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IM 8 Ch1.2.2 How Can I Solve The Proportion

CPM Materials modified by Mr. Deyo

Proportional relationships can be identified in both tables and graphs.

In the last lesson, you also used both of these representations to make predictions

about proportional situations.

Today you will continue to develop strategies for solving proportional

situations using an equation.

Preparation for 8.EE.7a, 8.EE.7b in Section 3.2


By the end of the period, I will apply different strategies for solving proporons wrien as equivalent raos.

I will demonstrate this by compleng Four‐Square notes and by solving problems in a pair/group acvity.

Learning TargetTitle: IM8 ‐ Ch. 1.2.2 How Can I Solve the Proporon? Date:


Home Work: Sec. 1.2.2Desc. Date Due

Review & Preview Pg.

Day 1 ‐ Problems 1‐57 to 1‐61


Team Roles

1) Resource Manager

2) Facilitator

3) Recorder/Reporter

4) Task Manager


Vocabulary1) proportion

2) crossproduct

3) 5D ProcessDDDDD


Kenny can make seven origami (foldedpaper) cranes in ten minutes. He read a story about a girl who made 1505 cranes, so he was curious how long it would take him to make that many without stopping.

P 152a

DISCUSSION POINTSWhat is this problem about?What is it asking you to do?

What information can help you answer this question?

How can you get the information you need?

a) Complete Kenny’s table below, and then explain how you did so.

Origami CranesCranes (#) Time (minutes)

0 07 10

1505 ?

How many minutes would it take Kenny to fold 1505 cranes?

How many hours?


Instead of solving this problem using a table or a graph, Kenny represented seven cranes in ten minutes as the ratio . Then he wrote an equivalent ratio as follows:

P 152b

b) Use two different strategies to find the missing value in the equivalent ratio.

Strategy 1 Strategy 2


P 153a

Giant One Method: Multiplying a ratio by 1 does not change the value of the ratio. You can write 1 in many forms, such as and .

In this course, this kind of fraction is called a “Giant One.” Find a value to use as a numerator and denominator in a Giant One, and then find the value of x in the equation below.

MULTIPLE STRATEGIESKenny’s class found several ways to solve . Three of the strategies that they used are presented in 153. Some of these strategies might be the same as what your class did in problem 152. However, others may be new. Work to understand each strategy so that you could use it to solve a new problem.


P 153b

Undoing Division Method:In this ratio, x is divided by 1505. You can undo the division by multiplying each side of the proportion by 1505 like this:Work with your team to explain how this strategy works.

Are the two ratios still equal? Why are both sides multiplied by 1505?

Simplify each side of the equation and find x.



P 153c

Fraction Buster Method: If multiplying both sides by 1505 gets rid of the denominator of the x, then you can use the same strategy to get rid of the 7 in the other denominator. Discuss this method with your team and decide if undoing both denominators is a reasonable strategy.

How does using this method help you solve the equation?

What else do you need to do to find x?



P 154aWhen he was little, Miguel could not sleep without his Captain Terrific action figure. It looked so lifelike because it was a perfect scale model. The actor who plays Captain Terrific on television is 216 cm tall. Miguel’s doll is 10 cm tall. If the doll’s neck is 0.93 cm long, how long is the actor’s neck? Use the Undoing Division Method to solve this proportion:

Undoing Division Method


P 154bThe Northwood School Math Club is having a tamale sale. The school has 1600 students, but the club members are not sure how many tamales to make. One day during lunch, the club asked random students if they would buy a tamale. They found that 15 out of 80 students surveyed said they would definitely buy a tamale. How many tamales should the Math Club expect to sell? Use the Fraction Busters Method to solve the proportion:

Fraction Busters Method


P 154cOn the school copy machine, Mr. Douglas reduced a triangle so that it would fit better in student portfolios. The shortest side of the original triangle was 22 cm; other measurements are shown in the diagram. How long was the longest side of the original triangle? Solve the proportion using the Giant One Method.

Giant One Method


P 155Elsie is starting a recycling club at her school and hopes to use the money earned from recycling cans to buy recycling bins for the school.

School Recycling Center

Elsie first needs to figure out how much the cans that can be collected at her school weigh, so she starts by weighing the cans in her recycling bin at home. She finds that 50 cans weigh 0.8 kg. The next day, Elsie counts cans at school and finds that her fellow students throw away 1240 cans each day. Solve the proportion below using a method of your choice to find how much all of the school’s cans weigh.


P 156CrossMultiplication Method:

ANOTHER STRATEGY

Juana's method is shown here.

Explain to Juana why her method is really just a shortcut based on the Fraction Buster Method.


P 157 Solve each of the following proportions.http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_57m.html

If Joan read 75 pages in 4 hours how long will it take her to read 250 pages?

http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_57m.html


P 158Mr. Wright was making a table to figure out how much it costs to send a certain number of regular letters through the mail. Use proportional reasoning to complete his table.

https://www.desmos.com/calculator/n7xtkkrjrr


https://www.desmos.com/calculator/n7xtkkrjrr



P 159 Kelly asked some of her classmates how many hours of sleep they get on school nights. Here are the results:

http://www.cpm.org/technology/general/stats/


Create a histogram for the data. (Refer to the glossary for assistance, if needed.)

http://www.cpm.org/technology/general/stats/



P 160Define a variable and then write and solve an equation for the problem below. Remember that you can use the 5D Process (described in the Lesson 1.1.3 Math Notes box) to help you get started. State your solution in a sentence.

Todd is 10 years older than Jamal. The sum of their ages is 64. How old are Todd and Jamal?




P 161Throughout this book, key problems have been selected as “checkpoints.” Each checkpoint problem is marked with an icon like the one at left. These checkpoint problems are provided so that you can check to be sure you are building skills at the expected level.This problem is a checkpoint for operations with signed fractions and decimals.

http://demo.textbooks.cpm.org/bookdb.php?title=cc3&name=reference.checkpoints&type=tcheckpoints

Simplify the following expressions.

Checkpoint 1http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_61m.html




P 161Throughout this book, key problems have been selected as “checkpoints.” Each checkpoint problem is marked with an icon like the one at left. These checkpoint problems are provided so that you can check to be sure you are building skills at the expected level.This problem is a checkpoint for operations with signed fractions and decimals.


Simplify the following expressions.

Checkpoint 1 (Continued)http://www.cpm.org/students/homework/CC3_Problems/CC3_Ch1_Answers/ch1_files/CC3_1_61m.html

If you needed help solving these problems correctly, then you need more practice. Review the Checkpoint 1 materials and try the practice problems. Also, consider getting help outside of class time. From this point on, you will be expected to do problems like these quickly and easily.



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