1. 5th Grade Module 1 – Lesson 12
Lesson 12: I can multiply a decimal fraction by single-digit whole numbers, including using estimation to confirm the placement of the decimal point.
5th Grade Module 1 – Lesson 12

2. 5th Grade Module 1 – Lesson 12
Time to Sprint!
Your teacher will give you the adding decimals sprint.
5th Grade Module 1 – Lesson 12

3. Find the Product Get your white boards ready! 4 x 2 ones = ______
Write the multiplication sentence.
2. Say the multiplication sentence in unit form.
4 x 2 = 8
4 x 2 ones =8 ones
5th Grade Module 1 – Lesson 12

4. 5th Grade Module 1 – Lesson 12
Write the multiplication sentence then say it in unit form for each problem. Record your work in your math notebook.
4 x 0.2
4 x 0.02
5 x 3
5 x 0.3
5 x 0.03
4 x 0.2 = 0.8
4 x 2 tenths = 8 tenths
6) 3 x 0.2
7) 3 x 0.03
8) 3 x 0.23
9) 2 x 0.14
4 x = 0.08
4 x 2 hundredths= 8 hundredths
5th Grade Module 1 – Lesson 12

5. 5th Grade Module 1 – Lesson 12
Application Problem
Patty buys 7 juice boxes a month for lunch. If one juice costs $2.79, how much does Patty spend on juice each month? Use an area model to solve.
5th Grade Module 1 – Lesson 12

6. 5th Grade Module 1 – Lesson 12
Application Problem
Patty buys 7 juice boxes a month for lunch. If one juice costs $2.79, how much does Patty spend on juice each month? Use an area model to solve. 2
7tenths
9hundredths 7
Extension: How much will Patty spend on juice in 10 months? In 12 months?
5th Grade Module 1 – Lesson 12

7. How are these three problems alike?
Concept Development
Have your whiteboards & notebooks ready!
31 x 4 = 124
3.1 x 4 = 12.4
0.31 x 4 = 1.24
How are these three problems alike?
In your notebook, use an area model to find the products.
*see next slide for solutions
5th Grade Module 1 – Lesson 12

8. 5th Grade Module 1 – Lesson 12
3 tens one
31 x 4 = 124
4 ones 4
12 tens =
3 ones tenth
3.1 x 4 = 12.4
4 tenths 4
12 ones =
3 tenths hundredths
0.31 x 4 = 1.24
4 hundredths 4
12 tenths =
5th Grade Module 1 – Lesson 12

9. Let’s look at these problems again…
31 x 4 = 124
3.1 x 4 = 12.4
0.31 x 4 = 1.24
How are the products of all three problems alike?
If the products have the same digits and those same digits are in the same order, do the products have the same value? Why or why not?
Turn and talk.
So, we can multiply the numerals first, then think about the units to help us place the decimal.
5th Grade Module 1 – Lesson 12

10. 5th Grade Module 1 – Lesson 12
5.1 x 6 =
What is the smallest unit in 5.1?
tenths
Multiply 5.1 by 10 to convert it to tenths. How many tenths is the same as 5.1?
51 tenths
Suppose our multiplication sentence was 51 x 6.
Multiply and record your multiplication vertically.
What is the product?
tenths
X 6
tenths
We know that our product will contain these digits, but is 306 a reasonable product for our actual problem of 5.1 x 6? Turn and talk.
Where does it make sense to place the decimal in 306? What is the product? Write your answer on your whiteboard.
30.6
5th Grade Module 1 – Lesson 12

11. 45.6 11.4 x 4 = What is the smallest unit in 11.4?
tenths
What power of 10 must I use to convert 11.4 to tenths? How many tenths are the same as 11 ones 4 tenths? Turn and talk.
101 =
114 tenths
tenths X
tenths
Multiply vertically to find the product of 114 tenths x 4.
We know that our product will contain the digits 456. How will we determine where to place our decimal? Turn & Talk. Record where you think the decimal should go.
45.6
5th Grade Module 1 – Lesson 12

12. Try this one with your partner in your notebook:
7.8 x 3 =
What is the smallest unit in 7.8?
What power of 10 must I use to convert 7.8 to tenths? How many tenths are the same as 7 ones 8 tenths?
Multiply vertically to find the product of 78 tenths x 3.
We know that our product will contain these digits. Determine where to place our decimal?
5th Grade Module 1 – Lesson 12

13. 5th Grade Module 1 – Lesson 12
3.12 x 4 Use hundredths to name 3.12 and multiply vertically by 4. What is the product? Below are 4 possible products for 3.12 x 4. Turn and talk to your partner about which of these products is reasonable Now confirm the actual product using an area model in your notebook. Be prepared to share your thinking!
3 1 2 hundredths X
hundredths
5th Grade Module 1 – Lesson 12

14. 5th Grade Module 1 – Lesson 12
3.12 x 4
3 ones
1 tenth
2 hundredths
12 ones
8 hundredths 4
4 tenths =
5th Grade Module 1 – Lesson 12

15. 3.22 x 5 Let’s Try Another Problem in Your Notebook!
Use hundredths to name 3.22 and multiply vertically by 5. What is the product?
Below are 4 possible products for 3.22 x 5. Turn and talk to your partner about which of these products is reasonable.
Confirm the actual product using an area model in your notebook. Be prepared to share your thinking!
*solution on next slide
5th Grade Module 1 – Lesson 12

16. 5th Grade Module 1 – Lesson 12
3.22 x 5
3 2 2 hundredths X
hundredths
3 ones
2 tenths
2 hundredths
15 ones
10 hundredths 5
10 tenths =
5th Grade Module 1 – Lesson 12

17. 5th Grade Module 1 – Lesson 12
Try this one on your own!
3.42 x 6
Use hundredths to name 3.42 and multiply vertically by 6. What is the product?
Here are 4 possible products for 3.42 x 6. Turn and talk to your partner about which of these products is reasonable.
Confirm the actual product using an area model in your notebook. Be prepared to share your thinking!
3 4 2 hundredths X
hundredths
*solution on next slide
5th Grade Module 1 – Lesson 12

18. 5th Grade Module 1 – Lesson 12
3.42 x 6
3 4 2 hundredths X
hundredths
3 ones
4 tenths
2 hundredths
18 ones
12 hundredths 6
24 tenths =
5th Grade Module 1 – Lesson 12

19. Which product is most reasonable?
0.733 x 4
Rename using its smallest units and multiply vertically by 4.
What is the product?
Which product is most reasonable?
7 3 3 thousandths
X 4
2.932
29.32
293.2
2,932
thousandths
5th Grade Module 1 – Lesson 12

20. Which product is most reasonable?
x 4
Rename using its smallest units and multiply vertically by 4.
What is the product?
Which product is most reasonable?
thousandths X
4.2932
42.932
429.32
4,293.2
42,932
thousandths
5th Grade Module 1 – Lesson 12

21. Now try this problem on your own…
Record your work in your math notebook.
5.733 x 4 = ____
Remember to rename using its smallest units and multiply vertically by 4.
Use reasoning to determine the decimal placement.
5th Grade Module 1 – Lesson 12

22. Get Ready to Complete the Problem Set on Your Own!
Complete Pages 1.E.23 & 1.E.24. You will have 10 minutes to work. Try your Best!
5th Grade Module 1 – Lesson 12

23. 5th Grade Module 1 – Lesson 10
Debrief
How can whole number multiplication help with decimal multiplication?
How does the area model help you to justify the placement of the decimal point for the product in 1(b)?
5th Grade Module 1 – Lesson 10

24. 5th Grade Module 1 – Lesson 12
Exit Ticket Time!
5th Grade Module 1 – Lesson 12