This problem is about a person named Ralph Lauren and he is making a patchwork quilt with a couple of constraints. His quilt will be sewn from rectangular patches and each patch is 3 inches by 5 inches. Ralph Lauren finds a box of material and pulls out a rectangular piece that is 17 inches wide by 22 inches long. Ralph Lauren wants to cut as many pieces as possible but will not sew any scraps together. The first scenario requires you to try and find as many 3x5 squares as you can in a 17 wide by 22 high quilt. The next scenario asks how many 9-by-10 squares you can create, how many 5-by-12 squares you can create and finally how many 10-by-12 squares you can create within the 17-by-22 quilt. The last scenario asks how many 3-by-5 squares we can create with a quilt that is 4 inched wide and 18 inches high. The question also asks us how many 3-by-5 squares we can get if the quilt was 8-by-9. My process was first drawing out the quilts on graph paper to make a scale for me to start out with. I then began to create the 3-by 5 squares within each quilt to the maximum I could fill it to. I repeated that step for each of the quilts and got the following answers from each:
1. "21" 3-by-5 squares
2. "2" 9- by-10 squares, "4" 5- by-12 squares and "2" 10-by-12 squares
3. "3" 3-by-5 squares and "4" 3-by-5 squares
A success I had with this problem is that I was able to work and collaborate with other people really well on this problem because it was simple to explain and very easy to visualize. A challenge I had with this problem was identifying length from width because sometimes I would mix the two up and if you have different dimensions, the answer can come out completely different. A habit of a mathematician I used was collaborate and listen because I worked on this POW with 3 other people who helped specify the dimensions for me. I also used being systematic because I had to use the same order of operations in order to get the correct answer each time I inputted a new variable. Overall this POW was great to enforce team work in terms of math.
1. "21" 3-by-5 squares
2. "2" 9- by-10 squares, "4" 5- by-12 squares and "2" 10-by-12 squares
3. "3" 3-by-5 squares and "4" 3-by-5 squares
A success I had with this problem is that I was able to work and collaborate with other people really well on this problem because it was simple to explain and very easy to visualize. A challenge I had with this problem was identifying length from width because sometimes I would mix the two up and if you have different dimensions, the answer can come out completely different. A habit of a mathematician I used was collaborate and listen because I worked on this POW with 3 other people who helped specify the dimensions for me. I also used being systematic because I had to use the same order of operations in order to get the correct answer each time I inputted a new variable. Overall this POW was great to enforce team work in terms of math.