After the “mixed” groups had gotten done discussing their different Versions amongst themselves, we brought their attention together for a whole-class discussion. Essentially our goal was to show (up on an overhead projector, for instance) all three Versions and get some of the overall class reactions to what they had just done. What follows are just some examples of the kinds of questions we asked:
► What do you know now that you didn’t know before discussions with your group members?
► What do you think are the important mathematical ideas behind the task?
► What do you see as the mathematical differences and similarities of all three Versions?
– Do you think one Version is easier or harder than another? Why?
– How did discussing the three Versions impact your understanding of the mathematics?
► What are some examples of products you’ve seen advertised in terms of money-per-quantity?
► What are some examples of products you’ve seen advertised in terms of money-per-quantity?
Some of the above questions, or some similar questions, may make good prompts for a homework assignment aimed at getting students to reflect on themes of proportional reasoning inherent in Ratio Triplets. We especially like questions that get students to talk about what they learned in terms of talking to each other and trying to communicate their own reasoning.
