More: In-Depth Discussion of the Reasoning Activities in "Teaching Fractions and Ratios for Understanding"

By Susan J. Lamon | Go to book overview

Chapter 7
Rational Numbers as Operators
1. Reducing a unit to half its size and then tripling the result in size is equivalent to_____.
2. Dividing something into 5 equal shares and then quadrupling each share is equivalent to_____.
3. Describe in symbols what happens in the pictures:
4. Make a picture showing a two-for-three operator with an input of 12 items and another picture of an eight-for-twelve operator with an input of 12 items. Predict some other exchangers that will yield the same result.
5. Use an area model to do the following multiplications:
 a. 2/5 × 5/6 b. 2/3 × 3/4 c. 1 1/2 × 1/3
6. Draw a picture to illustrate the action of a 2-for-8 operator on a 4-for- 3 operator on this set of objects:
7. What conclusions can you draw about the operators and their relative sizes, given the following machines?

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