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

By Susan J. Lamon | Go to book overview

Chapter 12
Change
1. Time changed; distance from your starting point changed. Your speed remained constant for the three hours.
2. Time changed; the surface area of the balloon changed; the volume of the balloon changed; your puffing rate remained the same for one minute.
3. Time changed; your distance from home changed; your speed remained constant until you got to school.
4. Time changed; distance from the top of the hill changed; speed changed.
5. The cost increases for each subscription option because each involves a different period of time and a different number of magazines. However, if you analyze each option in terms of a 3-month rate, you can see that in each case, the 3-month subscription cost does not change. Six months costs 2(\$13.50); 9 months costs 3(\$13.50), and 12 months costs 4(\$13.50). Therefore, the same rate applies whether you buy the magazine for a shorter period of time or for a longer period of time.
6. a. The amount of water in the bathtub depends on how long the water has been running.
 a. How fresh your bread is depends on how many days have passed Because you baked it. b. The amount of postage depends on the weight of your letter. c. Your height depends on your age.
7. a. ↓ ↓ Three books should cost \$17.40.
 a. Correct. The time to walk to the mall does not depend on how many people are walking together. b. You cannot correct this statement. People's weights do not work that way! c. ↑ ↓ If fewer people work on the project, it will take more time to complete the project. It will take 5 people 8 weeks to do it. d. ↑ ↑ It will take less time to write fewer invitations. It will take 24 minutes to write 6 invitations. e. The time it takes to drive does not depend on how many people are in the car. It will still take one person 15 minutes to drive to the game. f. The time it takes to swim a lap does not depend on how many people are swimming together.

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