Math 131

Spring 05

 

Fraction Strips  Size of Fractions

 

            For this homework, you should have fractions strips made from large paper (11x17) cut parallel to the long side of the paper.

 

For the first set of questions, use only strips representing halves, fourths, eighths, and sixteenths.

 

1.  For each of the fractions below, list all equivalent fractions represented on your strips (e.g.  should be listed next to  ):

 

             --                                                     --

 

 

             --                                                     --

 

What patterns do you notice?  Explain how your numerical patterns relate to the fraction strips. 

 

 

 

Without actually making a strip for thirty-seconds, list fractions with denominator 32 that will be equivalent to the above fractions.

 

 

 

2a.  List all fractions represented by your strips that are between  and .

 

 

 

b.  If you had a strip representing thirty-seconds, which fractions on that strip would be between  and ?

 

3.  What is the biggest fraction on your strips that is less than 1?   The next biggest?  How would your answers change if you had a strip representing thirty-seconds?

 

4a.   Use your strips to find half of each fraction below:

 

 --                                                     --                                         --

 

 

             --                                                     --                                           

 

b.  What patterns do you notice above?  Use the fraction strips to justify your numerical patterns.

 

 

 

 

 

c.  What is half of ?  What is half of ?  Explain.

 

 

 

 

Now include fraction strips for thirds, sixths, and twelfths. 

 

5.  For each of the fractions below, list all equivalent fractions represented on the new strips you added.

 

             --                                                     --

 

 

             --                                                     --

 

             --                                                      --                             --                                       

 

What patterns do you notice?  How do they compare to the patterns you found in problem 1?

 

 

 

 

6.  For each pair, circle the larger of the two fractions.  Then write down some fractions that are in between the two listed fractions:

 

   and         In-between _________________________________________

 

 

   and         In-between _________________________________________

 

 

   and         In-between _________________________________________

 

 

   and     In-between _________________________________________

 

 

   and       In-between _________________________________________

 

Now include fraction strips for fifths, sevenths, ninths, and tenths.

 

7.  List all fractions on your new strips that are between  and .

 

 

 

 

8.  Arrange the fractions on each list in order from smallest to largest:

 

            a.    ________________________________________

 

            b.      ________________________________________

 

            c.      ________________________________________

 

            d.     ________________________________________

e.  Each of the above lists has a “gimmick.”  What do the elements on each list have in common?  What patterns can you find that might help you order other lists of fractions?

 

 

 

 

 

9.   Arrange the fractions on each list in order from smallest to largest:

 

            a.    ________________________________________

 

            b.      ________________________________________

 

            c.      ________________________________________

 

            d.     ________________________________________

 

e.  Were any of these problems particularly tricky?  If so, what made the problem difficult?

 

 

 

 

 

10.  For each of the fractions below, list some other fractions that are close to it.  Note whether the fractions you list are smaller, equal, or greater.

 

            a.       _______________________________________________________

 

            b.     _______________________________________________________

 

            c.     _______________________________________________________

 

d.       _______________________________________________________

 

11.    Think about what you’ve learned from these exercises.  How useful do you find the fraction strips as a tool for understanding the size of fractions?  Explain.

 

 

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

 

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