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
re presenting halves , fourths, eighths, and
sixteenths.
1. For each of the fractions be low , list all equivalent
fractions represented on your strips
(e.g. 2/4 should be listed next to 1/2):
1/2--
1/4--
3/4--
5/8--
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 1/2 and 3/4.
b. If you had a strip representing thirty-seconds, which
fractions on that strip would be
between 1/2 and 3/4?
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:
1/2--
1/4--
1/8--
3/4--
3/8--
7/8
b. What patterns do you notice above? Use the fraction
strips to justify your numerical
patterns.
c. What is half of 1/16? What is half of 11/16? 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 .
1/2--
1/4--
3/4--
5/8--
1/3--
2/3--
10/12--
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:
1/4 and 1/2 In-between _________________________________________
7/8 and 2/3 In-between
_________________________________________
3/4 and 2/3 In-between
_________________________________________
5/12 and 11/12 In-between
_________________________________________
3/4 and 3/16 In-between
_________________________________________
Now include fraction strips for fifths, sevenths,
ninths, and tenths.
7. List all fractions on your new strips that are between
1/2 and 3/4.
8. Arrange the fractions on each list in order from
smallest to largest:
a. 3/5, 3/7 , 3/4 , 3/12 , 3/10________________________________________
b. 2/7 , 3/7 , 7/7, 6/7 ,
1/7________________________________________
c. 2/3 , 6/7 , 9/10 , 11/12 ,
3/4________________________________________
d. 3/7 , 4/9 , 2/3 , 3/5 ,
6/12________________________________________
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. 3/5 , 1/7 , 5/6 , 7/10 , 3/8________________________________________
b. 2/9 , 3/6 , 4/5 , 5/16 ,
6/7________________________________________
c. 1/3 , 2/7 , 3/10 , 4/12 ,
5/16________________________________________
d. 7/16 , 4/9 , 2/5 , 3/7 ,
5/12________________________________________
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.
3/7_______________________________________________________
b.
7/10_______________________________________________________
c.
13/16_______________________________________________________
d.
1/5_______________________________________________________
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
nonprofit,
educational use only.
