Problem: A number N is called “nice” if a square can be dissected into N non-overlapping squares. What numbers are “nice”? Why?
Problem Solving Process: During the entry phase I wrote down the number n is called nice and n can be cut up into nonoverlapping squares. For the want to know section, I wrote which squares are nice? Since I missed the first day of working on this problem, my group understood that only perfect squares were nice and we went right into the attack phase. For example, a 2 by 2, made 4 squares within itself. So we wrote down that 4 is a nice square. We thought for this problem that only integers can be used, meaning we could not use non whole numbers, when dissecting the squares. So we continued to dissect a 3 by 3, 4 by 4, and 5 by 5 and found how many squares can be dissected in them. In my free write I said, that next time we would try and analyze our data and see if we can see a pattern with what we had written down so far. …show more content…
Our conjecture was a nice square is a perfect square that can be dissected into different sizes of non overlapping squares. We then made a table, to better organize our data. We made four columns that consisted of the perimeter, number of squares found in each square, the area, and total amount of each solution. For example in a 3 by 3 we found that we could only dissect the square into two different solutions. We thought that this information was important because we thought we could only dissect the squares into whole number (integers). We continued to look at our table to see if we could find a relationship, but unfortunately we were unable to come up with a solution. At this point we became