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introduction to fraction bars

1. Justify your answer in each exercise preferably in two ways.
• Share a candy bar equally among four people.  How much of the candy bar does one person get?
• Share two candy bars equally among five people.  How much of one candy bar does one person get?
• Share 11 inches of licorice equally among 12 people.  How much ribbon is there for one person?
• Find 1/14 of 13 inches.

2. Equal fractions.
• Share one dollar equally among three people, Cheryl, Susan, and Eileen using Fraction Bars.  Now, find how many people could share one dollar so that one third of them would have the same amount of money as Cheryl.  Is there more than one solution? Also find the fraction of one dollar that one third of the people have.
• Chandra has 3/5 liter of coke.  Using Fraction Bars, make two other fractions of a liter of coke that are equal to 3/5 liter.

3. Fractions as operators.
• Given the following four-inch candy bar, find a way to share it among three people without erasing the mark.  How much of one inch does each person have?

• How could you partition a bar 1/3 inch long so that you can make a bar that is 1/2 inch long without making a bar one inch long?  What did you do to the 1/3 inch bar?
• Given the fraction 1/5, make three fractions equal to the fraction.  Now, do the same for 7/5.  Can you develop a rule for generating all fractions equal to a given fraction?

4. Co-measurement units
• Given a unit bar partitioned into halves, partition it again so you can pull out exactly one-third of the unit bar without destroying the halves.
• Given a unit bar that is partitioned into fifths, partition it again so you can pull out exactly 1/7 of the unit bar.
• What is a co-measurement unit for 1/4 and 1/3?  How many co-measurement units can you find?  What are they? What do they have in common?
• Find a quick way to find the greatest co-measurement unit of two unit fractions.

Adapted from L. P. Steffe’s Problem Set I:  Revisiting Fractional Operations, UGA

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