rug games write up!
Rug Games
A few diagrams have been drawn to represent rugs. There is a trap door directly over which opens and out falls a dart. The dart falls on any place randomly, meaning that every point on the rug has an equal chance of it being landed on. However, the rugs do have different designs with up to 3 different shades in a single rug. What is the probability of the dart landing on each of the colors of the rug?
For the first rug, my group members and I just sorta eyeballed it and sorta guessed the value of each region. I personally did not calculate the bottom region out of the whole. Instead I calculated what the region was within what seemed to be the last ⅓ of the rug. Which isn’t really helpful because we want the probability of a whole shade in the whole rug. But it was a good start for the activity.
When we got to the 2A-D, that was when I really started looking at the probability for the different shades in the rug itself. I first started by cutting each rug into equal shapes. Rugs A and B I cut into rectangles and rugs C and D I cut into triangles. Each cut somehow came from a cut that had already been made somewhere on the rug but I was now simply extending to cut the rug from one edge to another. Everything was just cut really smoothly.
Once I had all the shapes equally cut, I would count the total number of shapes in the rug.
If we look at B, I cut the rug into 20 equal pieces. This rug has 3 colors, gray, white, and black. (7 Gray Rectangles , 9 White Rectangles , 4 Black Rectangles) 20 will be the denominator for each of the probabilities (of the dart being landed on) and the numerator will be the number of shapes of the certain color.
With this activity, I didn’t exactly learn much, it was pretty easy. It just helped me practice my probability skills. I guess the habit of a mathematician that I used was being consistent. Just because I knew how to do it and found it easy, doesn’t mean I just decided not to do it. I know some people have the tendency to not do it because I mean what is the point of doing it if you already know; you aren’t learning anything so why bother. But I don’t know, I still like doing it. To make this problem better I would want to have students customize their own rugs (how we did in our journals) but make it a beautiful piece. (Challenge option: Weave an actual rug!!!) And with that, we could connect all the rugs and make a class QUILT. That would actually be pretty cool.
A few diagrams have been drawn to represent rugs. There is a trap door directly over which opens and out falls a dart. The dart falls on any place randomly, meaning that every point on the rug has an equal chance of it being landed on. However, the rugs do have different designs with up to 3 different shades in a single rug. What is the probability of the dart landing on each of the colors of the rug?
For the first rug, my group members and I just sorta eyeballed it and sorta guessed the value of each region. I personally did not calculate the bottom region out of the whole. Instead I calculated what the region was within what seemed to be the last ⅓ of the rug. Which isn’t really helpful because we want the probability of a whole shade in the whole rug. But it was a good start for the activity.
When we got to the 2A-D, that was when I really started looking at the probability for the different shades in the rug itself. I first started by cutting each rug into equal shapes. Rugs A and B I cut into rectangles and rugs C and D I cut into triangles. Each cut somehow came from a cut that had already been made somewhere on the rug but I was now simply extending to cut the rug from one edge to another. Everything was just cut really smoothly.
Once I had all the shapes equally cut, I would count the total number of shapes in the rug.
- 15 Rectangles
- 20 Rectangles
- 16 Triangles
- 32 Triangles
- 8 Gray Rectangles , 7 White Rectangles
- 7 Gray Rectangles , 9 White Rectangles , 4 Black Rectangles
- 6 Gray Triangles , 6 White Triangles , 4 Black Triangles
- 15 Gray Triangles , 17 White Triangles
If we look at B, I cut the rug into 20 equal pieces. This rug has 3 colors, gray, white, and black. (7 Gray Rectangles , 9 White Rectangles , 4 Black Rectangles) 20 will be the denominator for each of the probabilities (of the dart being landed on) and the numerator will be the number of shapes of the certain color.
- P(Gray)=7/20
- P(White)=9/20
- P(Black)=4/20
- P(Gray)=8/15 , P(White)=7/15
- P(Gray)=15/32 , P(White)=17/32
With this activity, I didn’t exactly learn much, it was pretty easy. It just helped me practice my probability skills. I guess the habit of a mathematician that I used was being consistent. Just because I knew how to do it and found it easy, doesn’t mean I just decided not to do it. I know some people have the tendency to not do it because I mean what is the point of doing it if you already know; you aren’t learning anything so why bother. But I don’t know, I still like doing it. To make this problem better I would want to have students customize their own rugs (how we did in our journals) but make it a beautiful piece. (Challenge option: Weave an actual rug!!!) And with that, we could connect all the rugs and make a class QUILT. That would actually be pretty cool.