Problem Statement:
Imagine that each diagram in this activity represents a rug. A trap door opens directly over the rug and a dart falls down, landing at random somewhere on the rug. “At random” means that every point on the rug has an equal chance of getting hit as every other point on the rug.
Process:
Since the square-shaped rug can be split into even pieces, I divided it into 12 pieces. 3 rows and 4 columns, depending on where the lines were and then creating more lines of similar length from each other, then I counted all of the squares.
Solution:
After counting the colored squares, I found that gray had 7/12 of the squares, and white had 5/12. The probability of being hit is 2/12 more than landing on white. Because the gray has more surface area than white, it has a greater chance of being hit by the dart.
Evaluation:
What did you learn from it? I learned that everything is not what it seems. Just because the size of something looks bigger doesn't mean that it really is.
Describe one Habit of a Mathematician that you used? Finding Patterns
How would you change the problem to make it better? I would make the first rug easier to understand so there’s a good foundation to work off of.
Did you enjoy working on it? I enjoyed working on this problem. It was fun and challenging,
Was it too hard or too easy? I personally found this problem a little bit challenging. I understood what I was supposed to be doing but I found out I wasn't doing it right at first but after I found out my error and corrected myself it was better and it was a little easier.
Imagine that each diagram in this activity represents a rug. A trap door opens directly over the rug and a dart falls down, landing at random somewhere on the rug. “At random” means that every point on the rug has an equal chance of getting hit as every other point on the rug.
Process:
Since the square-shaped rug can be split into even pieces, I divided it into 12 pieces. 3 rows and 4 columns, depending on where the lines were and then creating more lines of similar length from each other, then I counted all of the squares.
Solution:
After counting the colored squares, I found that gray had 7/12 of the squares, and white had 5/12. The probability of being hit is 2/12 more than landing on white. Because the gray has more surface area than white, it has a greater chance of being hit by the dart.
Evaluation:
What did you learn from it? I learned that everything is not what it seems. Just because the size of something looks bigger doesn't mean that it really is.
Describe one Habit of a Mathematician that you used? Finding Patterns
How would you change the problem to make it better? I would make the first rug easier to understand so there’s a good foundation to work off of.
Did you enjoy working on it? I enjoyed working on this problem. It was fun and challenging,
Was it too hard or too easy? I personally found this problem a little bit challenging. I understood what I was supposed to be doing but I found out I wasn't doing it right at first but after I found out my error and corrected myself it was better and it was a little easier.