PERCENT UNIT 6 Math 7 Plus

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.

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

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.

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%

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.

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 320. Allow them to verbalize and present a variety of ways to relate to the solution. Discuss how you got these answers.

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

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

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.

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.

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.

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%). . . 140 ÷ 5 = 28. So an additional 20% is $28. The cost next week will be $140 + $28 which is $168.

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.