Common Core State Standards

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

Lesson

Objective

Multiply multidigit whole numbers using area models and the standard algorithm.

2 Multiply Multidigit NumbersStudents can readily apply place value concepts to operations with whole numbers and decimals. Standard algorithms for computing with numbers employ place value concepts as useful steps. Algorithms summarize conceptual understanding in an efficient strategy. They are important tools of computation that students need to learn as they develop their math fluency.

VocabularyWrite a simple problem on the board, such as 25 + 37 = _____. Have students describe how they would find the answer. Look for common approaches.

■ Ask: What if we write out the steps we used to solve the problem?

Elicit all of the steps from students. [Step 1 might be to add the ones, 5 and 7, or the tens 20 and 30.]

■ Say: A step-by-step approach like we used here is called an algorithm.

Write algorithm on the board. Ask students what other computations they can do using an algorithm. [subtraction, multiplication]

■ An algorithm is a method, or procedure, for doing a mathematical computation.

Algorithms can

be used for

mental math, but

they are more

often associated

with paper and

pencil methods.

the StageSet

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Foundation Skill Practice

Use this VersaTiles® activity to help students activate their prior knowledge.

Use this short thinking exercise to jump-start the instructional session.

Warm-Up

Operations with Whole Numbers and Decimals

Online resources available at hand2mind.com/hosnumbergr5 VersaTiles® student book, page 20

20 Objective: Use multiples of 10 to � nd a product or a factor.

8 200 8,000 80 900 9

4,200 90,000 90 200,000 800 4,200,000

Patterns and Products

Find the missing number.

You can use what you know about multiplication facts to find the product of large numbers.

60 × 30 = ■ ■ × 8,000 = 560,000Think: 6 × 3 = 18 Think: 7 × 8 = 56

60 × 30 = 1,800 70 × 8,000 = 560,000So, 60 × 30 = 1,800. So, 70 × 8,000 = 560,000.

Find the missing number.

1 7 × 6 = 42, so 70 × 60 = ■ 2 8 × 6 = 48, so ■ × 60 = 48,000

3 4 × 2 = 8, so 40 × 200 = ■ 4 3 × 3 = 9, so 3,000 × 30 = ■

5 5 × 4 = 20, so 50 × 4,000 = ■ 6 7 × 6 = 42, so 70,000 × 60 = ■

7 9 × ■ = 72, so 90 × 800 = 72,000 8 5 × ■ = 45, so 50 × 900 = 45,000

9 3 × 8 = 24, so 30 × ■ = 2,400 10 2 × 7 = 14, so ■ × 70 = 14,000

11 4 × 9 = 36, so 4,000 × ■ = 360,000 12 9 × 2 = 18, so ■ × 200 = 180,000

2

Operations with Whole Numbers and Decimals ■ Lesson 2 Hands-On Standards® Number & Operations

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Suppose you know that 14 × 10 is 140.

a. Tell how you can figure out what 14 × 11 is.

b. Tell how you can figure out what 14 × 9 is.

Answer Key

ANSWER: a. 154, or (14 × 10) + 14; b. 126, or (14 × 10) – 14

COMMENTS & EXTENSIONS: It is important, especially when doing higher level math and when estimating, to be able to find shortcuts.

Mental arithmetic:

a. 99 × 32 = b. 9 × 14 =

c. 16 × 101 = d. 15 × 102 =

Tell how you got each answer.

Engage WHOLE CLASS

Present the problem 12 × 14 = __.

■ Ask: How can you use place value as a strategy to find the product?

Invite as many different responses as you can. Students might suggest decomposing 12 into 10 + 2 and finding the product as (10 × 14) + (2 × 14). Or they might instead suggest decomposing 14 into 10 + 4 and proceeding in similar fashion. If they suggest decomposing both factors, let them see if they can carry out that approach.

■ Ask: How do these strategies help you?

Acknowledge with students that the strategies may help them find the product mentally. At the minimum, they help students break down the problem into well-defined steps that will work every time.

the ConceptIntroduce

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Online resources available at hand2mind.com/hosnumbergr5

Explore & Explain

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Hands-On Standards® Number & Operations

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Operations With Whole Numbers and Decimals ■ Lesson 2

Multiply Multidigit Numbers

Try This ■ Model problem 1 using Base Ten Blocks and a Factor Track. Sketch your model. Label the area model, and complete the equation.

■ In problems 2–3, sketch an area model and find the product. ■ In problems 4–7, find the product.

1. 11 × 15 = (10 + 1) × (10 + 5)

= (____ × ____) + (____ × ____) + (____ × ____) + (____ × ____) = ____ + ____ + ____ + ____ = ____

2. 25 × 13

3. 125 × 23

4. 26 × 33

5. 134 × 24

6. 225 × 32

7. 316 × 22

Answer Key

10

10010

101

5

50

5

20

20010

603

5

50

15

100

200020

3003

20 5

400 100

60 15

10

100

156050

200325

1860

180 600

858

1612040080

600 2000

3216

1040

400150600

60007200

1220

600120200

60006952

1560

300100400

20002875

10

10

1

50

10

5

10

165

5 1 5

Explore & Explain SMALL GROUPS

Prepare ahead Each group of students will need a set of Base Ten Blocks and a Factor Track.

The activity helps students internalize the basic ideas of multiplication with multidigit numbers. Students will build and sketch a manipulative model, sketch area models, and develop their fluency with the standard algorithm. They should reason that as long as the steps in their computations make sense, it doesn’t matter whether they start from the right or the left.

Explore WHOLE CLASS

Distribute Base Ten Blocks and Factor Tracks. Have students build a model for 12 × 14, identify the four partial-product regions, and sketch the area model.

rectangle built with 1 flat, 6 rods, 8 units

The area model depicts the four main regions of the Factor Track model.

10 4

10

2 20 8

40100sketch of area model

Change the problem to 12 × 114. This product is too big to model on the Factor Track, but you can have students apply the reasoning by sketching the area model. Write the problem in vertical format. Have students walk you through the computation using an algorithm.

100 10 4

10

2 200 20 8

100 401,000

114 × 12 2 × 4 ➞ 8 2 × 10 ➞ 20 2 × 100 ➞ 200 10 × 4 ➞ 40 10 × 10 ➞ 100 10 × 100 ➞ 1,000

1,368

Materials

• Base Ten Blocks

• Factor Track™

Daily Routine

the ConceptReinforce

Online resources available at hand2mind.com/hosnumbergr5

Independent Practice

Use this VersaTiles® activity to give students more practice with the skills they learned in the lesson.

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Re-Engage

Use this page to give students additional concrete-to-representational-to-abstract practice.

Operations with Whole Numbers and Decimals

VersaTiles® student book, page 21

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Hands-On Standards® Number & Operations

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Operations With Whole Numbers and Decimals ■ Lesson 2

Multiply Multidigit Numbers

Use a Factor Track and Base Ten Blocks to build the model. Complete the number sentence.

1. 11 × 13 = (10 + 1) × (10 + 3)

= (10 × 10) + (1 × 10) + (10 × 3) + (1 × 3)

= _____ + _____ + _____ + _____ = _____

2. 12 × 22 = (10 + _____) × (20 + _____)

= (10 × 20) + (2 × 20)

+ (_____ × 2) + (_____ × 2)

= _____ + _____ + _____ + _____ = _____

Complete the area model for the problem. Find the product.

Find the product.

3. 26 × 13

20

10

3

6 4. 144 × 24

5. 46 × 34

6. 127 × 14

7. 225 × 31

8. 333 × 26

Answer Key

100

200 800

40

2000

100

20 18 60 60 200 338

28 80 400 70 200 1000 1778

18 180 1800 60 600 6000 8658

24 160 180 1200 1564

5 20 200

150 600 6000 6975

16 160 400 80 800 2000 3456

60 80

4

60 160400418 16

2

10 210 30 3 143

200 40 20 4 264

2

21Objective: Find the product of a 3- or 4-digit number multiplied by a

2-digit number.

1,344 9,154 32,875 77,188 40,896 43,350

31,347 118,560 6,360 29,600 10,020 10,575

Find the product.

1 15 × 424 2 398 × 23 3 167 × 60

4 925 × 32 5 71 × 576 6 43 × 729

7 25 × 1,315 8 38 × 3,120 9 17 × 2,550

10 46 × 1,678 11 235 × 45 12 112 × 12

44,404 30,240 43,407 133,056 120,921 32,760

30,463 78,616 6,656 85,325 9,684 49,335

Products on the Loose!

Find the product.

1 18 × 538 2 41 × 743 3 26 × 256

4 35 × 936 5 53 × 819 6 70 × 432

7 13 × 3,795 8 34 × 1,306 9 28 × 4,752

10 51 × 2,371 11 25 × 3,413 12 62 × 1,268

Explain & Elaborate WHOLE CLASS

Have students describe their approach to Problem 7.

■ Ask: Did you notice a pattern? Elicit that the computation generates three pairs of partial products in which, for each pair, one product is 10 times the other. Have students explain the reason for this pattern.

Evaluate WHOLE CLASS

Present the area model—

200 60 8

600 802000

■ Say: This is the area model for a multiplication problem. Figure out what the problem is and determine the product. [22 × 134 = 2,948]

Anchor PosterReview with your class the concepts of area models and the distributive property. Create an anchor poster with students. Include area models for single-digit and two-digit multiplication, with examples. Place the poster in the writing center.

Writing assignment: Create a third example to add to the anchor poster about multiplying a three-digit number by a two-digit number.

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Hands-On Standards® Number & Operations

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Operations With Whole Numbers and Decimals ■ Lesson 2

Multiply Multidigit Numbers

Try This ■ Model problem 1 using Base Ten Blocks and a Factor Track. Sketch your model. Label the area model, and complete the equation.

■ In problems 2–3, sketch an area model and find the product. ■ In problems 4–7, find the product.

1. 11 × 15 = (10 + 1) × (10 + 5)

= (____ × ____) + (____ × ____) + (____ × ____) + (____ × ____) = ____ + ____ + ____ + ____ = ____

2. 25 × 13

3. 125 × 23

4. 26 × 33

5. 134 × 24

6. 225 × 32

7. 316 × 22

21Objective: Find the product of a 3- or 4-digit number multiplied by a

2-digit number.

1,344 9,154 32,875 77,188 40,896 43,350

31,347 118,560 6,360 29,600 10,020 10,575

Find the product.

1 15 × 424 2 398 × 23 3 167 × 60

4 925 × 32 5 71 × 576 6 43 × 729

7 25 × 1,315 8 38 × 3,120 9 17 × 2,550

•• 46 × 1,678 •• 235 × 45 •• 112 × 12

44,404 30,240 43,407 133,056 120,921 32,760

30,463 78,616 6,656 85,325 9,684 49,335

Products on the Loose!

Find the product.

1 18 × 538 2 41 × 743 3 26 × 256

4 35 × 936 5 53 × 819 6 70 × 432

7 13 × 3,795 8 34 × 1,306 9 28 × 4,752

•• 51 × 2,371 •• 25 × 3,413 •• 62 × 1,268

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Hands-On Standards® Number & Operations

2

Operations With Whole Numbers and Decimals ■ Lesson 2

Multiply Multidigit Numbers

Use a Factor Track and Base Ten Blocks to build the model. Complete the number sentence.

1. 11 × 13 = (10 + 1) × (10 + 3)

= (10 × 10) + (1 × 10) + (10 × 3) + (1 × 3)

= _____ + _____ + _____ + _____ = _____

2. 12 × 22 = (10 + _____) × (20 + _____)

= (10 × 20) + (2 × 20)

+ (_____ × 2) + (_____ × 2)

= _____ + _____ + _____ + _____ = _____

Complete the area model for the problem. Find the product.

Find the product.

3. 26 × 13

20

10

3

6 4. 144 × 24

5. 46 × 34

6. 127 × 14

7. 225 × 31

8. 333 × 26