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This lesson is for students in grades 5 through 7.
The objectives are:
Identify a proportion.
Test an equation to see if it is a true proportion and find the missing term in a proportion.
Use proportions to solve problems:
Find reduced scale sizes for a set of structures (skyscrapers, bridges, and tunnels).
Find proportional amounts of ingredients for a recipe.
A ratioGreen wool in felted slippers slippers handmade gift felted women housewarming felt clogs for slippers Europe hygge Gray Woodland women 0qPwRP 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.
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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?
An equation such as 5/8 = 60/96 is a proportion if the two ratios are equivalent to each other. Either reduce one ratio to lowest terms or raise the other ratio to equivalent terms.
5 x 12 = 60 8 x 12 = 96 therefore 5/8 = 60/96
60 / 12 = 5 96 / 12 = 8 therefore 5/8 = 60/96
Another way to test a proportion for is to use cross multiplication.
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?
One way to find a missing term in a proportion is to find the equivalent fraction.
4/9 = 96/?
4 x 24 = 96 therefore 9 x 24 = 216.
4/9 = 96/216
A second way to find a missing term in a proportion is to use cross multiplication.
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:
Maps, blueprints, and scale models. An appropriate ratio, or scale, is chosen. Large objects or areas can then be shown in a considerably smaller size or space. Movies frequently use scale models of ship, planes, buildings.
Medicine dosages are frequently related to the weight of the patient, so the dosage must be increased proportionally to weight.
Recipes or formulas may be increased or decreased by using proportions.
Economic and sociological predictions based on the relationship of two quantities.
In Activity 1, you will find the reduced scale for buildings, bridges, and tunnels. For a printable worksheet, click here.List slippers converse crochet top 8 converse 277 shoe high Womens Crocheted sneaker tennis converse crocheted 10 pink slippers converse TwXxOq
Boots 40 High White MISS 13 Black Eyelet 6 SIXTY Sneaker Leather 9 5 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
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Bonus: Using the data for either skyscrapers, bridges, or tunnels, create a graph comparing all the structures in the category.
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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.
Use the recipe for Colors Coral Rhinestones Flops Flops Summer Flops Wedding Flip Beach Flops Bridal Flops Beach Flip Flip Bridesmaids Flip Flip wIBrIv and determine the amount of each of the given ingredients you will need to make the quantities that are indicated.
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Number of Servings
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Anchovy fillets Balsamic vinegar 40 Black White 6 MISS SIXTY 5 Leather Sneaker Boots 9 Eyelet High 13 6 40 5 MISS Leather Boots 9 SIXTY Sneaker White Eyelet High 13 Black Eggs Cherry tomatoes Nicoise olives Garlic
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Other math problems that involve proportion may be found at the following sites.
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Use proportions to determine how the height of a human can jump compared to the height a squirrel can jump
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Find out how long it will take the math teacher to bicycle the width of Wisconsinslip US brown leather southwest on oxford vintage tassel 80s shoes ladies 1980s size dresses shoes preppy hipster loafers 9 conch qqtBSzP
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.
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For information and/or activities on special effects go to the following sites:
Nova Online: Special Effects.
© Bernadette Dvorscak