Diagonals - Square Madness

I ended up doing the Diagonals work sheet today just because I wanted to see if I could figure out the answer, and I thought I did for a second until I tried a larger number of rows and columns

In class I thought I had  figured it out but that was because of the way that I had gone about trying to solve it. I was doing random sample squares with varying rows and columns which doesn't help to see any patterns. I still haven't figured it out since my answer seems to only work up to a certain size of square. This is just kind of a way to see the process I took for the next time I look at the problem.

The Steps:

Understand the Problem:
Find a mathematical expression that can determine the number of shaded squares

Devise a Plan:
When nothing works, looking for a pattern always gives some inkling of information. So here I just did a systematic approach of drawing squares keeping the rows constant and changing the columns. During class the issue I had in class was that we didn't keep a constant row or column so we didn't see what was staying constant throughout.

Carry out the Plan:

Look Back:
Well I thought I had figured it out for a second time but then tried it out with a random larger m and n ( 5 x 7) and it failed to give back the correct number. I think I'm a bit stuck for now and decided to clear my head after writing this. Another day to attempt it tomorrow.

Sorry for the delayed post, after going through with the assignment had a lot of things to catch up on over the weekend especially with the upcoming tests.

Anyways, this week we started delving deeper into proofs and so far it's seems really new to me though I haven't had time to look deeper into the notes for Chapter 3.

What I find slightly difficult is being able to decide which steps to do to to go from "P" to "Q", and how someone in the end decides which is the most logical step. Though this is bringing back a lot of memories with the left side == right side type of things we did in high school though I'm not sure if thats exactly what we're doing but I'm thinking it is. I'll be making a more detailed post about proofs next week.