Shauna and Tony were working together on a puzzle. Here are the two clues they were trying to put together:
Below is a snippet of their conversation:
Shauna: I see that these two pieces could be put together in two ways. You could slide the right one over so that the top P is on top of the triangle, or slide it over one more square so that the bottom P is on top of the E.
Tony: Okay, for the first one, the only overlap is the P on top of the triangle. That works, because 3 is a prime and a triangular number.
Shauna: The second one works, too, because the bottom P is on top of an E, and 2 is an even prime number.
Tony: Are there any more overlaps for that one?
Shauna: I don't think so.
Tony: I think that the top P is on top of something. Let's cut it out and try.
Shauna: Yes, that P is on top of an E. But we said that was okay before.
What does this conversation tell you about how the students are thinking about the problem?
How would you help them deal with any misconceptions they have?