Problem Statement/Process
This POW was all about working with rectangles of different sizes and trying to fit them in a bigger rectangle or "quilt". The first question asked us to find how many 3-by-5 (inches) pieces we can fit into the larger 17-by-22 piece of satin. We used graph paper to draw out this problem to figure out how many patches we can fit in the material. By using the diagram I drew, I was able to find that 21 3-by-5 pieces can fit into a rectangle that is 17 inches by 22 inches. As the problem goes on, the questions change the sizes of the patches and the piece of satin. The second question asks how many 9-by-10, 5-by-12, and 10-by-12 inch patches could fit inside a 17-by-22 piece of material. Question three asks us how many 3-by-5 patches we can fit into a piece of satin that is 4 inches wide and 18 inches tall, and a piece that is 8-by-9 inches. Finally, we were able to experiment by setting our own variables: the patch size and the satin size.
Solution/Results
I noticed that if the satin and the patches were somewhat proportional, then I could fit more patches in the satin. I thought that by using up all the material with proportional rectangles, I would be able to get the max rectangle pieces. I haven't tested this theory, however I did an experiment that was similar to my theory and I seemed to get many rectangles. My test was when I made the satin 17-by-22 and the patches were 2-by-7. 2 can go into 17 eight times and 7 can go into 22 three times. Since I used up most of the satin, I thought I would be able to use up all of the material if I made the small rectangles proportional to the large rectangle.
Reflection
I learned how to look at problems differently because there can be more than one way to solve a problem. If the rectangles were positioned a certain way, the max number of rectangles can vary. For example, in one of my test problems, 2x7 rectangles can fit into a 17x22 piece of satin 24 times or 25 times depending on the orientation of the rectangles. I feel I deserve a 9 out of 10 because I put effort into the thought process required for this problem. First, my mind went straight to taking the areas of both rectangles and dividing, however there is the constraint of not putting together excess pieces. I could've improved by double checking all my work to make sure I got the max amount of pieces, but I did not do that and saw that I there can be more rectangles as I finalized this POW. I used the HOAM of Staying Organized by keeping all my work in it's own area so I could clearly see what I was doing. Examples of me using the stay organized habit are in the pictures above.