Math 131

Spring 04

Fraction Rug Problems

 

            You may find applets at the site http://matti.usu.edu/nlvm/nav/vlibrary.html useful.  Look under Number and Operations 3-5 and Fractions  Rectangle Multiplication and Fractions (Improper)  Rectangle Multiplication (don’t be put off by the grade categorization).

            Write out your answers on another sheet of paper.

 

1.  Suppose you have a rug with dimensions  unit by  unit.  Call this your “original rug.”  What is the area of this rug?  Support your answer with a picture.

 

2.  Using your picture, explain how this area, which can be computed by finding  can be also computed by finding “half of a half.”

 

3.  List the dimensions of five other rectangular rugs that have the same area as your original rug and that have sides that are rational numbers, written as fractions or natural numbers (don’t make all of them have one side a natural number).  Draw pictures to show your rugs.

 

4.  What patterns do you notice (visual, numerical, whatever) between the rugs in question 3?  Can you relate fraction multiplication, in your examples, to finding “a fraction of a fraction” (e.g. one-third of three-fourths).

 

5.  Now find five rectangular rugs with area twice as large as your original rug.  Once again (as in all problem on this sheet), sides should be fractions and draw pictures to support your reasoning.  Look for patterns.

 

6.  Find five square rugs, with fractions for sides, whose areas are close to twice the area of your original rug.  Look for patterns, draw pictures, etc.

 

7.  Repeat questions 5 and 6 for rugs that are three times as large as the original rug.

 

8.  Repeat questions 5 and 6 for rugs that are four times as large as the original rug.

 

9.  Pick a new rug to replace the original rug  one whose area is not one of the areas you’ve worked with already.  Answer some of the questions for this new rug.

 

10.  When is the product of two fractions smaller than both fractions?  When is it larger than both fractions?  When is it between the two fractions?  When is it equal to one of the fractions?

 

11.    Summarize what you’ve found. 

 

   Copyright 2005, Debra K. Borkovitz.  You may copy or edit this material for non-profit, educational use only.

 

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