1. Engage NY Module 1
Lesson 10 – Objective: Subtract decimals using place value strategies and relate those to a written method.

2. Fluency Practice – Take out the Unit
Say the number
76 and 358 thousandths
Write 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

3. Fluency Practice – Add Decimals
5 tenths
3 tenths + 2 tenths = ______
How would the number sentence be written in decimal form?
= .5
5 hundredths + 4 hundredths = ___________
= .09
35 hundredths + 4 hundredths = __________
= .39
9 hundredths
39 hundredths

4. 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)

5. 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)

6. 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 seconds. The second 50 meters took him seconds. What was his total time?

7. 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.
= .2

8. 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 – = 5.002

9. 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

10. 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

11. Concept Development – Problem 2
8.3 – 6.4 = 1.9

12. 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

13. Concept Development – Problem 2
9.2 – 6.4 = 2.8

14. Concept Development – Problem 3
Solve the following problems using a place value chart or the standard algorithm.
0.831 – =
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
0.539 9 10 3 10
4.003
1.290
2.713
1.29

15. Concept Development – Problem 3
0.831 – = 0.539

16. Concept Development – Problem 3
4.003 – 1.29 = 2.713

17. Concept Development – Problem 3
6 – 4.08 =

18. End of Lesson
Problem Set
Debrief
Exit Ticket