I know formal ways of proving this, but I am doing research on how middle grade students create arguments to support conjectures. I would like to anticipate many more solutions before I enact the task. Can anyone help me find ways that middle grade students might approach proving this?
I have come to two approaches thus far from how they might approach it:
Formal: Let k, m be any integer, (2k+1)+(2m+1) and so on ....
An odd number is equal to even+1. So, we have (even+1)+(even+1). We know two even sum to an even number and 1+1 sums to two which is even. Again, the sum of two even numbers is even. Therefore, two odds add to an even.
The last approach assumes that even+even=even is accepted by the mathematical community which is a conversation we will have. Of course, students will come up with empirical arguments, but I'm looking for other ways students might try to justify this.