Possible Patches
For this POW we are given an example of a picture of a piece of fabric, its a 17 by 22. The problem tells us that we are trying to create as many possible pieces inside the patch as possible. It then gives us the length of how big they want the individual pieces to be which was 3 by 5. After it gives us that example it gives us questions with many other patches and pieces and different lengths of each one. Here is the problem in which we had to solve for.
1. How many 3 by 5 patches can Ralph Lauren get from the 17 by 22 inch piece of satin? Draw a diagram proving your answer. Use graph paper to draw out you patches as your proof.
2. How many 9 by 10 inch patches could Ralph get from this 17 by 22 inch piece of satin? Prove your answer. How many 5 by 12 inch patches? How many 10 by 12 inch patches?
3. Suppose Ralph Lauren found a piece of satin 4 inches wide and 18 inches long. How many 3 by 5 patches could he get from this piece? What if the satin were 8 inches by 9 inches?
4. Begin with the specific situations described in Question 1 to 3. Then experiment with other patch sizes and other sizes for the piece of satin. (Do 2-3 different experiments/variations.)
The process I went through while creating possible patches was quite simple. First I wrote down on the backside of the graph paper all the measurements for each question then I had to create a diagram for and solve. There was a total of 9 different measurements of patches and pieces that we had to create diagrams for. Then I started beginning to create the diagrams starting with the first one that they asked for, which was a 17 by 22 inch piece of cloth and make 3 by 5 fabric sized pieces within it. After I finished that diagram I moved onto the next one and so on. Then as I started making these diagrams I started trying to find how many pieces was I able to get out of it. At first I started arranging the pieces in perpendicular lines but then within the same fabric sheet I started trying to flip the pieces in a horizontal style. I figured out that within the piece of satin that you are trying to cut out, it depends on weather or not it's a good idea to flip the pieces around. So I discovered that the 1st diagram I created, it was best to have both different shapes of flipped pieces inside because as your making pieces within the fabric your trying to waste as little space as possible. So in certain areas I had to flip the shape to make it fit into a specific part of the fabric.
Below are all the answers that I got for each measurement:
1. 3 by 5 into 17 by 22 = 22
2. 9 by 10 into 17 by 22 = 2
3. 5 by 12 into 17 by 22 = 5
4. 10 by 12 into 17 by 22 = 2
5. 3 by 5 into 4 by 18 = 3
6. 3 by 5 into 8 by 9 = 3
7. 10 by 5 into 20 by 20 = 8
8. 1 by 3 into 7 by 15 = 34
9. 2 by 3 into 5 by 5 = 2
Below are the images of the diagrams that I made through out each of the 9 questions, not each diagram is in order so I labeled the number diagram that goes along with the number solution from 1-9. Each diagram has a number in it that represents how many pieces were able to fit inside it. The top 2 images are the required questions from 1-3, then the very bottom image are the specific measurements that I picked and used. Through out this POW I though it was a good exercise to just kinda bring back measurements and trying to work around the problem. A Habit of a Mathematician I feel I used well was staying organized because being able to go back to my answer sheet where I kept all my measurements and diagrams that I had to make was extremely helpful. I think that organization is key to any problem that you do during math because you want to be able to know what your doing and having everything you know in the right areas where you know where it is.
1. How many 3 by 5 patches can Ralph Lauren get from the 17 by 22 inch piece of satin? Draw a diagram proving your answer. Use graph paper to draw out you patches as your proof.
2. How many 9 by 10 inch patches could Ralph get from this 17 by 22 inch piece of satin? Prove your answer. How many 5 by 12 inch patches? How many 10 by 12 inch patches?
3. Suppose Ralph Lauren found a piece of satin 4 inches wide and 18 inches long. How many 3 by 5 patches could he get from this piece? What if the satin were 8 inches by 9 inches?
4. Begin with the specific situations described in Question 1 to 3. Then experiment with other patch sizes and other sizes for the piece of satin. (Do 2-3 different experiments/variations.)
The process I went through while creating possible patches was quite simple. First I wrote down on the backside of the graph paper all the measurements for each question then I had to create a diagram for and solve. There was a total of 9 different measurements of patches and pieces that we had to create diagrams for. Then I started beginning to create the diagrams starting with the first one that they asked for, which was a 17 by 22 inch piece of cloth and make 3 by 5 fabric sized pieces within it. After I finished that diagram I moved onto the next one and so on. Then as I started making these diagrams I started trying to find how many pieces was I able to get out of it. At first I started arranging the pieces in perpendicular lines but then within the same fabric sheet I started trying to flip the pieces in a horizontal style. I figured out that within the piece of satin that you are trying to cut out, it depends on weather or not it's a good idea to flip the pieces around. So I discovered that the 1st diagram I created, it was best to have both different shapes of flipped pieces inside because as your making pieces within the fabric your trying to waste as little space as possible. So in certain areas I had to flip the shape to make it fit into a specific part of the fabric.
Below are all the answers that I got for each measurement:
1. 3 by 5 into 17 by 22 = 22
2. 9 by 10 into 17 by 22 = 2
3. 5 by 12 into 17 by 22 = 5
4. 10 by 12 into 17 by 22 = 2
5. 3 by 5 into 4 by 18 = 3
6. 3 by 5 into 8 by 9 = 3
7. 10 by 5 into 20 by 20 = 8
8. 1 by 3 into 7 by 15 = 34
9. 2 by 3 into 5 by 5 = 2
Below are the images of the diagrams that I made through out each of the 9 questions, not each diagram is in order so I labeled the number diagram that goes along with the number solution from 1-9. Each diagram has a number in it that represents how many pieces were able to fit inside it. The top 2 images are the required questions from 1-3, then the very bottom image are the specific measurements that I picked and used. Through out this POW I though it was a good exercise to just kinda bring back measurements and trying to work around the problem. A Habit of a Mathematician I feel I used well was staying organized because being able to go back to my answer sheet where I kept all my measurements and diagrams that I had to make was extremely helpful. I think that organization is key to any problem that you do during math because you want to be able to know what your doing and having everything you know in the right areas where you know where it is.