Proportion

by

Bernadette Dvorscak


This lesson was created as a part of the SMART website and is hosted by the Illinois Institute of Technology

is awesome.

This lesson is for students in grades 5 through 7

 The objectives are:

A ratio a comparison of two quantities. The ratio of dogs to cats is 3 to 2.  The ratio of gerbils to guinea pigs is 9 to 6.  A proportion is a comparison of two quantities.  The ratio of 3 to 2 is the same as the ratio of 9 to 6.  


          

 

 For every three animals of one species there are two of the other species. These two ratios are equal to each other:  This is a proportion.

3/2 = 9/6

Hey! That look's like a pair of equivalent fractions.  Right, fractions are rational numbers.  When two fractions represent the same amount, they are equivalent fractions.  Two ratios that are equivalent to each other are a proportion.

How do you know if two ratios are a proportion?

5 x 12 = 60         8 x 12 = 96     therefore 5/8 = 60/96

60 / 12 = 5          96 / 12 = 8     therefore 5/8 = 60/96

7:3 = 28:12

Multiply 7 by 12.   7 x 12 = 84

Multiply 3 x 28.     3 x 28 = 84

Both products are 84, therefore 7:3 = 28:12

What if one term in a proportion is missing?  How can you find the missing term?

4/9 = 96/?

4 x 24 = 96  therefore 9 x 24 = 216.  

4/9 = 96/216

27/5 = 8/?

27 x = 5 . 8

27 x = 40

x = 40/27

x = 1.48

There are many real-life applications for proportions. Some of these are:

In Activity 1, you will find the reduced scale for buildings, bridges, and tunnels.  For a printable worksheet, click here.

Activity 1

In this activity, you will convert the actual height of skyscrapers or the actual length of bridges and tunnels into a reduced scale of inches. The scale you will use is 50 feet  = 1inch; this is the ratio of 50/1.  Round all answers to the nearest hundredth.  To find the actual height or length, click on the name of the structure. Remember to keep the order of the terms the same in both proportions.  

Name of structure

Actual height or length

Scale 

John Hancock Center    
Chrysler Building    
Petronas Tower    
Sears Tower    
Citicorp Center    
Sunshine Skyway Bridge    
Firth of Forth Bridge    
Golden Gate Bridge    
Akashi Kaikyo Bridge    
New River Gorge Bridge    
Channel Tunnel    
New York Third Water Tunnel    
Central Artery/Tunnel Project    
Seikan Tunnel    
Underground Canal    

Bonus:  Using the data for either skyscrapers, bridges, or tunnels, create a graph comparing all the structures in the category.  

(Building Big on the PBS website is an excellent resource for lessons.)

Answers to Activity 1

In Activity 2, you will either increase or decrease the amounts of a selected set of ingredients for a recipe.  For a printable worksheet, click here.

 Activity 2

Use the recipe for Salad Nicoise and determine the amount of each of the given ingredients you will need to make the quantities that are indicated.

 

Number of Servings

Ingredient

3

7

15

29

Anchovy fillets        
Balsamic vinegar        
Eggs        
Cherry tomatoes        
Nicoise olives        
Garlic        

          Answers to Activity 2

Other Resources

Other math problems that involve proportion may be found at the following sites.  

  Use proportions to find the quantities of each ingredient needed to make lemonade.

  Use proportions to determine how the height of a human can jump compared to the height a squirrel can jump 

  Use proportions to find the new dimensions of a picture whose area has been enlarged.

  Find out how long it will take the math teacher to bicycle the width of Wisconsin 

  Compare cat steps to dog steps

  Use proportion to compare the volume of two objects.

  Use proportion to find data about continental drift

The following unit deals with scale, ratio, and proportion through model building.

 http://www.cis.yale.edu/ynhti/curriculum/guides/1981/5/81.05.06.x.html

For information and/or activities on special effects go to the following sites: 

Nova Online:  Special Effects.


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© Bernadette Dvorscak