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1 Doing the Project materials

Recommended Use: After Lesson 4-6

Key ActivitiesStudents explore and practice U.S. traditional subtraction with decimals.

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 subtraction facts to find differences of decimals.

[Operations and Computation Goal 1]

• Subtract decimals.

[Operations and Computation Goal 2]

• Write and solve subtraction number stories with decimals.

[Operations and Computation Goal 2]

� Math Journal, pp. 13P–16P

� Student Reference Book, p. 40B

� $1, $10 bills (Math Masters, p. 428; optional)

� dimes, pennies (optional)

� base-10 blocks (optional)

2 Extending the Project materialsStudents solve decimal subtraction problems, first using the focus algorithm (trade-first

subtraction) and then using any algorithm they choose.� Online Additional Practice,

pp. 16A–16D

� Student Reference Book, pp. 34–37 and 40B

Objective To introduce U.S. traditional subtraction with decimals.

Algorithm Project 4 A15

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Math Journal, p. 13P

Student Page

U.S. Traditional Subtraction: Decimals 1PROJECT

4

Date Time

Algorithm Project 4

Use any strategy to solve the problem.

1. Seth paid $6.72 for his lunch. Lily paid $3.79 for her lunch. How much more did Seth’s lunch cost?

$ 2.93

Use U.S. traditional subtraction to solve each problem.

2. 9.75 - 4.32 = 5.43 3. 5.06 - 2.49 = 2.57

4. 2.84 = 8.2 - 5.36 5. $34.27 - $16.38 = $ 17.89

6. 22.69 = 50.08 - 27.39 7. 6.35 - 2.37 = 3.98

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1 Doing the Project

Solving a Decimal Subtraction INDEPENDENTACTIVITY

Problem(Math Journal, p.13P)

Ask students to solve Problem 1 on journal page 13P. Tell them they may use base-10 blocks, play money, paper and pencil, or any other tools they wish, except calculators.

Discussing Solutions WHOLE-CLASSACTIVITY

(Math Journal, p. 13P)

Discuss students’ solutions to Problem 1 on journal page 13P. $6.72 - $3.79 = $2.93 Expect that students will use several different methods, including modeling with base-10 blocks, counting up, using partial-differences subtraction, and using trade-first subtraction. Some students may also use U.S. traditional subtraction. Possible strategies:

� Modeling with base-10 blocks

Show 6.72 with blocks.

You want to take away 3.79. To do this, you need to first trade 1 flat for 10 longs and 1 long for 10 cubes.

Now remove 3 flats, 7 longs, and 9 cubes (3.79). Two flats, 9 longs, and 3 cubes are left. These blocks show 2.93.

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A16 Algorithm Project 4 U.S. Traditional Subtraction: Decimals

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� Using shorthand pictures of base-10 blocks (See margin.)

� Counting up

3.79+ 0.01

3.80+ 0.20

4.00+ 2.72

6.72

0.010.20

+ 2.722.93

6.72 - 3.79 = 2.93

� Using partial-differences subtraction

Subtract the 1s. 6 - 3 → Subtract the 0.1s. 0.7 - 0.7 → Subtract the 0.01s. 0.02 - 0.09 → Find the total. 3 - 0.07 →

� Using trade-first subtraction

� Using U.S. traditional subtraction

NOTE Trade-first subtraction resembles U.S. traditional subtraction, except that in trade-first subtraction, as the name implies, all the trading is done before any subtractions are carried out, allowing the person to concentrate on one task at a time.

Introducing U.S. Traditional WHOLE-CLASSACTIVITY

Subtraction for DecimalsAfter you have discussed students’ solutions, and even if one or more students used U.S. traditional subtraction, demonstrate it again as described on the next page.

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Draw a picture for 6.72.

Trade 1 flat for 10 longs and 1 long for 10 cubes.

Remove 3 flats, 7 longs, and 9 cubes.The drawing shows 2.93.

$6.72 - $3.79 = $2.93

6. 7 2 −−−−−

- 3. 7 9

3. 0 00. 0 0

−−−−−−−

- 0. 0 7 2. 9 3

Algorithm Project 4 A17

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Example 1: 6.72 - 3.79

Step 1:

Start with the 0.01s.Since 9 > 2, you need to regroup.Trade 1 tenth for 10 hundredths: 6.72 = 6 ones + 6 tenths + 12 hundredths.Subtract the 0.01s: 12 - 9 = 3.

Step 2:

Go to the 0.1s.Since 7 > 6, you need to regroup.Trade 1 one for 10 tenths: 6.72 = 5 ones + 16 tenths + 12 hundredths.Subtract the 0.1s: 16 - 7 = 9.

Step 3:

Go to the 1s. You don’t need to regroup.Subtract the 1s: 5 - 3 = 2.Remember to include the decimal point in the answer.

$6.72 - $3.79 = $2.93

Seth’s lunch cost $2.93 more than Lily’s lunch.

Example 2: 46.03 - 27.48

Step 1:

Start with the 0.01s.Since 8 > 3, you need to regroup.There are no tenths in 46.03, so trade 1 one for 10 tenths and then trade 1 tenth for 10 hundredths: 46.03 = 4 tens + 5 ones + 9 tenths + 13 hundredths.Subtract the 0.01s: 13 - 8 = 5.

Step 2:

Go to the 0.1s.You don’t need to regroup.Subtract the 0.1s: 9 - 4 = 5.

Step 3:

Go to the 1s. Since 7 > 5, you need to regroup.Trade 1 ten for 10 ones: 46.03 = 3 tens + 15 ones + 9 tenths + 13 hundredths.Subtract the ones: 15 - 7 = 8.

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A18 Algorithm Project 4 U.S. Traditional Subtraction: Decimals

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Math Journal, p. 15P

Student Page

Math Journal, p. 14P

Student Page

U.S. Traditional Subtraction: Decimals 2PROJECT

4

Date Time

Algorithm Project 4

Use U.S. traditional subtraction to solve each problem.

1. Joanna had $73.48 in her bank account. She wrote a check for $25.69. How much money is in her bank account now?

$ 47.79

2. 6.04 - 2.75 = 3.29 3. 8.73 - 4.21 = 4.52

4. 2.99 = 5.63 - 2.64 5. 31.5 - 7.82 = 23.68

6. $ 18.89 = $45.26 - $26.37 7. 60.08 - 43.29 = 16.79

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U.S. Traditional Subtraction: Decimals 3PROJECT

4

Date Time

Algorithm Project 4

Use U.S. traditional subtraction to solve each problem.

1. Riley bought two card games at the store. The total cost (before tax) was $9.25. One game cost $3.89. How much did the other game cost?

$ 5.36

2. Write a number story for $38.42 - $19.76.Solve your number story.

$18.66; Number stories vary.

Fill in the missing numbers in the subtraction problems.

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Step 4:

Go to the 10s.You don’t need to regroup.Subtract the 10s: 3 - 2 = 1.Remember to include the decimal point in the answer.

46.03 - 27.48 = 18.55

Example 3: 7.1 - 3.86

Step 1:

Write the problem in columns. Be sure to line up the places correctly.Since 3.86 has two decimal places, write 7.1 as 7.10.

Step 2:

Start with the 0.01s.Since 6 > 0, you need to regroup.Trade 1 tenth for 10 hundredths: 7.10 = 7 ones + 0 tenths + 10 hundredths.Subtract the 0.01s: 10 - 6 = 4.

Step 3:

Go to the 0.1s.Since 8 > 0, you need to regroup.Trade 1 one for 10 tenths:7.10 = 6 ones + 10 tenths + 10 hundredths.Subtract the 0.1s: 10 - 8 = 2.

Step 4:

Go to the 1s. You don’t need to regroup.Subtract the 1s: 6 - 3 = 3.Remember to include the decimal point in the answer.

7.1 - 3.86 = 3.24

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

Suggestions:

� $8.49 - $6.35 = ? $2.14

� 5.61 - 3.74 = ? 1.87

� 7.06 - 4.98 = ? 2.08

� 3.9 - 2.62 = ? 1.28

� $28.74 - $19.86 = ? $8.88

� 40.07 - 26.39 = ? 13.68

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Algorithm Project 4 A19

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Online Additional Practice, p. 16A

Online Master

Math Journal, p. 16P

Student Page

U.S. Traditional Subtraction: Decimals 4PROJECT

4

Date Time

Algorithm Project 4

Use U.S. traditional subtraction to solve each problem.

1. Quinn has two pieces of ribbon. The yellow ribbon is 12.42 meters long. The pink ribbon is 16.75 meters long. How much shorter is the yellow ribbon?

4.33 meters

2. Write a number story for 7.63 - 1.84. Solve your number story.

5.79; Number stories vary.

Fill in the missing numbers in the subtraction problems.

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Name Date Time

PROJECT

4 Trade-First Subtraction: DecimalsOnline Additional Practice

Algorithm Project 4

Use trade-first subtraction to solve each problem.

1. Matthew was building a house for his dog. He had a board that was 2.45 meters long. He cut off 1.75 meters. How long is the board now?

0.7 meters

2. 8.72 - 4.61 = 4.11 3. 9.02 - 5.87 = 3.15

4. 3.75 = 7.6 - 3.85 5. $82.43 - $56.77 = $ 25.66

6. 23.77 = 70.05 - 46.28 7. 6.54 - 3.59 = 2.95

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Practicing U.S. Traditional PARTNER ACTIVITY

Subtraction for Decimals(Math Journal, pp. 13P–16P; Student Reference Book, p. 40B)

When students are ready, have them solve Problems 2–7 on journal page 13P. They may find the example on Student Reference Book, page 40B helpful.

Journal pages 14P–16P provide students with additional practice using U.S. traditional subtraction. Use these journal pages as necessary.

2 Extending the Project

Solving Decimal Subtraction INDEPENDENTACTIVITY

Problems(Online Additional Practice, pp. 16A–16D; Student Reference Book,

pp. 34–37 and 40B)

Online practice pages 16A–16D provide students with additional practice solving decimal subtraction problems. Use these pages as necessary.

Encourage students to use the focus algorithm (trade-first subtraction) to solve the problems on practice page 16A. 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 34–37 and 40B helpful.

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

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A20 Algorithm Project 4 U.S. Traditional Subtraction: Decimals

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