U.S. Traditional Multiplication: Decimals

Algorithm

Project Projjec ect

Objective To introduce U.S. traditional multiplication for decimals.

www.everydaymathonline.com

eToolkit

Algorithms Practice

EM Facts Workshop Game™

Family Letters

Assessment Management

Doing the Project Recommended Use  After Lesson 98

Common Core State Standards

Curriculum Focal Points

Interactive Teacher’s Lesson Guide

Mathematical Practices

SMP1, SMP2, SMP3, SMP4, SMP5, SMP6, SMP8

Key Concepts and Skills • Identify places in whole numbers and decimals and the values of the digits in those places.  [Number and Numeration Goal 1]

• Use multiplication facts to calculate products of decimals and whole-number multipliers.  [Operations and Computation Goal 3]

• Write and solve multiplication number stories with decimals. 

Materials  Math Journal 1 or 2, pp. 21P–24P  Student Reference Book, p. 40C  $1 and $10 bills (Math Masters, p. 428; optional)  dimes and pennies (optional)

[Operations and Computation Goal 4]

Key Activities Students explore and practice U.S. traditional multiplication with decimals.

Extending the Project Ex Students solve decimal multiplication problems, first using the focus algorithm (partial-products multiplication) and then using any algorithm they choose.

Materials  Online Additional Practice, pp. 24A−24D  Student Reference Book, pp. 37A, 37B, and 40C

A26

Algorithm Project 6

U.S. Traditional Multiplication: Decimals

Student Page Date

1 Doing the Project

Time

PROJECT

6

U.S. Traditional Multiplication: Decimals 1

Algorithm Project 6

► Solving a Decimal Multiplication

Use any strategy to solve the problem.

INDEPENDENT ACTIVITY

1.

A turkey sandwich at Jason’s Deli costs $5.98. What is the cost of 4 turkey sandwiches? $

Problem

23.92

Use U.S. traditional multiplication to solve each problem. Use estimation or count decimal places to place the decimal point in your answers.

(Math Journal 1 or 2, p. 21P)

2.

12.64 ∗ 5 =

4.

$

Ask students to solve Problem 1 on journal page 21P. Tell them they may use play money, paper and pencil, or any other tools they wish, except calculators.

► Discussing Solutions

49.02

63.20 or 63.2

= 86 ∗ $0.57

3.

$9.12 ∗ 23 = $

209.76

5.

3 ∗ $45.80 = $

137.40

7.

426 ∗ 5.3 =

WHOLE-CLASS ACTIVITY

(Math Journal 1 or 2, p. 21P)

6.

Discuss students’ solutions to Problem 1 on journal page 21P. $5.98 ∗ 4 = $23.92 Expect that students will use several different methods, which may include modeling with play money, using repeated addition, using lattice multiplication, and using partialproducts multiplication. Some students may also use U.S. traditional multiplication. Possible strategies:

3,295.5

= 50.7 ∗ 65

2,257.8

Math Journal, p. 21P 21P-24P_EMCS_S_MJ1_G4_P06_576361.indd 21

3/4/11 11:57 AM

 Modeling with play money $1

$1

$1

$1

$1

$1

$1

$1

$1

$1

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$1

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$1

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$1

$1

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Use play money to show the cost of 4 sandwiches.

5 $1 + 5 $1 + 5 $1 + 5 $1 = 20 $1

or 2 $10

Combine the bills.

9 D + 9 D + 9 D + 9 D = 36 D or 3 $1

and 6 D

Combine the dimes.

8 P +5 8 P + 8 P + 8 P = 32 P or 3 D and 2 P Combine the pennies.

2 $10 + 3 $1 + 6 D + 3 D + 2 P = $23.92 Combine the bills and coins.

Algorithm Project 6

A27

 Using repeated addition $5.98 + $5.98 $10.00 $1.80 + $0.16 $11.96

$11.96 + $11.96 $22.00 $1.80 + $0.12 $23.92

 Using lattice multiplication 5 · 9

2

2

0

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6

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3· 9

2 2

4 ·

 Using partial-products multiplication

4 [$5.00]s → 4 [$0.90]s → 4 [$0.08]s →

$5. 9 8 ∗ 4 2 0. 0 0 3. 6 0 + 0. 3 2 $2 3. 9 2

 Using U.S. traditional multiplication 3 3

$5. 9 8 ∗ 4 $2 3. 9 2

► Introducing U.S. Traditional

WHOLE-CLASS ACTIVITY

Multiplication for Decimals After you have discussed students’ solutions, and even if one or more students used U.S. traditional multiplication, demonstrate it again as described below. Example 1: $5.98 ∗ 4 Step 1:

Start with the pennies. 4 ∗ 8 pennies = 32 pennies 32 pennies = 3 dimes + 2 pennies Step 2: Multiply the dimes. 4 ∗ 9 dimes = 36 dimes Remember the 3 dimes from Step 1. 36 dimes + 3 dimes = 39 dimes in all 39 dimes = $3 + 9 dimes

A28

Algorithm Project 6

U.S. Traditional Multiplication: Decimals

3

5.98 ∗ 4 2 3

3

5.98 ∗ 4 92

Student Page Step 3:

Date

3

3

5.98 ∗ 4 23.92

Multiply the dollars. 4 ∗ $5 = $20 Remember the $3 from Step 2. $20 + $3 = $23 in all $23 = 2 [$10]s + 3 [$1]s Remember to include the decimal point.

Time

PROJECT

U.S. Traditional Multiplication: Decimals 2

6

Algorithm Project 6 Use U.S. traditional multiplication to solve each problem. Use estimation or count decimal places to place the decimal point in your answers. 1.

Find the area of the rectangle.

121.80 or 121.8

m2

5m 24.36 m

2.

18 ∗ 30.09 =

541.62

3.

$24.05 ∗ 6 = $

144.30

5.

$8.53 ∗ 76 = $

648.28

7.

$5.21 ∗ 4 = $

20.84

$5.98 ∗ 4 = $23.92 Four turkey sandwiches cost $23.92. One way to use U.S. traditional multiplication with decimals is to multiply the factors as though they were whole numbers and then use estimation to place the decimal point.

22.78

4.

6.

= 34 ∗ 0.67

11,693.2 = 2.3 ∗ 5,084

Example 2: 14.85 ∗ 6 Step 1:

2 5 3

1485 ∗ 6 −−−−−− 8910

Multiply as though both factors were whole numbers. Step 2:

Math Journal, p. 22P 21P-24P_EMCS_S_MJ1_G4_P06_576361.indd 22

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Estimate the product: 14.85 is about 15, and 15 ∗ 6 = 90. NOTE This second method for multiplying decimals (used in Example 3) is useful when there are many decimal places in the factors, making it difficult to estimate the answer. For example, 0.078 ∗ 0.029 = 0.002262.

Step 3: Use the estimate to place the decimal point in the answer. The estimate is 90, so place the decimal point to make the answer close to 90: 89.10 is close to 90.

14.85 ∗ 6 = 89.10

Another way to use U.S. traditional multiplication with decimals is to multiply as though both factors were whole numbers and then find the total number of places to the right of the decimal points of both factors to determine where to place the decimal point.

Student Page Date

Time

PROJECT

U.S. Traditional Multiplication: Decimals 3

6

Algorithm Project 6

Example 3: 35

∗

8.62

Use U.S. traditional multiplication to solve each problem. Use estimation or count decimal places to place the decimal point in your answers.

1 3 1

Step 1: Multiply as though both factors were whole numbers. Step 2: Count the total number of places to the right of the decimal points of both factors. There are 0 places to the right of the decimal point in 35. There are 2 places to the right of the decimal point in 8.62. There are 2 decimal places in all.

862 ∗ 35 −−−−−−− 4310 + 25860 −−−−−−− 30170

35 ∗ 8.62 = 301.70

The average weight of a beagle puppy at birth is about 0.25 kg. At 6 months, a male beagle can weigh about 32 times as much. About how much can a 6-month-old male beagle weigh?

8.00 or 8 2.

Write a number story for 4.6 ∗ 28. Solve your number story.

128.8; Number stories vary.

3.

0

8 . 6

2

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3

3

6

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1 . 7

4.

2 1

+

3

kg

Fill in the missing digits in the multiplication problems.

Step 3: Place the decimal point 2 places from the right.

1.

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0 . Math Journal, p. 23P 21P-24P_EMCS_S_MJ1_G4_P06_576361.indd 23

3/4/11 11:57 AM

Algorithm Project 6

A29

Student Page Date

You may want to work several more examples with the whole class.

Time

PROJECT

U.S. Traditional Multiplication: Decimals 4

6

Algorithm Project 6

Suggestions:

Use U.S. traditional multiplication to solve each problem. Use estimation or count decimal places to place the decimal point in your answers. 1.

25.55 2.

 7.46 ∗ 3 = ? 22.38

Alicia has 7 pieces of yarn. Each piece is 3.65 meters long. What is the combined length of all 7 pieces?

 3 ∗ $43.21 = ? $129.63

m

 $0.67 ∗ 5 = ? $3.35

Write a number story for 5 ∗ $48.30. Solve your number story.

 8 ∗ 17.04 = ? 136.32

$241.50; Number stories vary.

 23 ∗ $40.06 = ? $921.38  5.6 ∗ 70 = ? 392

Fill in the missing digits in the multiplication problems. 3.

4.

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1 2 2 7 8 1 8 0 9 4 0. 7

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► Practicing U.S. Traditional

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PARTNER ACTIVITY

Multiplication for Decimals (Math Journal 1 or 2, pp. 21P–24P; Student Reference Book, p. 40C)

Math Journal, p. 24P 21P-24P_EMCS_S_MJ1_G4_P06_576361.indd 24

3/4/11 11:57 AM

When students are ready, have them solve Problems 2–7 on journal page 21P. They may find the examples on Student Reference Book, page 40C helpful. Journal pages 22P–24P provide students with additional practice using U.S. traditional multiplication. Use these journal pages as necessary.

Go to www.everydaymathonline.com to access the additional practice pages.

2 Extending the Project ► Solving Decimal Multiplication Problems

Online Master Name

Date

PROJECT

6

(Online Additional Practice, pp. 24A–24D; Student Reference Book, pp. 37A, 37B, and 40C)

Time

Partial-Products Multiplication: Decimals

Online Additional Practice

Algorithm Project 6

Online practice pages 24A–24D provide students with additional practice solving decimal multiplication problems. Use these pages as necessary.

Use partial-products multiplication to solve each problem. Use estimation to place the decimal point in your answers. 1.

A pack of 12 party invitations costs $8.95. Mrs. Becker bought 15 packs. How much money did she spend?

Copyright © Wright Group/McGraw-Hill

$

134.25

2.

$0.46 ∗ 83 = $

4.

$

6.

633.15

60.48

38.18

= 63 ∗ $10.05

= 7.56 ∗ 8

3.

7 ∗ 39.04 =

273.28

5.

71.21 ∗ 4 =

284.84

7.

9,406 ∗ 2.8 =

26,336.8

Encourage students to use the focus algorithm (partial-products multiplication) to solve the problems on practice page 24A. Invite them to use any algorithm they wish to solve the problems on the remaining pages. Students may find the examples on Student Reference Book, pages 37A, 37B, and 40C helpful.

Online Additional Practice, p. 24A EM3cuG4OP_24A-24D_P06.indd 24A

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Algorithm Project 6

INDEPENDENT ACTIVITY

3/31/10 5:35 PM

U.S. Traditional Multiplication: Decimals