1. NYS Math Module 1
Lesson 16
I can…
divide by exponents 5.NBT.2
find the quotient 5.NBT.7
Objective: Solve word problems using decimal operations.

2. Divide by Exponents
**8 minutes**
On your mark,
get set,
GO!

3. Find the Quotient 0.3 ÷ 2 = _____ 0.15 0.15 0.30 2 - 0 2 10 - 10
On your place value chart, draw 3 tenths in number disks.
3 tenths ÷ 2 = ___ hundredths ÷ 2 = ___ tenths ___ hundredths 30 1 5
0.15
Now solve using an algorithm. 2
0.30 -
0 2 10 - 10

4. Solve using an algorithm.
0.9 ÷ 5 = _____
0.18
0.18 5
0.90 -
0 5 40 - 40

5. Solve using an algorithm.
0.58 ÷ 4 = _____
0.145
0.145 4
0.580 -
0 4
0 18 - 16
2 0 -
2 0

6. Solve using an algorithm.
6.7 ÷ 5 = _____
1.34
1.34 5
6.70 - 5
1 7 - 15 20 - 20

7. Solve using an algorithm.
93 tenths ÷ 5 = _____
1.86
1.86 5
9.30 - 5 43 - 40 30 - 30

8. Word Problem
Jesse and three friends buy snacks for a hike. They buy trail mix for $5.42, apples for $2.55, and granola bars for $ If the four friends split the cost of the snacks equally, how much should each friend pay?
Step 1 – Add (total cost of snacks)
Step 2 – Divide (individual. Cost)
Step 3 – multiply (Check cost)
11.36 4
02.84 8 - 32 16 33
1 1
$5.42
$2.55
+$3.39
$11.36
2.84
X 4
11.36

9. Concept Development
Let’s read this word problem together:
This is the first problem on your problem set.
Mr. Frye distributed $126 equally among his 4 children for their weekly allowance. How much money did each child receive?
Let’s identify our variables. Who and what is this problem about?
Draw a bar.
$126
Mr. Frye’s money ?
Read the first sentence of the problem together.
What is the important information in that sentence?
Discuss with a partner.
How can we represent this on our diagram?
How can we represent the 4 children?
What is our unknown?
The amount of money each child receives.

10. $126
Mr. Frye’s money ?
126.0 4
031.5 12 - 04 20 06
4 units = $126
1 units = ?
1 units = $126 ÷ 4
= $31.50
How many unit bars are equal to $126?
4 units is the same as $126
How can we find the value of one unit?
Divide $126 by 4, because we have a whole that we are sharing equallly.
Write the equation that will give us the amount that each child receives?
$126 ÷ 4 = _______
Solve the problem and write down your answer in a complete sentence.
Each child received $31.50 for their weekly allowance.

11. ? Step 1: Step 2: 31.50 (from Dad) +10.50 (from John) $42.00
Let’s look at part b on your problem set.
Solve using a tape diagram.
$31.50 ?
Johns’ money
Step 1:
Step 2:
31.50 (from Dad)
(from John)
$42.00
Each of his siblings will get $42.00 in all.
31.50 3
10.50 30 - 15 00 1

12. Read problem #4 on your worksheet, identify the variable (who and what). Illustrate using a bar.
Brandon mixed 6.83 lbs. of cashews with 3.57 lbs. of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.35 lbs. of nuts left. What was the weight of each bag?
6.83
3.57
Brandon’s cashews/pistachios
Read the first sentence.
What is the important information in this sentence?
Tell a partner.
How can I represent this information on our tape diagram?
Draw two parts .
Should the parts be equal?
No.
Let’s read the next sentence.
How will we we represent this part of the problem?
Make a new bar , split into number of bags used and one part for what is left over. OR Erase bar separating nuts and split into even parts.

13. I am going to use the bar that I’ve already drawn
I am going to use the bar that I’ve already drawn. I’ll label my bags with the letter b and label the part that wasn’t put into a bag.
Brandon mixed 6.83 lbs. of cashews with 3.57 lbs. of pistachios. After filling up 6 bags that were the same size with the mixture, he had 0.35 lbs. of nuts left. What was the weight of each bag?
Brandon’s cashews/pistachios
left ? b b b b b
What is the question?
How much did each bag weight?
0.35
Where should we put our question mark?
Inside one of the units labeled b.
How will we find the value of 1 unit?
We need to divide by 6. We first have to take away the part that is not in a bag.
Perform your calculations.
State your answer in a complete sentence.

14. Each bag contained 1.675 lbs. of nuts.
= 10.4
6 units = 10.4
1 unit = ( ) ÷ 6
10.050 6
01.675 - 36 45 40 42 30
10.40
10.05
1 unit = lbs.
Each bag contained lbs. of nuts. - 30
Complete question 2, 3, and 5 on your worksheet, using tape diagrams and calculations to solve.

15. Step 1: Step 2: 89 cm + 23 cm 112 cm Problem #2 0.89 m 1.78 m 2 - 1 6
Olivia’s height
Step 2:
Ava’s height
89 cm
+ 23 cm
112 cm
1.78 m 2
0.89 m
1 6 - 18 1
Olivia is 89 cm tall.
Ava is 112 cm tall.

16. Step 1: Problem #3 Step 2: 286.00 35.75 + 510.00 X 8 $ 796.00 286.00
Total of payments
Step 2:
Total cost of payments
286.00 $
35.75
X 8
286.00
Step 3:
Savings
796.00 $
Mr. Hower will save$96.01 if he pays cash.

17. Problem #5a Step 1: Step 2: 8.85 kg of flour will be left. 475 g X 4
Figure out how much flour the store bought.
Step 2:
Flour used for muffins
475 g
X 4
1900g
8.85 kg of flour will be left. 2
3 2
3.5
X 4
14.0 kg
Step 3:
Convert to kg
1900 g = 1.9kg
Step 4:
Flour used for bread
0.65
X 5
3.25 kg
3 2
Step 5:
Total flour used
Step 6:
Flour left over
3.25
+ 1.90
5.15kg 1
14.00
8.85kg

18. 3 bins will be needed to store all the remaining flour.
Problem #5b
Step 1:
How many bins?
8.85 3
2.95 6 - 27 15 28 - 15
3 bins will be needed to store all the remaining flour.

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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: