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©Curriculum Associates, LLC Copying is not permitted 34a LESSON OVERVIEW Lesson 5 Multiply Whole Numbers Prerequisite Skills Lesson Objectives Lesson 5 Multiply Whole Numbers Learning Progression multiplication. They use the distributive property and area models to break apart factors and compute partial products. They combine partial products to ﬁnd products. In Grade 5 students are expected to multiply ﬂuently using the standard algorithm. Students will need to be able to multiply ﬂuently using the standard algorithm when they learn to multiply decimals later in Grade 5. Students will be expected to be ﬂuent with multiplication in future grades. In Grade 4 students used basic multiplication facts and an understanding of place value to multiply three- and four-digit numbers by a one-digit number and to multiply a two-digit number by a two-digit number. They built a conceptual understanding of multi-digit multiplication by multiplying with area models and ﬁnding partial products. In this lesson students apply place-value understanding as they begin to use the standard algorithm for distributive property when one of the factors of a product is written as a sum, multiplying each addend by the other factor before adding does not change the product; for example, 3 3 12 5 (3 3 10) 1 (3 3 2) Review the following key terms. factor a number that is multiplied product the result of multiplication partial products a strategy used to multiply multi-digit numbers; the products you get in each step are called “partial products”. For example, the partial products for 124 3 3 are 3 3 100 or 300, 3 3 20 or 60, and 3 3 4 or 12. Lesson Vocabulary • Understand place value. • Recall basic multiplication facts. • Multiply two-digit numbers by two-digit numbers. • Use an area model to multiply. • Use the formula for area to solve problems. Content Objectives • Multiply three-digit numbers by two-digit numbers. • Use the distributive property to break apart factors in order to solve multi-digit multiplication problems. • Use the standard algorithm to solve multi-digit multiplication problems with whole numbers. Language Objectives • Deﬁne partial products and use the term in a discussion with a partner. • Draw an area model to represent a multi-digit multiplication problem and discuss its relationship to the partial products and product. Domain Number and Operations in Base Ten Cluster B. Perform operations with multi-digit whole numbers and with decimals to hundredths. Standards 5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm. Standards for Mathematical Practice (SMP) 1 Make sense of problems and persevere in solving them. 2 Reason abstractly and quantitatively. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics. 5 Use appropriate tools strategically. 6 Attend to precision. 7 Look for and make use of structure. 8 Look for and express regularity in repeated reasoning. CCSS Focus

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©Curriculum Associates, LLC Copying is not permitted34a

LESSON OVERVIEW

Lesson 5 Multiply Whole Numbers

Prerequisite SkillsLesson Objectives

Lesson 5 Multiply Whole Numbers

Learning Progression

multiplication. They use the distributive property and area models to break apart factors and compute partial products. They combine partial products to find products.

In Grade 5 students are expected to multiply fluently using the standard algorithm. Students will need to be able to multiply fluently using the standard algorithm when they learn to multiply decimals later in Grade 5. Students will be expected to be fluent with multiplication in future grades.

In Grade 4 students used basic multiplication facts and an understanding of place value to multiply three- and four-digit numbers by a one-digit number and to multiply a two-digit number by a two-digit number. They built a conceptual understanding of multi-digit multiplication by multiplying with area models and finding partial products.

In this lesson students apply place-value understanding as they begin to use the standard algorithm for

• distributive property when one of the factors of a product is written as a sum, multiplying each addend by the other factor before adding does not change the product; for example, 3 3 12 5 (3 3 10) 1 (3 3 2)

Review the following key terms.

• factor a number that is multiplied

• product the result of multiplication

• partial products a strategy used to multiply multi-digit numbers; the products you get in each step are called “partial products”. For example, the partial products for 124 3 3 are 3 3 100 or 300, 3 3 20 or 60, and 3 3 4 or 12.

Lesson Vocabulary

• Understand place value.

• Recall basic multiplication facts.

• Multiply two-digit numbers by two-digit numbers.

• Use an area model to multiply.

• Use the formula for area to solve problems.

Content Objectives• Multiply three-digit numbers by

two-digit numbers.

• Use the distributive property to break apart factors in order to solve multi-digit multiplication problems.

• Use the standard algorithm to solve multi-digit multiplication problems with whole numbers.

Language Objectives• Define partial products and use the

term in a discussion with a partner.

• Draw an area model to represent a multi-digit multiplication problem and discuss its relationship to the partial products and product.

DomainNumber and Operations in Base Ten

ClusterB. Perform operations with multi-digit

whole numbers and with decimals to hundredths.

Standards5.NBT.B.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Standards for Mathematical Practice (SMP)1 Make sense of problems and persevere

in solving them.

2 Reason abstractly and quantitatively.

3 Construct viable arguments and critique the reasoning of others.

4 Model with mathematics.

5 Use appropriate tools strategically.

6 Attend to precision.

7 Look for and make use of structure.

8 Look for and express regularity in repeated reasoning.

CCSS Focus

Lesson Pacing Guide

©Curriculum Associates, LLC Copying is not permitted 34b

Teacher-Toolbox.com

Whole Class Instruction

Lesson 5

Lesson 5 Multiply Whole Numbers

Small Group Differentiation

Personalized Learning

ReteachReady Prerequisite Lessons 45–90 min

Grade 4• Lesson 11 Multiply Whole Numbers

Student-led ActivitiesMath Center Activities 30–40 min

Grade 4 (Lesson 11)• 4.23 Multiplying by One-Digit Numbers• 4.24 Multiplying by Two-Digit Numbers

Grade 5 (Lesson 5)• 5.15 Use Multiplication Vocabulary• 5.16 Equivalent Multiplication Expressions

Independenti-Ready Lessons* 10–20 min

Grade 4 (Lesson 11)• Multiplying Two-Digit Numbers by

One-Digit Numbers• Multiply Whole Numbers

Teacher-led Activities Tools for Instruction 15–20 min

Grade 4 (Lesson 11) • Multiply Three-Digit Numbers by

One-Digit Numbers• Multiply by One-Digit Numbers

Day 145–60 minutes

Toolbox: Interactive Tutorial* Multiply by Two-Digit Numbers

Practice and Problem SolvingAssign pages 39–42.

Introduction

• Use What You Know 10 min• Find Out More 10 min• Reflect 5 min

Modeled and Guided Instruction

Learn About Multiplying Three-Digit Numbers• Model It/Model It 10 min• Connect It 10 min• Try It 5 min

Day 245–60 minutes

Guided Practice

Practice Multiplying Whole Numbers• Example 5 min• Problems 7–9 15 min• Pair/Share 15 min• Solutions 10 min

Practice and Problem SolvingAssign pages 43–44.

Day 345–60 minutes

Independent Practice

Practice Multiplying Whole Numbers• Problems 1–6 20 min• Quick Check and Remediation 10 min• Hands-On or Challenge Activity 15 min

Toolbox: Lesson QuizLesson 5 Quiz

* We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson.

Introduction

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Lesson 5 Multiply Whole Numbers

Lesson 5 Multiply Whole Numbers

Mathematical Discourse

1 How does knowing the width of the grassy section and the cement sidewalk help you solve this problem?

This helps break the factor 46 into tens and ones. The grassy section is 40 (4 tens) feet wide. The cement sidewalk is 6 feet wide. This helps us find the partial products.

2 How does the area model help you solve the problem?

It shows a picture of the product and breaks apart the factors to easily identify them and help find the partial products.

3 Why is it okay to add the partial products?

The area model shows that the sum of the partial products is the total area, or the entire product.

Students explore multiplying a three-digit number by a two-digit number. Students use the idea of an area model, along with the distributive property. Then students investigate the partial products that result from multiplying a three-digit number by a two-digit number. They break apart one factor into a sum based on place value. Then they combine the partial products using the format of the standard algorithm.

• Work through Use What You Know as a class.

• Tell students that this page models a way to think about multiplying greater numbers.

• Have students read the problem at the top of the page.

SMP TIP Make Sense of ProblemsHelp students to make sense of the problem. Draw a simplified model, showing only the outer (127 3 46) rectangle. Ask students how the model helps them understand the question that is asked. Then fill in the details and ask how the details in the model help them make a plan and find the solution. (SMP 1)

• Have students describe the area model shown. Point out the grassy section and the section for the cement sidewalk.

• Discuss the first three questions. Point out that students now have a plan for solving the problem.

Mathematical Discourse 1

• Have students find the partial products for the grassy section and the cement sidewalk.

• Ask students to explain their answers for the last two questions.

Mathematical Discourse 2

• Be sure students understand why the two partial products must be added in the final step.

Mathematical Discourse 3

At A Glance

Step By Step

Introduction

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Use What You Know

Lesson 5 Multiply Whole Numbers

Lesson 5Multiply Whole Numbers

The area model above shows the length and width of each space.

a. What is the total length of the outdoor space?

What is the total width?

b. How is the area of each space found?

c. How can you find the total area?

d. The product of 127 and 46 is the total area of the outdoor area. How can you find the

area for grass?

How can you find the area for the sidewalk?

e. What is the total area?

A mall is designing an outdoor space. The available space is 127 feet by 46 feet. The plan is for a grassy section with a width of 40 feet. Next to the grass will be a cement sidewalk with a width of 6 feet. What is the area of the available space in square feet?

100 feet

40 feet

6 feet

46 feet

20 feet 7 feet

127 feet

? ? ?

??4,000 square feet

In grade 4, you multiplied two-digit numbers by two-digit numbers. Now you’ll multiply three-digit numbers by two-digit numbers. Take a look at this problem.

not to scale

5.NBT.B.5

Possible answer: Multiply the length and

width of each rectangular section in the model.

127 feet

46 feet

Possible answer: Add the partial products together.

Possible answer: Add the partial products 4,000, 800, and 280

products 600, 120, and 42

5,842 square feet

34

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Lesson 5

Lesson 5 Multiply Whole Numbers

©Curriculum Associates, LLC Copying is not permitted. 35

Find Out More

Lesson 5 Multiply Whole Numbers

One way to multiply multi-digit numbers is to find partial products. Break apart one of the factors into parts. Then multiply each of the parts by the other factor to get parts of the product, or partial products. Then, add the partial products to find the total product.

• One way to show using partial products to find 127 3 46:

Break apart 46 into (40 + 6): 127 3 46 5 127 3 (40 1 6)

Find each partial product.

1273 40

5,080

1273 6

762

partial products

Then find the sum of the two partial products.

5,080 1 762 5 5,842

• Another way to show using partial products to find 127 3 46:

1273 46

7621 5,080

5,842

area for sidewalk area for grass

total area

Reflect1 How is multiplying by a three-digit number similar to multiplying by a

two-digit number?

Possible answer: You follow the same procedure for both by adding partial

products.

35

• Read Find Out More as a class.

• Have student volunteers find each partial product on the board to verify the results.

• Point out that the example at the end of Find Out More shows the format for the standard algorithm, which students will use throughout the lesson.

Visual Model

• Students complete Reflect in pairs or on their own. Discuss as a group.

Real-World Connection

Assign Practice and Problem Solving pages 39–40 after students have completed this section.

Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING

Visual ModelUse the area model to illustrate the standard algorithm.

• Copy the area model shown in the illustration on the previous page onto the board.

• To the right of the grassy section, write the partial product 5,080. To the right of the cement sidewalk, write the partial product 762.

• Above the partial products, write the problem 127 3 46 in standard vertical format, with a horizontal line separating the problem and the partial products.

• Draw another horizontal line below the partial products and write the “1” sign.

• Have a student write the complete product below.

Real-World Connection

Discuss with students everyday situations in which people might multiply three-digit numbers.

Example: Suppose customers in a bowling alley play 416 games every day during the month of February. That’s 416 games each day for 28 days. Ask each student to write a real-world problem that involves multiplying a two-digit number by a three-digit number. Allow students access to magazines and newspapers to gather ideas. Have students present their examples to the class. Then have students swap problems and solve them.

Modeled and Guided Instruction

36 ©Curriculum Associates, LLC Copying is not permittedLesson 5 Multiply Whole Numbers

Lesson 5 Multiply Whole Numbers

Mathematical Discourse

1 Where do you see 100 1 20 1 8 in the first Model It?

They are above the area model, and 100, 20, and 8 are factors in each row of the area model.

2 Where do you see 100 1 20 1 8 in the second Model It?

They are each factors next to the partial products in vertical format.

3 How are these related?

You multiply each part of 128 by 35 in both models.

Concept ExtensionUse the distributive property to multiply three-digit numbers mentally.

• Write “153 3 21” on the board.

• Demonstrate how to mentally multiply, thinking aloud so that students can follow each step.

• First, multiply by 20, adding the partial products as you go. 100 3 20 5 2,000 and 50 3 20 5 1,000, so that’s 3,000 so far. 3 3 20 5 60, for a partial product of 3,060.

• Next, multiply 153 by 1, and add this to 3,060. 3,060 1 100 5 3,160, plus 50 more equals 3,210, plus 3 more equals 3,213.

• Give students a problem to try with a partner, such as 144 3 32. [4,608]

Modeled and Guided Instruction

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Lesson 5

Multiplying Three-Digit Numbers

Lesson 5 Multiply Whole Numbers

Read the problem below. Then explore different ways to multiply a three-digit number by a two-digit number.

There are 128 pens in a full box. How many pens are in 35 full boxes?

Model It Use an area model to show partial products.

Sketch a rectangle with dimensions 128 by 35.

128 3 35

128 is 100 1 20 1 8.

35 is 30 1 5.

30 3 100 5 3,000 30 3 20 5 600 30 3 8 5 240

100 20 8

5 3 100 5 500

30

1

1 1

5 5 3 20 5 100 5 3 8 5 40

First row: 3,000 1 600 1 240 5 3,840

Second row: 500 1 100 1 40 5 640

So, 128 3 35 5 3,840 1 640 5 4,480.

Model It Use the distributive property to find partial products and add them.

128 3 35 5 128 3 (30 1 5)

128 3 (30 1 5) 5 (128 3 30) 1 (128 3 5)

1283 30

240600

1 3,000

3,840

(30 3 8) (30 3 20) (30 3 100)

1283 5

40100

1 500

640

(5 3 8) (5 3 20) (5 3 100)

3,840 1 640 5 4,48036

Students explore the use of an area model to multiply a three-digit number by a two-digit number. They then look at the same problem in another way, using the distributive property. Then students revisit this problem and further investigate the meaning of the partial products in solving the problem. Then they solve a new problem.

• Read the problem at the top of the page as a class.

• Have students write an equation to solve the problem. [128 3 35 5 ?]

Model It• Read Model It as a class. Have students

describe how the model shows the partial products.

Model It• Direct students’ attention to Model It. Point

out that the factor 35 is broken apart as 30 1 5.

• Have students point to where each partial product and its factors are found in the vertical multiplication. [Each partial product is shown beneath the horizontal line for the problem. Each pair of factors are shown in parentheses next to each partial product.]

• Have students indicate where the partial products are added. [last line in Model It]

• Tell students that, no matter which method is used, the process involves breaking the numbers apart to find partial products, and the result is the same.

Mathematical Discourse 1–3

Concept Extension

At A Glance

Step By Step

©Curriculum Associates, LLC Copying is not permitted 37Lesson 5 Multiply Whole Numbers

Lesson 5

Hands-On ActivityUse base-ten blocks to model multiplying with partial products.

Materials: base-ten blocks (flats, longs, and cubes)

• Say: Let’s use base-ten blocks to model part of the problem from the previous page.

• Have students draw an area model with 100, 20, and 8 along the top, and 30 and 5 on one side. Shade in the row of partial products with 5 as a factor. This is the part the students will multiply.

• Multiply 5 3 8 ones. Students place 40 ones (cubes) in the rectangle representing this partial product in the area model.

• Multiply 5 3 2 tens. Students place 10 tens (longs) in the area model.

• Multiply 5 3 1 hundred. Students place 5 hundreds (5 flats) in the area model.

• Add these partial products. Students trade 40 ones for 4 tens. Next, they trade 10 tens for 1 hundred. Verify that students have 6 hundreds, 4 tens, and 0 ones (640).

©Curriculum Associates, LLC Copying is not permitted. 37Lesson 5 Multiply Whole Numbers

Connect It Now you will compare the two ways to multiply using partial products.

2 Why is the area model divided into six sections?

3 How do the three partial products in each multiplication equation in the second

Model It relate to the three sections in each row of the area model?

4 Would the product change if 30 and 5 on the left side of the area model were

changed to 20, 10, and 5? Explain.

5 List two diff erent ways you could break up the factors in 239 3 64 to fi nd the

product. Explain why both ways would have the same product.

Try It Use what you just learned about multiplying numbers to solve this problem. Show your work on a separate sheet of paper.

6 A bookshelf at a library holds 156 books. There are 15 bookshelves in the children’s section. How many children’s books can the library place on the bookshelves?

Possible answer: Each section

shows a partial product. There are 6 partial products so there are 6 sections.

Each partial product in an equation is the same as the partial product in one

section of each row of the area model.

No; Possible explanation: Instead of a partial

product of 3,000, you would have partial products of 2,000 and 1,000. Instead

of 600, you would have 400 and 200. Instead of 240, you would have 160 and

80. The sum of all the partial products would still be the same.

200 1 30 1 9 and 60 1 4 or 100 1 100 1 30 1 9 and 50 1 10 1 4. As long as

the sum of the numbers equals the factor and you find all the partial

products, the partial products will add up to the same product.

2,340 books

37

Connect It• Point out that Connect It refers to the

problem on the previous page.

• For problems 2 and 3, make sure students can explain the relationship between each partial product and each factor.

• Have students demonstrate their solutions to problem 5 and explain why they broke up the factors the way they did.

Hands-On Activity

Try It• Students complete Try It on their own.

Circulate to provide support and monitor understanding.

6 Solution2,340 books; Students may write 156 as 100 1 50 1 6 and write 15 as 10 1 5 to find partial products. Then, they add the partial products.

Error Alert Students who wrote 936 may have forgotten to show that the “1” in 15 is 1 ten. They need to account for the ten by placing a 0 in the ones place for the partial product of 10 3 156. 10 3 156 5 1,560

Assign Practice and Problem Solving pages 41–42 after students have completed this section.

Step By Step

Mathematics PRACTICE AND PROBLEM SOLVING

Guided Practice

Teacher Notes

38 ©Curriculum Associates, LLC Copying is not permittedLesson 5 Multiply Whole Numbers

Lesson 5 Multiply Whole Numbers Guided Practice

Practice

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Lesson 5

Multiplying Whole Numbers

Example

Lesson 5 Multiply Whole Numbers

Pair/ShareHow are the regrouped ones and tens used to find the partial products?

Pair/ShareShow and explain howto solve this problemusing a differentmethod.

7 A certain dishwasher uses 29 kilowatts of energy per hour. If the dishwasher was used 156 hours last year, how many kilowatts of energy did the dishwasher use last year?

Solution

There are 366 days in a leap year and 24 hours in a day. How many hours are in a leap year?

Look at how you could show your work.

3663 241,464

1 7,3208,784

21

21

Solution

Study the example below. Then solve problems 7–9.

8,784 hours

Why does the product of 366 and 2 tens have a 0 in the ones place?

What is the role of place value when multiplying two numbers?

4,524 kilowatts

Possible student work using the standard algorithm:

1563 291,404

1 3,1204,524

15 5

1

38

Students study a model that uses the standard algorithm for multiplication. Then they solve word problems using the standard algorithm or other methods.

• Ask students to solve the problems individually. Circulate to monitor and provide support. Look for students to show complete work for the method they chose to use. Students should be able to explain what they have done.

• Pair/Share When students have completed each problem, have them Pair/Share to discuss their solutions with a partner or in a group.

• Students should be able to apply the distributive property in different ways: partial products, the area model, and the standard algorithm.

Example 8,784 hours; The standard algorithm is shown as one way to solve the problem. Students could also solve the problem by using an area model.

7 Solution4,524 kilowatts; Students could solve the problem by using the standard algorithm. See possible work on the Student Book page.

DOK 2

At A Glance

Step By Step

Solutions

Teacher Notes

©Curriculum Associates, LLC Copying is not permitted 39Lesson 5 Multiply Whole Numbers

Lesson 5

©Curriculum Associates, LLC Copying is not permitted. 39Lesson 5 Multiply Whole Numbers

Pair/ShareDoes Jared’s answer make sense?

Pair/ShareWhy is multiplication used to solve this problem? What other operation is used?

8 If 1 stamp costs 45 cents, what does a roll of 125 stamps cost in cents? What is this amount in dollars and cents?

Solution

9 Raquel can type 63 words every minute. Rick can type 73 words every minute. How many more words can Rick type than Raquel in 135 minutes? Circle the letter of the correct answer.

A 1,350

B 4,599

C 8,505

D 9,855

Jared chose B as the correct answer. How did he get that answer?

How could I first estimate the answer to this problem?

How can I use the difference in the number of words typed by Rick and Raquel every minute to solve this problem?

Possible student work using the standard algorithm:

1253 45

6251 5,000

5,625

11 2

2

5,625 4 100 5 56.25

He multiplied the number of words per minute, 63, that

Raquel can type by the number of words per minute, 73, that

Rick can type.

5,625 cents; \$56.25

39

8 Solution5,625 cents; \$56.25; Students could solve this problem by using the standard algorithm. See possible work on the Student Book page.

DOK 2

9 SolutionA; Students could use the standard algorithm to first multiply 63 3 135 and 73 3 135, and then subtract. They could also first subtract 63 from 73, and then multiply the difference, 10, by 135.

Explain to students why the other two answer choices are not correct:

C is not correct because it is how many words Raquel types in 135 minutes.

D is not correct because it is how many words Rick types in 135 minutes.

DOK 3

Assign Practice and Problem Solving pages 43–44 after students have completed this section.

Solutions

Mathematics PRACTICE AND PROBLEM SOLVING

Independent Practice

40 ©Curriculum Associates, LLC Copying is not permittedLesson 5 Multiply Whole Numbers

Lesson 5 Multiply Whole Numbers

Quick Check and Remediation

If the error is . . . Students may . . . To remediate . . .

1,144

not recognize the place value implications of multiplying by a digit in the tens place.

Have students multiply 143 3 6. Then have students multiply 143 3 20. Refer back to the original problem and remind the students that 26 5 20 1 6.

3,108

not understand how to use regrouping with the multiplication standard algorithm.

Display the standard algorithm solution next to the partial products solution and help students see where the regrouped values come from.

can solve the problem using partial products or area model, but cannot find the solution using the standard algorithm

not understand the efficiencies built into the standard algorithm.

Work through the standard algorithm step by step with students, showing them equal connections at each point. For the area model, work through cell by cell. For partial products, show how the standard algorithm handles all of the “times ones” in a single row.

any other incorrect response

need practice with basic multiplication facts.

Have students quickly draw dot arrays for each basic fact, or count by 2s or 6s, while solving the original problem.

• Ask students to use the standard algorithm and one other method to multiply 143 3 26. [3,718]

• For students who are struggling, use the chart to guide remediation.

• After providing remediation, check students’ understanding. Ask students to multiply 252 3 18. [4,536]

• If a student is still having difficulty, use Ready Instruction, Grade 4, Lesson 11.

Independent Practice

Practice

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Lesson 5

Multiplying Whole Numbers

Lesson 5 Multiply Whole Numbers

Solve the problems.

1 Mrs. Cady constructs a cube with 512 magnetic blocks. Students in her two classes will each make an identical cube. There are 28 students in one class and 25 students in the other class. How many blocks does she need for all her students?

A 5,120

B 12,800

C 14,336

D 27,136

2 What are the values of the regrouped amounts in the multiplication below?

4353 173,045

1 4,3507,395

2 3

A 2 and 3

B 20 and 3

C 200 and 30

D 2,000 and 300

3 Choose Yes or No to tell whether the expression is equivalent to 179 3 44.

a. 179 3 (4 1 4) Yes No

b. (179 3 40) 1 (179 3 4) Yes No

c. (100 3 4) 1 (70 3 4) 1 (9 3 4) Yes No

d. 4,000 1 2,800 1 360 1 400 1 280 1 36 Yes No

e. (100 3 44) 1 (70 3 44) 1 (9 3 44) Yes No

3

3

3

3

3

40

Students use the standard algorithm and other methods to solve three-digit by two-digit multiplication problems that might appear on a mathematics test.

1 Solution

D; This is a two-step problem. Add 28 1 25 to get 53 students. Then multiply 53 by 512.

DOK 2

2 SolutionC; The 2 represents 2 hundreds. The 3 represents 3 tens.

DOK 1

3 Solutiona. No; b. Yes; c. No; d. Yes; e. Yes

DOK 1

At A Glance

Solutions

©Curriculum Associates, LLC Copying is not permitted 41Lesson 5 Multiply Whole Numbers

Lesson 5

Self Check

©Curriculum Associates, LLC Copying is not permitted. 41Lesson 5 Multiply Whole Numbers

Go back and see what you can check off on the Self Check on page 1.

4 Show two diff erent ways to complete the multiplication problem.

3 1 4

3 5

1 6

3 1 4

3 5

1 6

5 At the start of the day there are 78 boxes of DVDs in a warehouse. Each box has 116 DVDs. Then 19 of the boxes are shipped. Now how many DVDs are left in the warehouse?

6 Use the distributive property two diff erent ways to fi nd the product of 127 and 32.

Possible student work using the standard algorithm.

78 2 19 5 59

1163 59

1,0441 5,800

6,844

1 53

116 3 59 5 6,844

6,844

Possible student work:

First way: 32 3 127 5 32 3 (100 1 20 1 7) 5 3,200 1 640 1 224 5 4,064

Second way: 32 3 127 5 30 3 (100 1 20 1 7) 1 2(100 1 20 1 7) 5

(3,000 1 600 1 210) 1 (200 1 40 1 14) 5 4,064

4 9

6 9 5 8 5 2

41

Hands-On Activity Model the distributive property using base-ten materials.

Materials: prepared cards with the words “1 hundred,” “1 ten,” and “1.”

• Write “13 3 121” at the top of a sheet of paper.

• Have a student write 13 and 121 as hundreds, tens, and ones. [13 5 10 1 3, 121 5 100 1 20 1 1].

• Write “10 3 121 5 10 3 (100 1 20 1 1) 5 .”

• Have a student write “(10 3 100) 1” and lay down 10 “1 hundred” cards. Have a student write “(10 3 20) 1” and lay down 20 “1 ten” cards. Another student writes “(10 3 1)” and lays down 10 “1” cards.

• Do likewise for “3 3 121.”

• Add the cards for 10 3 121 to get 1,210 and the cards for 3 3 121. [363] Then add 1,210 1 363. [1,573]

Challenge Activity Extend the multiplication algorithm to greater numbers.

• Challenge students to describe a process for multiplying a three-digit number, or even a four-digit number, by a three-digit number.

• Students should be able to look for and use the regularity in the processes studied to extend the process for additional place values. Students may wish to approach this using an area model or partial products before extending to the standard algorithm.

• If needed, help them begin by writing each factor in expanded form. For example, to multiply 4,203 by 182, start by writing 4,203 5 4,000 1 200 1 3 and 182 5 100 1 80 1 2.

4 SolutionSee completed multiplications on the Student Book page. The missing digit in the ones place can only be a 4 or 9 for the product to have a 6 in the ones place.

DOK 2

5 Solution6,844; This is a two-step problem. First, subtract 19 boxes from the 78 that had been in the warehouse. Then multiply 59 by the number of DVDs in each box. See possible student work on the Student Book page.

DOK 2

6 SolutionStudent work could include breaking apart the factor 32 into 30 1 2 and multiplying each number by 127; and breaking apart the factor 127 into 100 1 20 1 7 and multiplying each number by 32. See possible student work on the Student Book page.

DOK 2

Solutions

Lesson 5 Multiply Whole Numbers41b ©Curriculum Associates, LLC Copying is not permitted

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Lesson 5 Multiply Whole Numbers

LESSON QUIZ

Copying permitted for classroom use.Grade 5 Lesson 5 Multiply Whole Numbers

Name ___________________________________________________________ Date ____________________

Lesson 5 Quiz continued

4 Jannelle can drive an average of 295 miles on one tank of gas. How many miles can she drive on 16 tanks of gas?

Part A

Sarah creates an area model to solve the problem.

Write a number on each blank to complete the area model.

Use the numbers in the box.

10 1 30 50 2,000 900

90 540 300 200 5,400 5

200 90

50

6 1,200

Part B

How many miles can Jannelle drive on 16 tanks of gas?

Copying permitted for classroom use.Grade 5 Lesson 5 Multiply Whole Numbers

Name ___________________________________________________________ Date ____________________

Lesson 5 QuizReady® Mathematics

Solve the problems.

1 A grocery store has 184 shelves for bottled goods. Each shelf can hold 27 bottles. How many bottles will the shelves hold in all?

2 Which expressions are equivalent to 647 3 39?

Circle all the correct answers.

A 6(30 1 9) 1 4(30 1 9) 1 7(30 1 9)

B 600(30 1 9) 1 40(30 1 9) 1 7(30 1 9)

C (647 3 3) 1 (647 3 9)

D (600 3 30) 1 (600 3 9) 1 (40 3 30) 1 (40 3 9) 1 (7 3 30) 1 (7 3 9)

E (6 3 30) 1 (6 3 9) 1 (4 3 30) 1 (4 3 9) 1 (7 3 30) 1 (7 3 9)

3 Write a number on each blank to complete two diff erent multiplication problems.

8 1 4 8 1 4

3 4 3 4

3 8 3 8

Overview

Assign the Lesson 5 Quiz and have students work independently to complete it.

Use the results of the quiz to assess students’ understanding of the content of the lesson and to identify areas for reteaching. See the Lesson Pacing Guide at the beginning of the lesson for suggested instructional resources.

Tested Skills

Assesses 5.NBT.B.5

Problems on this assessment form require students to be able to multiply three-digit numbers by two-digit numbers using the standard algorithm, the distributive property, partial products, and area models. Students will also need to be familiar with basic multiplication facts, writing two- and three-digit numbers in expanded form, and the commutative and associative properties of multiplication.

Lesson 5 Multiply Whole Numbers 41c©Curriculum Associates, LLC Copying is not permitted

Lesson 5

Grade 5 Lesson 5 Multiply Whole Numbers ©Curriculum Associates, LLC

Lesson 5 Quiz Answer Key

1. 4,968DOK 2

2. B, DDOK 1

3. 814 3 42 5 34,188814 3 47 5 38,258DOK 2

4. Part A:

200 90 5

10 2000 900 50

6 1,200 540 30

DOK 2

Part B:4,720DOK 1

Common Misconceptions and Errors

Errors may result if students:

• forget to show that a digit represents a number of tens or hundreds by placing a zero in the tens and/or ones places.

• multiply the three-digit number by each digit of the two-digit number instead of the value of each digit in the two-digit number.

• write two- or three-digit numbers in expanded form incorrectly.