1. Solving Percent Problems with a Double Number Line Model

2. Warm Up
CONTENT OBJECTIVE: Students will be able to construct and interpret a double number line model for solving percent problems involving finding the whole or a part or the percent.
LANGUAGE OBJECTIVE: Students will be able to describe verbally to another student their understanding of double number lines. They will listen to the other student share.
1. The ratio of the number of girls to the number of boys in a chess club is 3 to 2. There are 14 boys in the chess club. What is the number of girls in the chess club?
2. A florist sells 8 roses for a total of $10. Each rose costs the same amount.
What is the cost of 12 roses? 21
girls
boys 7 7 7
roses
cost 8
$10 4 $5 7 7
Answer:
21 girls
Answer:
$15 14 12
$15
Agenda

3. Launch Rihanna is a very popular musical artist.
Her 2012 album Unapologetic has sold close to 1 million copies worldwide.
The album can be bought at most places for $15. How much money would you expect that Rihanna has made from the sales of Unapologetic?
There are many costs that have to be paid from the sale of an album before the artist can receive her share of the profits.
Based on most information we can assume that Rihanna only received 5% of the total sales of the album. How much money is that?
Agenda

4. Launch New Tool: Double Number Lines
Today we are going to learn how to calculate the percent of an amount.
We are going to use a tool called the Double Number Line.
To find out how much money Rihanna is estimated to have made from the sale of Unapologetic we need the total sales of the album and the percent she received.
$15 per album x 1 million albums sold = $15 million sales of all albums
Again, Rihanna only received about 5% of the total sales of the album.
Let’s use a double number line to determine: How much money is that?
Agenda

5. Launch $0 $1.5 $15 percent Sales New Tool: Double Number Lines 50% 10%
$15 per album x 1 million albums sold = $15 million sales of all albums
How much money is 5% of $15 million?
Rihanna only received about 5% of the total sales of the album.
So Rihanna received about $750,000 from the sales
of an album that made $15,000,000.
$0.75 $0
$1.5
$15
percent
Sales
(in millions)
50%
10%
20%
30%
40%
60%
70%
80%
90% 0%
100% 5%
$15 million sales worldwide
5% or $750,000
Agenda

6. Launch Let’s learn how to use the double number line tool.
New Tool: Double Number Lines
Let’s learn how to use the double number line tool.
Agenda

7. Explore
New Tool: Double Number Lines
1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 80
percent
shots 0%
100%
We are going to make a double number line to compare
shots to percentage. Then we can easily find the percent.
She took 20 shots, so we have to put 20 in the right
position on the number line. First let’s find half.
First, we set up the zeroes. Zero shots is zero percent.
It says she took 80 total shots, so 80 is 100% of the shots.
Agenda

8. Explore
1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made? 20 40
75% 60 80
percent
shots 0%
25%
50%
100%
Let’s fill out the other side of the number line.
Half of the 80 shots, is 40. And half of 100% is 50%.
The question asks for the percent that is equal to 20 out of 80.
So, where do I put the 20?
It’s half of 40!
You can see that every number of shots is lined up with a percent.
The answer is 25%.
We find halfway between 0 and 40. What percent is that?
Agenda

9. Explore
1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made?
25%
percent
shots 0%
100% 80
50% 40 20
75% 60
Partners: Take turns asking and answering:
Lefty – Ask Righty “How did we figure out where to put 20?”
Righty – Ask Lefty “How do we know that 20 shots = 25%?”
Agenda

10. Explore – Let’s do the next one together!
2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? ?
percent
candies 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
This time we know the part of the bag and the percent but not the total. We can still use a double number line.
Next we need to put 30% in the right position. We can’t just put it anywhere. It has to be the right spot.
First we need to mark out zero and 100%
Do you have any ideas?
Agenda

11. Explore – Let’s do the next one together!
2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? 6 ?
percent
candies 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
We know that 30% is equal to 6 candies. So we can put 6 across from 30%.
Can you use this information to find out how much 100% is?
Think, Pair, Share: See if you can find an answer. Then, tell your speaking partner. Listen to your partner’s idea.
Agenda

12. Explore – Let’s do the next one together!
2.) There are 6 candies in a bag that is 30% full. How many candies are in a full bag? 2 4 6 8 10 12 14 16 18 20
percent
candies 0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Here is one way to solve it. There are many ways.
Answer:
20 candies
Agenda

13. On Your Own – Try this one!
3.) A class conducts a survey of 1,000 students. The survey reveals that 20% of the students speak Spanish. How many students is this?
percent
students 0%
100%
1,000
100
10%
200
20%
300
30%
400
40%
500
600
60%
700
70%
800
80%
900
90%
50%
Answer: 200 students speak Spanish.
Agenda

14. Percents in Life taxes discounts tips
Here are a few examples of situations in which adults calculate
with percents in real life.
taxes
discounts
tips
Agenda

15. Taxes and Tips are a percent added on to a cost.
4.) Cheryl had breakfast in the diner and the bill came to $ She
would like to leave a 20% tip. How much should she leave altogether?
5.) Martin wants to purchase a book that costs $12. The sales tax
Is 5%. If Martin has $13, can he purchase the book?
Both of these problems can be solved with the same double number line.
percent
dollars 0%
100%
$12
Agenda

16. Taxes and Tips are a percent added on to a cost.
4.) Cheryl had breakfast in the diner and the bill came to $ She
would like to leave a 20% tip. How much should she leave altogether?
Just remember to add the tip to the total amount if you are looking
for the total cost!
Answer: $ $2.40 = $14.40
percent
dollars 0%
100%
$12.00
$1.20
10%
$2.40
20%
$3.60
30%
$4.80
40%
$6.00
$7.20
60%
$8.40
70%
$9.60
80%
$10.80
90%
50%
Agenda

17. Taxes and Tips are a percent added on to a cost.
5.) Martin wants to purchase a book that costs $12. The sales tax
Is 5%. If Martin has $13, can he purchase the book?
How do you find 5% on this number line? Do you have any ideas?
5% is halfway between 0% and 10%. What is half of $1.20?
percent
dollars 0%
100%
$12.00
$1.20
10%
$2.40
20%
$3.60
30%
$4.80
40%
$6.00
$7.20
60%
$8.40
70%
$9.60
80%
$10.80
90%
50%
Agenda

18. Taxes and Tips are a percent added on to a cost.
5.) Martin wants to purchase a book that costs $12. The sales tax
Is 5%. If Martin has $13, can he purchase the book?
Don’t forget that a tax is also an amount added on to the total.
Answer: He does have enough money because $ $0.60 = $12.60 total cost with tax.
$0.60
percent
dollars 0%
100%
$12.00
$1.20
10%
$2.40
20%
$3.60
30%
$4.80
40%
$6.00
$7.20
60%
$8.40
70%
$9.60
80%
$10.80
90%
50% 5%
Agenda

19. Discounts are an amount taken OFF of a total cost.
6.) Sam got a $12 discount off a $48 purchase. What percent
discount did he get?
The question could have asked: how much did Sam pay for a purchase that was 25% off of the original price of $48. What would the answer be?
I can see that $24 is half of $48. And $12 is half of $24.
So, what’s half of 50%?
$ $12.00 = $36.00 is the cost of the purchase after a 25% discount.
percent
dollars 0%
100%
$48
$12
$24
Answer:
25%
50%
25%
Remember: If the question asks for the total cost you must subtract the discount.
Agenda

20. Try These! Independent Practice
1.) Alexis bought a CD player. She does not remember the price, but
she does know that the 5% sales tax came to $ What was the price of the CD player?
2.) Customers left Jill $2.50 as a tip. The tip was 20% of the total. How much was the bill?
Agenda

21. What is the answer to this problem?
Summary
1.) Carly made 20 out of 80 shots while practicing basketball. What is the percentage of shots that Carly made?
25%
percent
shots 0%
100% 80
50% 40 20
75% 60
What is the answer to this problem?
Partners – Take turns describing how to solve this problem, step by step.
Agenda