1. NYS Math Module 1
Lesson 11
I can…
take out the unit 5.NBT.1
add, subtract, and multiply decimals 5.NBT.7
Objective: Multiply a decimal fraction by single-digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used.

2. Take Out the Unit 1.234 = ____ thousandths 1234
Say this number:
1.234 = ____ thousandths
1234
Think about how many thousandths are in
How much is one thousand, thousandths?
1.000 = 1
One thousand thousandths = 1 whole
Say this number:
= _________________
65 ones 247 thousandths

3. 76.358 = 7 tens ____ thousandths 6 358 6358
On your board, fill in the blank.
= 7 tens ____ thousandths
6 358
6358
Let’s try another one.
= 763 tenths ____ thousandths 58 58
What do you notice? Discuss with your partner.

4. 76.358 = ____ hundredths 8 thousandths 7635
Last one.
76 35
= ____ hundredths 8 thousandths
7635

5. Add and Subtract Decimals
Write the addition sentences in decimal form.
7258 thousandths + 1 thousandth = _______
= 7.259
7 ones 258 thousandths + 3 hundredths = _______
= 7.288
7 ones 258 thousandths + 4 tenths = _______
= 7.658

6. Let’s try some more… 6 ones 453 thousandths + 4 hundredths = _______
= 6.493

7. Tell your partner how you are solving these problems.
2 ones 37 thousandths + 5 tenths = _______
=2.537
Tell your partner how you are solving these problems.
You add the number to the corresponding place value.
=2.537
Both the “0” and “5” are in the tenths place, so you add 0 +5 = 5. All the other place values did not change.

8. 6 ones 35 hundredths + 7 thousandths = _______
= 6.357

9. Write the subtraction sentence in decimal form.
4 ones 8 hundredths – 2 ones = _______
= 2.08
9 tenths 7 thousandths – 4 thousandths = _______
= 0.903
4 ones 582 thousandths – 3 hundredths = _______
4.582 – 0.3 = 4.552

10. 9 ones 708 thousandths – 4 tenths = _______
9.708 – 0.4 = 9.308

11. 4 ones 73 thousandths – 4 hundredths = _______
4.073 – 0.4 = 3.673

12. Word Problem
After school, Marcus ran 3.2km and Cindy ran 1.95km. Who ran farther? How much farther?
3.20
1.95 -
1.25

13. Concept Development Show 2 tenths on your place value chart.
ones
tenths
Make 3 copies of 2 tenths.
How many tenths to you have in all?
6 tenths
Write a number sentence to express how we made 6 tenths.
= 0.6
3 copies of 2 tenths is ____________
6 tenths
3 x 0.2 = 0.6
Read the equation in unit form.

14. How was 4 x 3 tenths different from 3 x 3 tenths?
Find the value of 3 x 0.3 and 4 x 0.3.
ones
tenths
ones
tenths
9 tenths
12 tenths
How was 4 x 3 tenths different from 3 x 3 tenths?
12 tenths makes a number greater than 1 whole
4 copies of 3 tenths is _______________.
12 tenths
12 tenths is the same as _______________.
1 and 2 tenths

15. How can we use our knowledge from the previous problems to solve this?
2 x 0.43 = _______
0.86
We make copies of hundredths like we make copies of tenths. Hundredths is a different unit, but we can multiply it just like tenths.
Use your place value chart to find the product. Complete the sentence, “2 copies of 43 hundredths is __________.”
0.86
Read what your place value chart shows.
Two groups of 4 tenths = 0.8
Two groups of 3 hundredths= 0.06

16. Solve this problem using your disks.
4 x = _______
1.692
0.423 X
1.692
Read the product that is shown on your place value chart.
How was this problem different?
We had to bundle 10 thousandths to make 1 hundredth.
Did any other units have to be regrouped?
Yes, the tenths. We had to regroup 10 tenths to make 1 whole.
Show how you found the product using an area model and equation.

17. Solve this problem using an area model.
6 x 1.21 = _______
7.26
Draw an area model.
How many sections do we have?
3; ones, tenths, and hundredths
1.21
X 6
7.26 6 6
12 tenths
6 hundredths
= 7.26
I am multiplying each number by what? 6
With a partner, solve the equation using an area model and an equation.

18. Solve this problem using an area model and an equation.
7 x 2.41 = _______
16.87 7 14
28 tenths
7 hundredths
= 16.87
2.41
X 7
16.87

19. Last one..
8 x 2.34 = _______
18.72 8 16
24 tenths
32 hundredths
= 18.72
2.34
X 8
18.72

20. Thank you for your purchase.
To view more of my products visit:
Backgrounds and clip art provided by:
Worksheets in this file are from NYS Math Module 1 Grade 5. I have simply minimized the pages to reduce the use of paper. For the entire module visit: