POW Rough Draft
March 11, 13
Problem Statement: on an 8x8 checkerboard, they’re many different size squares within that one. There are many 2x2’s, 3x3’s, 4x4’s etc, on that one 8x8 board. You must find exactly how many 2x2, 3x3, 4x4, 5x5, 6x6, 7x7, and 8x8’s are on the 8x8 checkerboard. They are all over and around the checkerboard, but you must be careful to not repeat because they do overlap or go on top of each other. 1. Altogether, how many squares are there on an entire 8x8 checkerboard? 2. What if you didn’t have an 8x8 checkerboard? What if it was 9x9? How could you determine exactly how many squares are on that checkerboard.
Process: I began working with my tutor on my POW. She came up with the idea to use a checkerboard (the kind on paper) to help me. I thought it was a good idea, but I wasn’t sure if it was going to work. I still went along with it to just try it out. When I began I realized how confusing it would be to use my pencil to count all the squares. My tutor Ms. Earnest suggested that I cut out some of the checkerboards into smaller sections. I wanted to cut them out to make one 2x2, 3x3, 4x4, 5x5, 6x6 and a 7x7 to help me more. I used the cut out boards to find out how many squares there actually are. I started with the first cut out, which was 2x2. I began moving it across the bigger board, the entire 8x8 checkerboard. I kept going until I was sure I went all around the board and got all the 2x2 squares possible. I had to be careful, and pay close attention because if I messed up I had to start over. I did this for all the cut outs all the way up to 7x7. I didn’t go up to 8x8 because the whole board was an 8x8 and it was obvious the answer would be only 1. My classmate Ashley claims to have already found the answer to the POW. She told me a shortcut to use with the checkerboard cutouts. She told me I only had to count the squares going up with the 2x2 one time, and whatever number I get I should...