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

By Susan J. Lamon | Go to book overview

Chapter 2
Relative and Absolute Thinking
1. B contains 5 more stars than box A, and it contains 2 2/3 times the number of stars in box A. Box A contains 3/8 times the number of stars in box B. Another way to say it is that set A is 3/8 of set B. If a group is defined as a set of 2 stars, the A contains 1 1/2 groups and B contains 4 groups.
2. You cannot tell which pool has the greater capacity if you know only the ground-level dimensions of the pools. The capacity depends on the area you can see (length x width of the pool) as well as on the depth. So, for example, if the depth of the first pool were 2 feet and the depth of the second pool were 14 feet, the capacity of the second pool would be greater. If the depth of the first pool were 6 feet and the depth of the second pool were 35 feet, the capacity of the first pool would be 480 cubic feet, while the capacity of the second would be only 240 cubic feet.
3. $10 off the dress is a 22% savings ($10/$44.99), whereas $10 off the blouse represents a more substantial discount ($10/$26.99) of 37%.
4. How orangy a drink will taste depends on the amount of orange mix as compared to the amount of water in the drink. One can of orange juice in a quart of water will taste more orangy than a can of orange juice dissolved in a half gallon of water.
5. There are many characteristics that are measured as a comparison of two quantities. A few examples are given here. Gas consumption in your car cannot be measured merely by counting how many gallons of gas your car used. Knowing a person's weight cannot tell you if the person is overweight. To determine whether a light will be strong enough for reading, it is not enough to know the bulb's wattage. All of these characteristics require a comparison of quantities.
6. A grasshopper is much smaller than a human. Yet, pound for pound, it can jump much higher than a human can jump. Our mass is probably more than 1,000 times greater than that of a grasshopper, but we cannot jump 1,000 times as high as it can.

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