1. PERCENT
UNIT 6
Math 7 Plus

2. In this presentation we are going to
think of percent in terms of parts
and use DOUBLE LINE GRAPHS and
a variation of TAPE DIAGRAMS
to solve problems.

3. First let’s consider double line graphs:
According to the double line graph below, we know that 1400 would represent 100%
700
1400 0%
50%
100%
So to find 50% of that, I would think of dividing the line in ½ between zero and 1400 : 50% = 50 = 1
Since 100% ÷ 2 = 50% I would also do 1400 ÷ 2 to get 700

4. So what if we wanted to find 25%....ideas?
We could take 100% divided by 4 to get 25% which means we would also divide 1400 by 4.
1400 ÷ 4 = 350
350
700
1400 0%
25%
50%
100%
Or we could take 50% divided by 2 to get 25% which means we would also divide 700 by 2.
700 ÷ 2 = 350
Hopefully students will come up with 100 divided by 4 or they may use 50% divided by 2….both work. The point is to get them coming up with the relationships.
Either way we get 25% will be 350 so now let’s
plug it in on the number line.

5. Now take a few minutes to discuss with the person next to you
how you would find 75%.
350
700
1400 0%
25%
50%
100%
Take a few minutes for students to share thoughts for 75%

6. We will advance to the next slide to check your answers.
Take a moment to consider how we would divide this number line up for 20% then share with the person sitting next to you.
Take a few moments to share those thoughts as a whole group now. 0%
100%
Give students a moment to discuss then as whole group ….divide into 5 parts…students should note that 20% is 1/5 of 100%.
Now draw this double number line on your paper and use it to find 20% of 400
and 80% of 400.
We will advance to the next slide to check your answers.

7. Discuss how you got these answers.80
320
400 0%
20%
40%
60%
80%
100%
Students should be able to relate 20% to 1/5 and verbalize how to use that to come up with 80% as well as recognizing 100% divided by 5 leads to 400 divided by 5. They may use 20% times 4 equals 80% so 80 times 4 gets Allow them to verbalize and present a variety of ways to relate to the solution.
Discuss how you got these answers.

8. Now you try using a double line graph to solve the following:
Sammie has spent $1,320 this month which is
75% of his monthly paycheck. Use a double number line graph to determine the amount
of his monthly check.
Solution shown on next slide

9. X 4
÷ 3
$1,320
$1,760
$440 0%
25%
50%
75%
100%
÷ 3
X 4

10. We will still consider the parts represented in a percent problem.
Now let’s look at a way to use TAPE DIAGRAMS to solve some percent problems.
We will still consider the parts represented in a percent problem.
Things to remember:
*We previously found that 20% was the same thing as 1/5 so we divided our number line into 5 parts.
*We also found that 25% was the same thing as 1/4 so we divided our number line into 4 parts.
*These facts helped us use a number line to break down the parts and solve percent problems.

11. Let’s look at using tape diagrams to solve a problem:
After a 20% discount, the price of a SuperSick skateboard is $140. What was the price before the discount?
Hmmm…if you get 20% off……that means
you are paying 80%...lets set up a tape diagram…
First we show what would be 100% in 5 parts because of the 20%
100%
20%
20%
20%
20%
20%
80%
The 80% represents $140 and is shown to be 4 of the parts.
So $140 ÷ 4 = $35. That means each section (20%) represents $35.
Which means your discount was $35 and that added onto
the $140 makes the original price of the skateboard $175.

12. NOW you try using a tape diagram to solve a problem:
After a 25% discount, the price of a new television is $600. What was the price before the discount? CLICK FOR THE ANSWER
Hmmm…if you get 25% off……that means
you are paying 75%...lets set up a tape diagram…
First we show what would be 100% in 4 parts because of the 25%
100%
25%
25%
25%
25%
75%
The 75% represents $600 and is shown to be 3 of the parts.
So $600 ÷ 3 = $200. That means each section (25%) represents $200
Which means your discount was $200 and that added onto
the $600 makes the original price of the television $800.

13. The cost next week will be $140 + $28 which is $168.
You can also use a tape diagram to solve a problem when an increase has occurs. Let’s look at this problem.
A SuperSick skateboard costs $140 now, but its price will go up by 20% next week. What will the new price be after the increase?
First we show what would be 100% in 5 parts because of the 20% but this time the $140 represents 100% of the cost now.
The increase would be an additional 20% which means the final NEW price is 100% + 20% more = 120% of original.
100%
Additional 20%
20%
20%
20%
20%
20%
20%
Since 20% is 1/5 of the total (100% ÷ 5 = 20%) we can divide the $140 by 5 to get one section (20%) ÷ 5 = 28.
So an additional 20% is $28.
The cost next week will be $140 + $28 which is $168.

14. NOW you try using a tape diagram to solve a problem:
Anna owns a jewelry store. She has ordered a bracelet for $30 and plans on marking it up 10% to sell in the store. Find the price the bracelet will cost in the store after the 10% increase.
CLICK FOR THE ANSWER
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10%
10% would mean using 100% ÷ 10 for the parts and
each part representing 10%.
10% would mean using 1/10 and 30 ÷ 10 is 3 so
each section represents $3.
The additional 10% would be an additional $3.00.
Anna’s original cost of $30 plus the additional $3.00 would make the cost of the bracelet in the store $33.00.