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Ratio and proportions for MathVillage

Ratios with three things - NOTES

In the previous lesson we learned that ratios are a way to compare two or more things. In this lesson we will focus on the Òor more thingsÓ part of ratios.
Example 1: Mr. Lee is making drink that calls for 2 ounces of soda for every 3 ounces of cranberry juice. If he wants to make 60 ounces of the drink, how much soda will he need to use‌

Method 1: Using a ratio table

We need three columns because we are interested in the ratio of soda to juice to total amount of drink. So, really, we are interested in the ratio 2:3:5 and want to manipulate the table so the third column in the table is a 60.
Method 2: Using ratios

The initial ratio of 2:3:5 can be scaled up by a factor of 12 to get the ratio 24:36:60. This means Mr. Lee will need 24 ounces of soda.

Example 2: The ratio of the number of JimÕs marbles to JennÕs is 2 : 1 and the ratio of the number of JennÕs marbles to GinaÕs is 4 : 5. Find the ratio of the number of JimÕs marbles to JennÕs to GinaÕs.

Method 1
Method 2
 

Example 3: Aaron and Barbara are sharing $2000 in the ratio of 3 : 2. How much money does each person get‌

Method 1
Method 2 Method 3
   
   

Ratios with three things - CLASSWORK

  1. The ratio of the number of men to the number of women in a bus is 3 : 1. The ratio of the number of women to the number of children is 3 : 5. Find the ratio of the number of men to the number of women to the number of children.
Men Women Children
3 1  
  3 5
     

  1. The ratio of fans cheering for the home team vs. the visiting team is 7 to 2. If there are 18,000 fans at the game, how many are cheering for the home team‌
Home Visiting Total
7 2  
    18,000

  1. A ribbon is 64 centimeters long. If it is cut into two pieces in the ratio of 3 to 1, how long is each of the two pieces‌
Longer Piece Shorter Piece Total Length
3 1  
    64

  1. John and Theresa have just been paid for painting a house and share the money in the ratio of 5:3. If Theresa gets $240 in this deal, how much money were they paid for painting the house‌
John Theresa $
5 3  
  240  

  1. The ratio of Math classes to English classes is 8 : 6. The ratio of PE classes to English classes is 2 :3. What is the ratio of Math classes to English classes to PE classes‌
Math English PE
8 6  
  3 2
     

The Orange Juice Problem – ACTIVITY

Teacher notes:
1. The purpose of this lesson is to show students the many methods for comparing ratios that they are ALREADY familiar with:
a. Method 1: common numerators
b. Method 2: common denominators
c. Method 3: convert ratios to decimals or fractions
d. Method 4: unit rates
2. The most important thing is to show that converting ratios to decimals is essentially the SAME as unit rates. The only difference is the 1 in the denominator is assumed without actually writing it.
3. Post the four recipes and give students four or five minutes to solve.
4. Spend the next 15 minutes or so having students share their solution methods.
5. Compare and contrast the different solution methods that are shared.

Four recipes
Recipe A
2 cups of orange concentrate
3 cups of cold water
Recipe B
1 cup of orange concentrate
4 cups of cold water
Recipe C
4 cups of orange concentrate
8 cups of cold water
Recipe D
3 cups of orange concentrate
5 cups of cold water

Show all necessary work to answer the following two questions:
1. Which recipe will make the orange juice that is the most ÒorangeyÓ‌
2. Which recipe will make the least ÒorangeyÓ juice‌

Grading Rubric

Mathematical correctness
12 9 6 3
All math strategies are reasonable and correctly calculated All math strategies are reasonable, but some calculations are missing or incorrect Some math strategies are incorrect, but calculations are mostly correct Poor math strategies and poor calculations
Poster effectiveness
4 3 2 1
Poster uses words, pictures, and symbols to effectively communicate at least one of the methods used Poster effectively communicates method, but is missing words, pictures, or symbols Does not clearly communicate entire solution method Poster does not communicate at all
 
 

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