1. Using Proportions
Dittamo Lewis Notes 2012

2. Objective
You will be able to solve Real World Problems by using proportions (when appropriate).

3. Are proportions the way to go?
Billy ate seven apples, Johnny ate twelve apples. How many total apples did they eat?
The recipe calls for 3 eggs for 24 cookies. How many eggs would you need for 240 cookies?
3) The length of the model of the car is 8 inches and the width is 3 inches. If the actual car is six feet long, how wide is the actual car?
4) Mary said that 40% of the boys at her party were HOT. If there were 12 boys at her party, how many were hot?
5) Reggie Bush gained four yards on his first run. His following runs went like this: lost 3, gained 5, lost 15, gained 1. What was his total yardage for these plays?
6) If Jamal can run 100 meters in 14 seconds, how long would it take him to run one mile? No
Yes
Yes
Maybe ! No
No, why?

4. Write a proportion,solve it, and answer the question.
For each problem:
Write a proportion,solve it,
and answer the question.

5. $128 Squeaky the Hampster earns $96
for 6 hours of work. How much does she
earn in 8 hours?
$128

6. from 48 ounces of clay, how many bowls can
If 3 bowls can be made
from 48 ounces of clay, how many bowls can
be made from 96 oz of clay?
6 bowls

7. Jim Nasium drove 135 miles to visit the White House. His car used 7
Jim Nasium drove 135 miles to visit the White House. His car used 7.5 gallons of gas. How many gallons would the car use for a 225 mile trip?
12.5 gallons
Sample answer: If there was a lot of traffic for part of the trip, gas mileage would change.
How could we slightly change this problem to make it NOT appropriate for using a proportion?

8. What is the width of the larger stick figure?
These two stick figures are similar. What does similar mean?
What is the width of the larger stick figure?
8 feet
12 feet
Knowing the two figures are similar the proportion between the two stick figures is 8 feet:12 feet.
Once written as a fraction 8/12 reduces to 2/3. So the proportion between the two stick figures is 2:3.
If the proportion is 2:3 then the student should set up this equation and solve for x:
2 / 3 = 4 / x
2 * x = 3 * 4
x = 12 / 2
x = 6 feet
4 feet
x feet
six feet

9. A picture measuring 25 cm long is enlarged on a copying machine to be 30 cm long. If the width of the original picture is 15 cm, what is the width of the copy?
18 cm

10. Rusty Pipes paid $750 for 600 square feet of roofing
Rusty Pipes paid $750 for 600 square feet of roofing. If he needs 240 ft2 more, what is the extra cost?
$300

11. Billy Bob grabbed a big handful of Fruit Loops
Billy Bob grabbed a big handful of Fruit Loops. He counted 18 red, 24 yellow, 28 green and 30 blue. If a magical squirrel told Billy Bob that there are 450 pieces of Fruit Loops in his bowl, how many yellow pieces should Billy Bob expect to be in the bowl?
108 yellow

12. Stewy’s boss told him to check over 3,000 light bulbs to see how many were defective. But Stewy was lazy. He only checked 100 bulbs. He found that 8 were defective. How many should he report were defective to his boss?
240 were defective

13. Chuck Norris can smash 20 boulders every three hours with his bare hands. How many boulders can he smash in 4 days?
640 boulders

14. The end ! ! !!
(Except for CLOSURE)

15. Closure
What if the Dittamo Toy Company wanted to make a doll of YOU to promote their new line of Richards Middle School Mathletes. Before they make the doll they want your expert mathematical opinion about what you think you are going to look like when they shrink you to a standard doll size of 12 inches tall. Write one paragraph about how you think you are going to turn out as a doll in terms of your head size, waist size, foot size, arm length, and leg length.