Different Products
Why do this problem?
This problem, along with the rest of the problems in the Proof for All (st)ages feature, provides an excellent context for observing, conjecturing and thinking about proof, and for appreciating the power of algebra.
Possible approach
Key question
Is there a way to represent the products of pairs that will help to explain the patterns you noticed?
Possible support
This problem could also be approached purely numerically, as an exercise in developing fluency with multiplication tables while looking for pattern and structure.
Before embarking on this problem, students could take a look at I Like to Prove It!, which contains a collection of more accessible problems that also challenge students to develop convincing arguments.
Possible extension
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