1. Learning Objective
We will solve problems involving a percent of a quantity1.
What are we going to do?
What does quantity mean?
Quantity means __________.
CFU
Common Core 7.RP
Activate Prior Knowledge
If ratios are equivalent, then you can find a missing value.
If 6 pounds of beans cost $15, how much will 2 pounds of beans cost? How much will 8 pounds of beans cost? 1.
pounds
dollars 6 15 2 8 5 20
If 12 cups of flour are needed to bake 9 pies, how many cups are needed to bake 3 pies? How many cups of flour are needed to bake 12 pies?
Students, you already know how to use equivalent ratios to find an unknown value. Now, we will solve problems involving percent of a quantity.
Make Connection 2.
cups
pies 12 9 3 4 16
1 an amount
Vocabulary

2. Percent of a Quantity A percent (%) is part of 100.
Concept Development
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship2.
Percent of a Quantity
Complete the statement below. Explain your answer.
If Joanna has downloaded 60 MB of the file, the download is
_____ complete.
If Joanna has downloaded
_______, the download is 80% complete.
CFU
Johanna is downloading a 120 MB file.
If she has downloaded 90 MB, the download is 75% complete.
If she has downloaded 48 MB, the download is 40% complete.
If she has downloaded 72 MB, the download is 60% complete.
If she has downloaded 30 MB, the download is 25% complete.
50%
96 MB
Megabytes 12 24 48 60 72 96
120 6 30 90 1% 5%
10%
20%
25%
50% 0%
10%
20%
25%
30%
40%
50%
60%
70%
75%
80%
90%
100%
2 the way things are connected
Vocabulary

3. Examples: 40% = 2  20% 75% = 3  25% 70% = 7  10%
Strategy Development (Optional)
What percent am I asked to find and what percent am I given?
Which simple percent divides both given and needed percent?
After I calculate the simple percent, what do I multiply by to find the percent in the problem?
Thinking Process
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
Find 40%, given 100%
The Strategy
A simple percent (5%, 10%, 20%, 25%, or 50%) can be used to calculate any percent in the problem.
Examples: 40% = 2  20% 75% = 3  25% 70% = 7  10%
20% (10% and 5% also work)
220 people answered a food survey.
1. 40% of the people surveyed reported they had food allergies. How many people had food allergies?
___________________________________________________________
2. 75% of the people reported that they eat a full, healthy breakfast. How many people eat a full, healthy breakfast?
20% × 2 = 40%
Explain how you would apply the strategy to #2.
CFU
÷ 5
 2 1.
People
220
220 ÷ 5
(220 ÷ 5)  2
People
Percent
100
100 ÷ 5
(100 ÷ 5)  2
÷ 5
 2
(220 ÷ 5) × 2
(220 ÷ 4) × 3
220
÷ 4
 3 2.
 2
 3
÷ 5
÷ 4 1% 5%
10%
20%
25%
50%
People
220
220 ÷ 4
(220 ÷ 4)  3
(100 ÷ 4)  3
75%
Percent
100
÷ 4
100 ÷ 4 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
 3

4. People  2  3 ÷ 5 ÷ 4 A percent (%) is part of 100.
Skill Development/Guided Practice
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
On the double number line, record3 the given information and the percent to find.
Determine which simple percent to calculate; 5, 10, 20, 25, or 50%.
Calculate this percent of the quantity.
Solve for the unknown by using the simple percent and quantity.
Interpret4 the solution.
Solve problems involving a percent of a quantity using a double number line. 1 a 2 3 4
How did I/you determine which simple percent to use?
How did I/you use the double number line to solve the percent problem?
CFU 2 3
220 people answered a food survey.
1. 40% of the people surveyed reported they had food allergies. How many people had food allergies?
___________________________________________________________
2. 75% of the people reported that they eat a full, healthy breakfast. How many people eat a full, healthy breakfast?
÷ 5
 2
People
220 44 88
88 of the 220 people surveyed had food allergies.
Percent
100 20 40
÷ 5
 2
165 of the 220 people surveyed eat a full, healthy breakfast.
÷ 4
 3 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% 5% 1%
People
People
220 55
165 44 55 88
165
220
Percent
100 25 75
÷ 4
 3
 2
 3
÷ 5
÷ 4
20%
25%
50%
75%
3 make a note
4 explain
Vocabulary

5. ÷ 3  4 ÷ 3  5 Songs Pigs A percent (%) is part of 100.
Skill Development/Guided Practice (continued)
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
How did I/you determine which simple percent to use?
How did I/you use the double number line to solve the percent problem?
CFU 2 3
On the double number line, record the given information and the percent to find.
Determine which simple percent to calculate; 5, 10, 20, 25, or 50%.
Calculate this percent of the quantity.
Solve for the unknown by using the simple percent and quantity.
Interpret the solution.
Solve problems involving a percent of a quantity using a double number line. 1 a 2 3 4
3. On his MP3 player, Sal had 123 songs that were rock. That was 75% of all his songs. How many total songs did he have on his MP3 player?
4. Andrea has 102 pigs at her Mom’s farm. That is 60% of all her pigs. Find the total number of pigs Andrea owns.
Songs
Pigs 41
123
164 34
102
170
÷ 3
 4
÷ 3
 5
75%
÷ 3
 4
÷ 3
 5
Songs
123 41
164
Pigs
102 34
170
Percent 75 25
100
Percent 60 20
100
÷ 3
 4
÷ 3
 5
Sal has 164 songs on his MP3 player.
Andrea owns 170 pigs total.

6. percent quantity given simple percent
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
Skill Closure
On the double number line, record the given information and the percent to find.
Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle)
Calculate this percent of the quantity.
Solve for the unknown by using the simple percent and quantity.
Interpret the solution.
Solve problems involving a percent of a quantity using a double number line. 1 a 2 3 4
÷ 4
 3
1. 75% of 80 patients in one hospital were in intensive care. How many patients were in intensive care?
Patients 80 20 60
Percent
100 25 75 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% 5%
25% 1%
Patients
÷ 4
 3 60 80 20
60 of the 80 patients are in intensive care.
 3
÷ 4
20%
25%
50%
75%
Access Common Core
Word Bank
percent quantity given simple percent
Explain how you determined which simple percent to use and how you used it to solve the problem.
Answers may vary.
Summary Closure
What did you learn today about solving problems involving a percent of a quantity?
(Pair-Share) Use words from the word bank.

7. Independent Practice
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
On the double number line, record the given information and the percent to find.
Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle)
Calculate this percent of the quantity.
Solve for the unknown by using the simple percent and quantity.
Interpret the solution.
Solve problems involving a percent of a quantity using a double number line. 1 a 2 3 4
people came to the football game. 60% used student passes. How many people got in using a student pass?
2. Five schools were in the band competition. Forty-five band members were from our school, which was 25% of the total band members. How many total band members were in the competition?
People
Band Members
500
1500
2500
180 45
 3
÷ 5
 4
÷ 5
 3
 4
People
2500
500
1500
Band Members 45
180
Percent
100 20 60
Percent 25
100
÷ 5
 3
 4
1,500 people of the 2500 got in using a student pass.
There were 180 total band members in the competition.

8. Independent Practice (continued)
A percent (%) is part of 100.
A percent of a quantity is part of a total.
Equivalent ratios on a double number line can be used to show the percent relationship.
On the double number line, record the given information and the percent to find.
Determine which simple percent to calculate; 5, 10, 20, 25, or 50%. (circle)
Calculate this percent of the quantity.
Solve for the unknown by using the simple percent and quantity.
Interpret the solution.
Solve problems involving a percent of a quantity using a double number line. 1 a 2 3 4
students were asked to choose their favorite snow-cone flavor. Twenty percent voted for strawberry. How many students preferred strawberry?
4. Farmer John has 120 cows. Seventy-five percent of his cows are underweight. Find the quantity of cows that are underweight.
Students
Cows 32
160 30 90
120
÷ 5
 3
÷ 4
75%
÷ 5
÷ 4
 3
Students
160 32
Cows
120 30 90
Percent
100 20
Percent
100 25 75
÷ 5
÷ 4
 3
32 of the 160 students preferred the flavor of strawberry.
90 of Farmer John’s cows are underweight.

9. The sweater will be discounted $10.
Periodic Review 1
1. A clothing store offers a 25% discount on all items in the store. The original price of a sweater is $40; how much is the discount amount?
2. The basketball player set a record by scoring 55 points in one game. 40% of his points were one-point free throws. How many points were free throws? 10 40 22 55
25%
÷ 4
÷ 5
 2
Price 40 10
Points 55 11 22
Percent
100 25
Percent
100 20 40
÷ 4
÷ 5
 2
The sweater will be discounted $10.
The player got 22 points from the free throw line.
Access Common Core
260 coffee mugs were sold last weekend.
For every multiple of 5%, find the number of coffee mugs. Record the amounts on the double number line. 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100% 5%
25%
260 26 52 78
104
130
156
182
208
234 13 39 65 91
117
143
169
195
221
247