Pow: Possible Patches

POW: Possible Patches

Problem Statement

Keisha is making a quilt and will be sewing rectangular patches of material. The patches are 3 inches by 5 inches. The satin piece that she is using is 17 inches wide and 22 inches long. I need to find how many 3 by 5 inch patches Keisha can get from the 17 by 22 piece of satin, how many 9 by 10 patches of satin, how many 5 by 12 inch patches of satin, and 10 by 12 inch patches of satin. I need to know if she found 4 inches wide by 18 inches long how many 3 by 5 inch patches she could get if the satin was 8 inches by 9 inches. These questions are difficult to figure out but can become easier to understand when written down.

Process

My first thought was to draw a scale version of the problem on graph paper and see how many patches I could get. I drew a 17 inch by a 22 inch rectangle and cut it into 3 inch by 5 inch sections. I got a 20 pieces when I cut them first vertically. I got 21 pieces when I cut them horizontally. For the third try I did every other row horizontal and vertical but was unable the numbers didn't increase like I thought they would. I asked a few people sitting next to me Chris, Scott, and Ravon about the problem. I realized that maybe if I multiplied 17 by 22 which are 374 and divide it by the patches 3 by 5 which is 15 I may be able to come up with the possible number of possible patches. When I did this I found the number 24.93. This number is a patch of 24 and when I finally tried for the sixth time I came up with this conclusion. When I asked Chris and Scott for help they were very willing to explain. Ravon missed some days but did take the time to explain a little to me as well. Chris was nice enough to show me how to draw the conclusion. I wasn't able to find out the answers to the other patches. I think it was because I focused to much on the first one. I regret not paying full attention in class to my peers, because I would most likely know how to do the other patches as well. The way I did the first answer is most likely how you can figure out the other answers. If you do 17 by 22 which is 374 and divide that by 9 by 10 which is 90 you get 4.156. I came up with the conclusion that if you divide the product of what you get for your piece of satin and how many patches it will give you an idea for the possible answer that you should get. You should then just begin to sketch the answer out and figure out how you can get that many patches.

Results

When I struggled the most Alliyah and I paired up together. She is the one who helped me figure out my solution the most. At my house we worked the most on what we need to work on to figure out what we need to do to try to come up with a conclusion as to how we can figure out what the possible answer can be. I have only a few diagrams that I did to show my work for finding