After students have played several rounds of the game, they will begin to develop insights into the best choice of spinners to use. Interrupt their game-playing occasionally so student pairs can share their observations.
A question such as the following will help develop this insight:
- David spun 4 × 9 = 36, but he has no room on his board for any of the rectangles for 36. So he lost his turn. What could he do on his next turn? (He could use the small spinner so his product isn't as big.)
After the game is over, ask students questions about their strategies:
- Did you usually use the numbers that you spun or did you often try to use other factor pairs for the same product? What were your reasons for your choices? Do you think some choices were better than others? Why?
- How did you arrange your rectangles? Did you try to use as few gaps as possible (as in Figure 2) or did you spread out your rectangles (as in Figure 3)? Do you think one method is better than the other? Why?
- Did you develop a strategy for choosing which spinner to use?
- Did you choose the same spinners at the beginning of the game as you did at the end of the game? Explain.
A good strategy is to use two spins from Spinner 1–10 at the beginning of the game and two spins from Spinner 1–4 near the end of the game. This way, the player gets to fill in large rectangles when his or her grid is empty and small rectangles when space gets tight.
Observe students as they play Floor Tiler and note the rectangles they draw on their game boards. Use this information to assess their progress toward representing and solving multiplication and division problems using rectangular arrays [E1].
The Lesson 6 Workshop provides targeted practice.
