Session 2: Ordering Fractions



SREB Readiness Indicator Addressed: Read, write, compare, order, and represent in a variety of forms: integers, fractions, decimals, percents, and numbers written in scientific and exponential notation (SREB Indicator #1).

Activity Rationale: The NCTM’s Principles and Standards for School Mathematics states that students in the middle grades can develop a deep understanding of rational numbers through experiences with a variety of models --- such as fraction strips, number lines, 100 grids, area models, and objects --- as the models offer students concrete representations of abstract ideas and support students’ meaningful uses of representations and their flexible movements among them to solve problems. Additionally, NCTM recommends that students at the middle level order and compare fractions, which many students find difficult. For example, fewer than one-third of the thirteen-year-old U.S. students tested in the National Assessment of Educational Progress (NAEP) in 1988 correctly chose the largest number from 3/4, 9/16, 5/8, and 2/3 (Kouba, Carpenter, and Swafford 1989). Students’ difficulties with comparison of fractions have also been documented in more recent NAEP administrations (Kouba, Zawojewski, and Strutchens 1997). Visual images of fractions should help many students think flexibly in comparing fractions.

This activity illustrates how interactive applets can be used to help students locate fractions on a number line. It requires creating a representation of two fractions then finding another fraction that is located on the number line between those two given fractions.

Experience It!

Part A: Using Fraction Pointer

1. Go to .

2. To find out how the tool works, click the How button at the top of the screen.

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3. Follow the instructions to match the number line values to the diagrams for the two given fractions. Then find one fraction that lies between the two given fractions. While you experience the process, think about the methods you use to represent the fractions. Record your thinking. For example, how did you decide how many pieces to break the area into?

4. Experiment with using both the circle and the square. Which is easier for you to use? Is it easier for you to reduce fractions when using the circle or the square?

5. Do two problems. Draw the area representations of the fractions and put them on the number lines below. Additionally, express the two fractions you found in lowest terms.

a. Use the square shape.

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b. Use the circle shape.

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6. What skills do students gain from using the square area model that they don’t gain using the circular model?

Part B: Using Bounded Fraction Pointer

The Bounded Fraction Pointer () is similar to the previous tool, but it lets you determine the left and right boundary fractions before finding one in between.

To enter the left boundary fraction (the fraction with the smaller value), enter the first fraction then click Set.

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• To enter the right boundary fraction (the fraction with the larger value), enter the second fraction then click Set.

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1. Use the Bounded Fraction Pointer to find a fraction between the following sets of fractions.

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b. [pic]

2. The Fraction Pointer and the Bounded Fraction Pointer function in slightly different ways. Explain the circumstances in which each would be most beneficial.

References

Kouba, Vicki L., and Thomas P. Carpender. "Number and Operations?" Results from the Fourth Mathematics Assessment of the National Assessment of Educational Progress. Ed. Mary M. Lindquist. Reston, VA: National Council of Teachers of mathematics, 1989. 64-93.

Kouba, Vicki L., Judith S. Zawojewski, and Marilyn E. Strutchens. "What Do Students Know About Numbers and Operations?" Results from the Sixth Mathematics Assessment of the National Assessment of Educational Progress. Eds. Patricia Ann Kenney and Edward A. Silver. Reston, VA: National Council of Teachers of mathematics, 1997. 87-140.

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