More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

By Susan J. Lamon | Go to book overview

Chapter 3
Fractions and Rational Numbers
1. One example is a combination problem: Joe's ice cream store sells three different flavors of ice cream, a choice of large or small cone or dish, and four different toppings. How many different purchases can you make at Joe's? A second example is an area problem: A rectangle is 5 cm. long and 3 cm. wide. What is its area? Another common type is a multiplicative comparison problem: Last month, Jack collected money from 135 customers on his paper route.
2. This month, he collected from 3/5 as many as last month. How many customers paid their bills this month?
3. A common example is a speed problem: If Mrs. Jones traveled 145 miles in 2 1/2 hours, what was her average speed for her trip? When you divide miles by hours, you get miles per hour.
4. Here is an example: For a project he is doing, Mr. Carter needs 15 pieces of rope each 3/8 of a meter long. He has 5 meters of rope in the garage. How many pieces can he cut from the rope he has before he needs to buy more?
5. Here is one example: If a yard of material costs $3.95, how much will 3/8 of a yard cost?
6. $.44 per 88 grams means or. This says 1 cent per 2 grams. Another way to read it is to separate the fractional number from the label: . This is one-half cent per gram.
7. This is a division problem. To obtain a rate of travel, you compare how much distance has been traveled to the time it took to travel. 4 miles in 15 minutes can be written in several ways: (4 miles per 15 minutes is the same rate as 1 mile per 3.75 minutes). Another way is (4 miles per 15 minutes is the same rate as 16 miles per 1 hour.)

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