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# Fractions and Slopes

This Demonstration shows some of the ways fractions are related to the integer grid and the slopes of linear functions. It offers an alternative to part-whole region ("pizza") models for introducing fractions in late elementary and middle school. Set the slope of the line by selecting (with the red locator) a point in the integer lattice. Vary (using the blue locator) and observe the values output on . See what you can find out about fractions with different settings.

### DETAILS

The following questions hint at some of the ways one might use this fraction generator in instructional settings.
1. What determines the value of the output number? Explain. If the output is turned off, how might it be inferred from displayed information?
2. If the value of the slope is hidden, how can you infer it?
3. If the input is hidden, how could you infer it ? Will your method work for all inputs and slopes?
4. How is the Demonstration related to multiplication and division?
5. How is the Demonstration related to rational numbers? To equivalence of rational numbers?
6. What sorts of issues raised by the Demonstration are likely to intrigue or puzzle your students?
Snapshot 1: Why does show the value in this snapshot?
Snapshot 2: Can you infer the value of the slope?
Snapshot 3: A negative slope is displayed.
This Demonstration was developed at the Poincaré Institute for Mathematics Education, an NSF-funded Math and Science Partnership (NSF MSP DUE-0962863) of Tufts University, TERC, and school districts in MA, NH, and ME.

### PERMANENT CITATION

Contributed by: David W. Carraher (TERC) and Boris Hasselblatt (Tufts University)
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