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
100 2
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
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%.
0 350 700 1400
0% 25% 50% 100%

6. 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%
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. 80 320 400
0% 20% 40% 60% 80% 100%
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. X4
÷3
$1,320 $1,760
$440
0% 25% 50% 75% 100%
÷3
X4

10. 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. 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%). . . 140 ÷ 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.