1. Engage NY Module 1 LESSON 13
Objective: Divide decimals by single-digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method.

2. SPRINT – SUBTRACT DECIMALS
This Sprint will help students build automaticity in subtracting decimals without regrouping.

3. FIND THE PRODUCT
4 X 3 = _____. Say the multiplication sentence in unit form.
4 x 3 ones = 12 ones
4 x 0.2 = _____. Say the multiplication sentence in unit form.
4 x 2 tenths = 8 tenths

4. FIND THE PRODUCT
4 X 3.2 = _____. Say the multiplication sentence in unit form.
4 x 3 ones 2 tenths = 12 ones 8 tenths = 12.8
4 x 3.21 = _____. Say the multiplication sentence in unit form.
4 x 3 ones 2 tenths 1 hundredth = 12 ones 8 tenths 4 hundredths = 12.84

5. FIND THE PRODUCT
9 X 2 = _____. Say the multiplication sentence in unit form.
9 x 2 ones = 18 ones = 18
9 x 0.1 = _____. Say the multiplication sentence in unit form.
9 x 1 tenth = 9 tenths = 0.9

6. FIND THE PRODUCT
9 X 0.03 = _____. Say the multiplication sentence in unit form.
9 x 3 hundredths = 27 hundredths = 0.27
9 x 2.13 = _____. Say the multiplication sentence in unit form.
9 x 2 ones 1 tenth 3 hundredths = 18 ones 9 tenths 27 hundredths = 19.17

7. FIND THE PRODUCT
4.012 x 4 = _____. Say the multiplication sentence in unit form.
4 ones 12 thousandths x 4 = 16 ones 48 thousandths =
5 x = _____. Say the multiplication sentence in unit form.
5 x 3 ones 237 thousandths = 15 ones 10 tenths 15 hundredths 35 thousandths =

8. COMPARE DECIMAL FRACTIONS
Compare the following numbers using >, <, or =.
13.78_____ 13.86
13.78 < 13.86
0.78 _____
0.78 = 𝟕𝟖 𝟏𝟎𝟎
439.3 _____ 4.39
439.3 > 4.39

9. COMPARE DECIMAL FRACTIONS
Compare the following numbers using >, <, or =.
5.08 _____ fifty-eight tenths
5.08 < 5.8
Thirty-five and 9 thousandths _____ 4 tens
< 40

10. APPLICATION PROBLEM
Louis buys 4 chocolates. Each chocolate costs $2.35. Louis multiplies 4 x 235 and gets place the decimal to show the cost of the chocolates and explain your reasoning using words, numbers, and pictures.
He paid $9.40 for the chocolates. The decimal has to go between the 9 and the 4 because when Louis multiplies 4 and 235 it means 940 hundredths which is 9 wholes and 40 hundredths.
The only place that makes sense is between the 9 and the 4 because he will pay between (4 x $2) and (4 x $3).
8.00
1.20
+0.20
$9.40 4

11. Concept Development - Problem 1
Solve 0.9 ÷ 3 using disks on your place value chart. (9 tenths ÷ 3 = ______)
Show 9 tenths with your disks.
Divide 9 tenths into 3 equal groups.
How many tenths are in each group?

12. Concept Development - Problem 1
0.9 ÷ 3 = 0.3
Read the number sentence using unit form.
9 tenths divided by 3 equals 3 tenths.
How does unit form help us divide?
When we identify the units, then it’s just like dividing 9 apples into 3 groups. If you know what unit you are sharing, then it’s just like whole number division. You can just think about the basic fact.
3 groups of _______ = 0.9
What is the missing number in our equation?
3 tenths (0.3)

13. Concept Development - Problem 2
Solve 0.24 ÷ 4 using disks on your place value chart. (24 hundredths ÷ 4 = ______)
Ones
Tenths
Hundredths
Show 24 hundredths with your disks.
Divide 24 hundredths into 4 equal groups.
How many hundredths are in each group?
There are 6 hundredths in each group.
4 groups of _______ = 0.24
Write a division sentence for this problem.
0.24 ÷ 4 = 0.06

14. Concept Development - Problem 3
Solve ÷ 8 using disks on your place value chart. (32 thousandths ÷ 8 = ______)
Tenths
Hundredths
Thousandths
Show 32 thousandths with your disks.
Divide 32 thousandths into 8 equal groups.
How many thousandths are in each group?
There are 4 thousandths in each group.
8 groups of _______ = 0.032
Write a division sentence for this problem.
0.032 ÷ 8 = 0.004

15. Concept Development - Problem 3
Solve ÷ 8 using disks on your place value chart. (32 thousandths ÷ 8 = ______)
Tenths
Hundredths
Thousandths
Show 32 thousandths with your disks.
Divide 32 thousandths into 8 equal groups.
How many thousandths are in each group?
There are 4 thousandths in each group.
8 groups of _______ = 0.032
Write a division sentence for this problem.
0.032 ÷ 8 = 0.004

16. Concept Development - Problem 4
1.5 ÷ 5 = ______. Read the equation using unit form.
Fifteen tenths divided by 5.
What is useful about reading the decimal as 15 tenths?
When you say the units, it’s like a basic fact.
What is 15 tenths divided by 5?
3 tenths
1.5 ÷ 5 = 0.3

17. Concept Development - Problem 5
1.05 ÷ 5 = ______. Read the equation using unit form.
105 hundredths divided by 5.
Is there another way to decompose (name or group) this quantity?
1 one and 5 hundredths or 10 tenths and 5 hundredths.
Which way of naming 1.05 is most useful when dividing by 5? Why? Talk with those at your table then solve the problem.
10 tenths and 5 hundredths because they are both multiples of 5. This makes it easy to use basic facts and divide mentally. The answer is 2 tenths and 1 hundredth.
105 hundredths is easier because I know 100 is 20 fives so 105 is 1 more, 21. The answer is 21 hundredths.
1.05 ÷ 5 = 0.21

18. Concept Development - Problem 6
3.015 ÷ 5 = ______. Read the equation using unit form.
3 and 15 thousandths divided by 5.
Is there another way to decompose (name or group) this quantity?
3015 thousandths or 30 tenths and 15 thousandths or 301 hundredths and 5 thousandths.
Which way of naming is most useful when dividing by 5? Why? Talk with those at your table then solve the problem.
3.015 ÷ 5 = 0.601

19. Concept Development - Problem 7
4.8 ÷ 6 = ÷ 6 = 8
What relationship do you notice between these two equations? How are they alike?
8 is 10 times greater than 0.8.
48 is 10 times greater than 4.8.
The digits in the dividends are the same, the divisor is the same and the digits in the quotient are the same.
How can 48 ÷ 6 help you with 4.8 ÷ 6? Share your thoughts with those at your table.
If you think of the basic fact first, then you can get a quick answer. Then you just have to remember what units were really in the problem. This one was really 48 tenths.
The division is the same; the units are the only difference.

20. Concept Development - Problem 8
4.08 ÷ 8 = ÷ 8 = 51
What relationship do you notice between these two equations? How are they alike?
408 is 100 times greater than 4.08.
51 is 100 times greater than
The digits in the dividends are the same, the divisor is the same and the digits in the quotient are the same.
How can 408 ÷ 8 help you with 4.08 ÷ 8? Share your thoughts with those at your table.

21. Concept Development - Problem 9
÷ 7 = ,021 ÷ 7 = 9,003
What relationship do you notice between these two equations? How are they alike?
63,021 is 1000 times greater than
9,003 is 1000 times greater than
The digits in the dividends are the same, the divisor is the same and the digits in the quotient are the same.
How can 63,021 ÷ 7 help you with ÷ 7? Share your thoughts with those at your table.

22. Problem Set, Debriefing, Exit Ticket, and Homework
Complete Problem Set in small groups.
Check answers and discuss difficulties.
Handout Exit Ticket and independently.
Handout Homework.