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### Engage NY Module 1

Lesson 10 – Objective: Subtract decimals using place value strategies and relate those to a written method.

Fluency Practice – Take out the Unit

- Say the number 76.358
- 76 and 358 thousandths

- Write 76.358 in unit form
- 7 tens, 6 ones, 3 tenths 5 hundredths, 8 thousandths
- 7 tens _______ thousandths
- 7 tens 6 ones ______ thousandths
- 763 tenths _____ thousandths
- 76 ones 3 tenths ____ thousandths
- _____ hundredths 8 thousandths

6358

358

58

58

7635

Fluency Practice – Add Decimals

- 3 tenths + 2 tenths = ______
- How would the number sentence be written in decimal form?
- .3 + .2 = .5

- 5 hundredths + 4 hundredths = ___________
- How would the number sentence be written in decimal form?
- .05 + .04 = .09

- 35 hundredths + 4 hundredths = __________
- How would the number sentence be written in decimal form?
- .35 + .04 = .39

5 tenths

9 hundredths

39 hundredths

Fluency Practice – One Unit Less

- What is the decimal 1 less than 5 tenths (.5)?
- 4 tenths (.4)

- What is the decimal 1 less than 5 hundredths (.05)?
- 4 hundredths (.04)

- What is the decimal 1 less than 5 thousandths (.005)?
- 4 thousandths (.004)

- What is the decimal 1 less than 7 hundredths (.07)?
- 6 hundredths (.006)

- What is the decimal 1 less than 9 tenths (.9)?
- 8 tenths (.8)

Fluency Practice – One Unit Less

- What is the decimal 1 thousandths less than 29 thousandths (.029)?
- 28 thousandths (.028)

- What is the decimal 1 tenth less than 61 hundredths (.61)?
- 51 hundredths (.51)

- What is the decimal 1 thousandths less than 61 thousandths (.061)?
- 60 thousandths (.060) or 6 hundredths

- What is the decimal 1 hundredth less than 61 thousandths (.061)?
- 51 thousandths (.051)

- What is the decimal 1 hundredth less than 549 thousandths (.549)?
- 539 thousandths (.539)

Application Problem

At the 2012 London Olympics, Michael Phelps won the gold medal in the men’s 100 meter butterfly. He swam the first 50 meters in 26.96 seconds. The second 50 meters took him 25.39 seconds. What was his total time?

Concept Development – Problem 1

- 5 tenths – 3 tenths = ______
- Explain your reasoning when solving this subtraction sentence.
- Since the units are alike we can just subtract. 5-3 = 2. This problem is very similar to 5 ones minus 2 ones, 1 or 5 people minus 2 people; the units may change but the basic fact 5-2=3 is always true.

.5 - .3 = .2

Concept Development – Problem 1

- 7 ones 5 thousandths – 2 ones 3 thousandths =
- Solve using a place value chart and record our thinking vertically, using the algorithm.
- What did you have to think about as you wrote the problem vertically?
- Like units are being subtracted, so my work should also show that. Ones with ones and thousandths with thousandths.

7.005

-2.003

----------

5.003

7.005 – 2.003 = 5.002

Concept Development – Problem 1

- Solve 9 tens 5 tenths – 3 tenths = __
- Explain to your neighbor how you’ll solve this one.
- In word form, these units look similar, but they’re not. I’ll just subtract 3 tenths from 5 tenths.

- 90.5
- 0.3
- -----
- 90.2

90.5 – 0.3

Concept Development – Problem 2

- 83 tenths – 6 ones 4 tenths = ______ How is this problem different from the problems we’ve seen previously? (8.3 – 6.4 = ____)
- These problems will involve regrouping.

- What are some ways we could solve this problem?
- Using disk on a place value chart or standard algorithm.

- Explain how you solved the problem.
- I had to regroup before we could subtract tenths from tenths. I had to borrow a whole group from the ones. A whole group is 10 tenths. I added the 10 tenths to the 3 tenths to get 13 tenths. I then took 13 tenths minus 4 tenths. Then we subtracted ones from ones, using the same process as whole numbers.

7

13

8.3

-6.4

------

1.9

Concept Development – Problem 2

8.3 – 6.4 = 1.9

Concept Development – Problem 2

- 9.2 – 6 ones 4 tenths = ______ How is this problem different from the problems we’ve seen previously? (9.2 – 6.4 = ____)
- These problems will involve regrouping.

- What are some ways we could solve this problem?
- Using disk on a place value chart or standard algorithm.

- Explain how you solved the problem.
- I had to regroup before we could subtract tenths from tenths. I had to borrow a whole group from the ones. A whole group is 10 tenths. I added the 10 tenths to the 3 tenths to get 13 tenths. I then took 13 tenths minus 4 tenths. Then we subtracted ones from ones, using the same process as whole numbers.

12

8

9.2

-6.4

------

2.8

Concept Development – Problem 2

9.2 – 6.4 = 2.8

Concept Development – Problem 3

- Solve the following problems using a place value chart or the standard algorithm.
- 0.831 – 0.292 =
- 4.003 – 1.29 =
- What do you notice about the thousandths place in 1.29?

- 6 – 4.08 =

0.539

2.713

1.92

9

5

10

10

7

12

6

6.00

-4.08

-------

1.92

2

11

0.831

- 0.292

---------

0.539

9

10

3

10

- 4.003
- 1.290
- --------
- 2.713

1.29

Concept Development – Problem 3

0.831 – 0.292 = 0.539

Concept Development – Problem 3

4.003 – 1.29 = 2.713

Concept Development – Problem 3

6 – 4.08 =

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