Share Solution Strategies. Discuss students' solutions to Questions 10–12. Choose a variety of solution strategies for each question.
- Explain what happens when you try to solve Question 10 using a graph. (Possible response: If I follow the dotted line from 150 over to the line I drew with the ruler and then follow the other dotted line down to the horizontal axis, it hits between 7 and 8 gumballs. So I know 150 is enough to buy 7 gumballs but not 8. 7 × 20¢ = 140¢. 150¢ − 140¢ = 10¢ left over.)
- Could you use the graph to solve Questions 11 and 12? Explain. (Possible response: The data for the cost of 12 and 24 gumballs was not on the graph. The numbers did not go up that high, but I found combinations of 12 and 24 gumballs on the graph and added. For example 5 + 7 = 12 so I could find the cost of 5 gumballs and 7 gumballs on the graph and add the amounts to get the cost of 12 gumballs.)
- Share your solution strategies for Questions 11 and 12. (Possible solution strategies include reasoning from known facts, using patterns in the data, repeated addition, or multiplication. Students could double the cost for 12 gumballs to find the cost of 24 gumballs.
- Which solution strategy was the most efficient for solving Question [10, 11, or 12]?
Ask students to answer Question 13. This is another chance to find yet another way to find a way to reason about multiplication.
- Look at all the strategies we have posted. Did anyone come up with a strategy we have not seen yet?
- Do you think this is an efficient strategy?
