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RepresentationSession 05 Overviewtab atab btab cTab dtab eReference
Part D

Applying Representation
  Introduction | Arrays and Fractions | Problem Reflection | Classroom Practice | Representation in Action | Classroom Checklist | Your Journal


Reflect on the following questions. After you've formulated your own answers, select "Show Answer" to see our response.

Question: What do students need to know about fractions in order to solve the Arrays and Fractions problem?

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Our Answer:
Students need to be able to read the symbol "1/5" and to give it meaning in order to interpret the problem. For example, some students may interpret it as "1 out of every 5" while others think of it as "1 out of 5 equal groups."

Question: In this problem, students found 1/5 of 14 streamers. How would a problem asking them to find 1/5 of 14 chocolate bars, dollars, or balloons be different?

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Our Answer:
An array representation does not work easily for this problem because 5 is not a factor of 14, and partitioning 14 items into 5 equal groups shifts the problem to a common division model. It is important for students to think about when a particular model, such as an array, does and doesn't help in solving a particular type of problem. If the denominator of the fraction doesn't divide evenly into the whole number, the remainder has to be dealt with according to the situation. Streamers can be torn into smaller pieces (and the result represented by 2 4/5), whereas balloons cannot. Likewise, chocolate bars would need to be broken, which is difficult to do evenly, and dollars would need to be changed into dimes.

Question: What opportunities for learning are offered by having students work on this problem with both arrays and fractions? How do the array representations help students find a fraction of a quantity?

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Our Answer:
The arrays give another representation related to denominators. The denominator can be thought of as the number of equal rows that is desired. It helps to show that a whole number per row is the result if the denominator is a factor of the given quantity. Students discover that an array model doesn't work as well when the result of dividing the total by the denominator is not a whole number per row, but they also learn that an array might be successful later with another kind of problem involving fractions.

Question: You've seen that an array was not entirely useful in dividing 14 into fifths. What other representations might be more useful in solving the problem?

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Our Answer:
One idea is to fold a strip of paper 14 inches long into five equal parts and then measure the length of one part.

Next  Watch students tackle this problem

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