1. Lesson 12- Objective: Multiply a decimal fraction by single-digit whole numbers including using estimation to confirm the placement of the decimal point.
Engage NY Module 12

2. Fluency Practice – Add Decimals (Sprint)
3 + 1 =____
= _____
= ___
= ______
= ___
= _____
= ___
= ______
= ___
= ______
= ___
= _____
= ___
= _____
= ____
= ____
= ____
= _____ 4
2.84
4.5
3.51
4.52
7.651
5.836 42
5.62
6.218
4.629
4.728
13.589
18.642
27.148
3.997
42.58
41.789

3. Fluency Practice – Find the Product
4 x 2 ones = (what is another way to write this sentence)
4 x 2 = or
4 x 2 ones = 8 ones
4 x 2 tenths = (what is another way to write this sentence)
4 x 0.2 = or
4 x 2 tenths = 8 tenths
4 x 0.02 = (what is another way to write this sentence)
4 x 2 hundredths = or
4 x 0.02 = 0.08 8
0.8
8 hundredths

4. Fluency Practice – Find the Product
5 x 3 ones = (what is another way to write this sentence)
3 x 2 = or
5 x 3 ones = 15 ones
5 x 3 tenths = (what is another way to write this sentence)
5 x 0.3 = or
5 x 3 tenths = 15 tenths
5 x 0.03 = (what is another way to write this sentence)
5 x 3 hundredths = or
5 x 0.03 = 0.15 15
1.5
15 hundredths

5. Fluency Practice – Find the Product
3 x 0.2 =
3 x 0.03 =
3 x 0.23 =
3 x x 0.03 = =
2 x 0.14 =
2 x x 0.04 =
0.6 or 6 tenths
0.09 or 9 hundredths
0.69 or 69 hundredths
0.18 or 18 hundredths

6. Application Problem
Patty buys 7 juice boxes a month for lunch. If one juice costs $2.79, how much money does Patty spend on juice each month?
Use an area model to solve
Extension: How much will Patty spend on juice in 10 months? In 12 months?
Patty spends $19.53 on juice boxes a month.
2 ones
7 tenths
9 hundredths 7
14 ones
49 tenths
63 hundredths
$2.79 ……
1 month
2 month
7 month
Patty’s $
= = 19.53
$19.53 x 12 = x x 2 = = $234.36
$19.53 x 10 = $195.30

7. Concept Development - Problem 1-3
0.31 x 4 = You can look at this using an area model.
31 x 4 = You can look at this using an area model.
3.1 x 4 = You can look at this using an area model.
3 tens
1 one +
3 ones
1 tenth +
3 tenths
1 hundredth + 4
12 tens
4 ones 4
12 ones
4 tenths 4
12 tenths
4 hundredths
4 ones
12 tens
Or 120 + +
12 tenths or 1 ones 2 tenths or 1.2
4 hundredths
12 ones +
4 tenths
12 ones 4 tenths or 12.4
124 ones or 124
12 tenths + 4 hundredths or 1 ones 2 tenths 4 hundredths or or 1.24
Make a rectangle for each digit on the left of the X sign.

8. Concept Development – Problem 1-3
Looking back at the 3 examples how are the products alike?
They all have 1, 2, and 4 in the product and they are in the same order.
Do the products have the same value? Why or Why not?
No, the values are different because the units that we multiplied are different.
The decimal is not in the same place in every product.
The digits that we multiplied are the same, but you have to think about the units to make sure the answer is right.
Something to keep in my mind is that when multiplying you can multiply the numbers first and think about the units to help place the decimal.

9. Concept Development - Problem 4
5.1 x 6 = You can look at this using an area model or determining the smallest units.
What is the smallest units?
Tenths
How many tenths and how did you figure that out?
51 tenths, by multiplying 5.1 x 10 because it takes 10 tenths to make 1 one.
Now look at the multiplication as 51 x 6 or (5 tens x one x 6) = 30 tens + 6 ones = 300 ones + 6 ones = 306 ones.
Is it reasonable to say our answer is 306 ones? Why or Why not?
No because were talking about 51 tenths or 5 x 6 is 30, so the answer should be around 30 and not We could say it would be reasonable to say 306 tenths.
How can 306 tenths be renamed?
30 ones 6 tenths or 3 tens, 0 ones, 6 tenths
What is the answer to 5.1 x 6?
30.6

10. Concept Development - Problem 5
11.4 x 4 = You can look at this using an area model or determining the smallest units.
What is the smallest units?
Tenths
What power of 10 must we use to convert 11.4 to tenths?
101
How many tenths does 11.4 equal?
114 tenths
Now look at the multiplication as 114 x 6 or (1 hundred x ten x ones x 4) = 4 hundreds + 4 tens + 16 ones or 400 ones + 40 ones + 16 ones = 456 ones.
Is it reasonable to say our answer is 456 ones? Why or Why not?
No because were talking about 114 tenths or 11 x 4 is 44, so the answer should be around 44 and not We could say it would be reasonable to say 456 tenths.
How can 456 tenths be renamed?
45 ones 6 tenths or 4 tens, 5 ones, 6 tenths
What is the answer to 11.4 x 4?
45.6

11. Concept Development - Problem 6
Now try 7.8 x 3 using the area model or asking what the smallest unit is and solving from there.
23.4

12. Concept Development - Problem 7-8
3.12 x 4 = You can look at this using an area model.
3.22 x 5 = You can look at this using an area model.
3 ones
1 tenth + +
2 hundredths
2 hundredths
3 ones
2 tenths + +
8 hundredths 4
12 ones
4 tenths
10 hundredths 5
15 ones
10 tenths
0.4 12 + +
0.08 15 + 1 +
0.1
12.48
16.1
Make a rectangle for each digit on the left of the X sign.

13. Concept Development - Problem 9-10
Now try 3.42 x 6 = using area model.
20.52
Now try solving 3.91 x 4 using the area model or unit form.
15.64

14. Concept Development - Problem 11-13
With a partner try solving the following problems in your spiral math notebook.
Now try x 4= using area model.
2.932
Now try solving x 4 using the area model or unit form.
42.932
Now try solving x 4 using the area model or unit form.
22.932

15. End of Lesson
Problem Set
Debrief
Exit Ticket