In the 5th POW of the year, we were tasked with finding how many pieces (of equal size) a piece of cloth could be cut into, without sewing scraps together to make pieces. For instance, I found that a 17x22 inch piece of cloth could be cut into twenty three 3x5 pieces.
I used a really hands on approach to do this problem. After getting the assignment, I went and got a piece of graph paper, and started drawing squares. I did this for pretty much the whole problem, until I finished the main assignment, and made a table with all of my data in it. Sadly, though, I couldn’t really see any patterns.
As I said before, the first 17x22 inch piece of cloth could be cut into twenty 3x5 patches. As for the other 17x22 pieces, a piece of cloth that size could be cut into two 9x10 pieces, six 5x12 pieces, and two 10x12 pieces. We also had to look at 4x18 pieces of cloth, which could be cut into three 3x5 pieces, and 8x9, which could be cut into four 3x5’s. Finally, we had to play around with pieces of cloth and patch sizes, which you can see in the graph below.
I used a really hands on approach to do this problem. After getting the assignment, I went and got a piece of graph paper, and started drawing squares. I did this for pretty much the whole problem, until I finished the main assignment, and made a table with all of my data in it. Sadly, though, I couldn’t really see any patterns.
As I said before, the first 17x22 inch piece of cloth could be cut into twenty 3x5 patches. As for the other 17x22 pieces, a piece of cloth that size could be cut into two 9x10 pieces, six 5x12 pieces, and two 10x12 pieces. We also had to look at 4x18 pieces of cloth, which could be cut into three 3x5 pieces, and 8x9, which could be cut into four 3x5’s. Finally, we had to play around with pieces of cloth and patch sizes, which you can see in the graph below.
In this problem, I used the habits of a mathematician stay organized, and visualize. Stay organized was used in my organization of the boxes (I’m pretty sure I maximized the amount of boxes), as well as the fact that I made a table to organize my data. I used visualize because I drew out all of the boxes.