 20 50 35

30

19. WRITE Math Michelle bought some pinwheels for a dollar and paid in dimes. How many dimes did she use? Explain.

201 Chapter 4

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

SCIENCE SOCIAL STUDIES

Materials pictures of ants, ladybugs, and other insects

• Insects are arthropods. An arthropod is an invertebrate (an animal with no backbone) that has a segmented body.

• The insect body has 3 parts: the head, the thorax, which is the middle of the body, and the abdomen, which is the back. Insects have 6 legs.

• The mass of an object is the amount of matter the object has. An ant can carry 5, 10, and even 30 times its mass.

• Have students write and solve word problems. For example: If an ant has a mass of 3 milligrams, how much can it carry? 5 3 3 5 15 mg; 10 3 3 5 30 mg

• The United States and Canada use dollars that are worth 100 cents.

• Mexico uses new (nuevo) pesos. One peso is equal to 100 centavos. There are coins worth 5, 10, 20, and 50 centavos.

• Both Canada and the United States have nickels worth 5 cents. If you had 4 nickels, how many cents would you have? 20 cents

• If you had 6 five-centavos coins, how many centavos would you have? 30 centavos

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Field Trip Choices

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Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (3.OA.A.3)

1. Mrs. Hinely grows roses. There are 6 roses on each of her 10 rose bushes. How many roses in all are on Mrs. Hinely’s rose bushes?

2. Find the product.

5 × 8

_

Spiral Review (3.OA.D.9, 3.NBT.A.1, 3.MD.B.3)

3. Mr. Miller’s class voted on where to go for a field trip. Use the picture graph to find which choice had the most votes.

4. Zack made this table for his survey.

How many votes were cast?

5. Which of the following is an even number?

25, 28, 31, 37

6. Estimate the sum.

202

479 + 89

__

60 roses

zoo

28

47 votes

Possible answer: about 600

40

Lesson 4.2 202

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.