What is this problem?
We were first given a sheet of paper that had a total of 35 different shapes on it(diagram down below) . Our main goal was to do five things. We had to label the shapes with numbers , determine why they decided to use those shapes, identify patterns, come up with what shape 36 would look like, and figure out how this activity relates to connecting the two half's of our brain.
The Process
I first started by doing the easiest thing, which was label the numbers. I then tried to look for patterns and immediately noticed that there was going to be more than one. In the beginning I wasn't really focusing on what shape 36 would look like. I was mostly just working with my group to identify patterns and write down things that we noticed. We noticed that all the circles were prime numbers , the first seven numbers were the base figures, and that all the rectangles were divisible by 4 and 2. After we wrote down the basic information that we saw, then we started to determine what 36 would look like. We figured out that shapes 12 and 24 were made of four blocks in the shape of triangle. We also figured out that 9, 18, and 27 make a triangle shape. In these patterns the next number would be 36 (12, 24, 36 // 9, 18, 27, 36) . We also noticed that every two shapes there's a triangle involved, therefore we made the conclusion that shape 36 would be a triangle. We didn't know what the shape would exactly look like, but we knew that it had to somehow have a triangle in it.
Other Student's Process
On the second day of this problem we were placed with a different group of people. I didn't necessarily have an answer but I explained to them why I thought shape 36 would be somehow a triangle. G actually had the idea that shape 36 would be a triangle made up of 9 2x2 squares, whereas Janelle had the idea that shape 36 would look like shape 27 but it would have 12 circle on each side. Both had valid proof, which made It hard to choose the "right' answer. I knew that shape 36 would have to be a combination of a triangle and square because 36 is divisible by 3,4 and 6.
The Solution
We all shared our ideas and what we thought shape 36 would look like, but we did not get a clear answer. We all got the same idea and agreed that it would be some kind of a triangle but we all had different ideas of what it would look like.
Problem Evaluation
Personally I loved this math problem. It was a great way to start the year and it really got my brain thinking once again after not really doing math all summer. It allowed me to be creative and really think outside of the box. I like that Kirby didn't give us the answer, because it allowed us to all work together and share our ideas. I would love to do more problems like this because I know that problems like this will really strengthen my math skills.
Self Evaluation
I think I did very well with this problem. I worked with different people but also came up with my personal ideas. I would give ,myself an A because I was able to tackle this interesting problem and even though I don't have a solid answer, I don't think that matter with the grade I should get because in my opinion math isn't all about the final answer, but the process you had to go through to get your final answer in the end. While working on this problem I feel like I grew a lot in the growth mindset quality. Last year wast my best year of math because one of the math units we focused on was very hard for me to understand, and since I had two mathletes in my table I wouldn't really try to attempt the problem because I knew I wasn't as smart as them. I let my negative attitude get the best of me and in other words gave up easily, but during this problem that mind set changed. I knew that if I really wanted to figure out the question that I could and this mindset helped me a lot and is something I am going to continue to do.
Edits
Overall I received pretty positive feedback from my CFF group. The only piece of advice they gave me was to add another picture so that its easier to understand. This feedback was very important and helped me make my write up better. I decided to add a picture of my work so you can see my thought process and what I did to get my answer. I also added one of my growths in the 6 qualities of a mathmatician "While working on this problem I feel like I grew a lot in the growth mindset quality. Last year wast my best year of math because one of the math units we focused on was very hard for me to understand, and since I had two mathletes in my table I wouldn't really try to attempt the problem because I knew I wasn't as smart as them. I let my negative attitude get the best of me and in other words gave up easily, but during this problem that mind set changed. I knew that if I really wanted to figure out the question that I could and this mindset helped me a lot and is something I am going to continue to do" to the self evaluation part of my write up.
We were first given a sheet of paper that had a total of 35 different shapes on it(diagram down below) . Our main goal was to do five things. We had to label the shapes with numbers , determine why they decided to use those shapes, identify patterns, come up with what shape 36 would look like, and figure out how this activity relates to connecting the two half's of our brain.
The Process
I first started by doing the easiest thing, which was label the numbers. I then tried to look for patterns and immediately noticed that there was going to be more than one. In the beginning I wasn't really focusing on what shape 36 would look like. I was mostly just working with my group to identify patterns and write down things that we noticed. We noticed that all the circles were prime numbers , the first seven numbers were the base figures, and that all the rectangles were divisible by 4 and 2. After we wrote down the basic information that we saw, then we started to determine what 36 would look like. We figured out that shapes 12 and 24 were made of four blocks in the shape of triangle. We also figured out that 9, 18, and 27 make a triangle shape. In these patterns the next number would be 36 (12, 24, 36 // 9, 18, 27, 36) . We also noticed that every two shapes there's a triangle involved, therefore we made the conclusion that shape 36 would be a triangle. We didn't know what the shape would exactly look like, but we knew that it had to somehow have a triangle in it.
Other Student's Process
On the second day of this problem we were placed with a different group of people. I didn't necessarily have an answer but I explained to them why I thought shape 36 would be somehow a triangle. G actually had the idea that shape 36 would be a triangle made up of 9 2x2 squares, whereas Janelle had the idea that shape 36 would look like shape 27 but it would have 12 circle on each side. Both had valid proof, which made It hard to choose the "right' answer. I knew that shape 36 would have to be a combination of a triangle and square because 36 is divisible by 3,4 and 6.
The Solution
We all shared our ideas and what we thought shape 36 would look like, but we did not get a clear answer. We all got the same idea and agreed that it would be some kind of a triangle but we all had different ideas of what it would look like.
Problem Evaluation
Personally I loved this math problem. It was a great way to start the year and it really got my brain thinking once again after not really doing math all summer. It allowed me to be creative and really think outside of the box. I like that Kirby didn't give us the answer, because it allowed us to all work together and share our ideas. I would love to do more problems like this because I know that problems like this will really strengthen my math skills.
Self Evaluation
I think I did very well with this problem. I worked with different people but also came up with my personal ideas. I would give ,myself an A because I was able to tackle this interesting problem and even though I don't have a solid answer, I don't think that matter with the grade I should get because in my opinion math isn't all about the final answer, but the process you had to go through to get your final answer in the end. While working on this problem I feel like I grew a lot in the growth mindset quality. Last year wast my best year of math because one of the math units we focused on was very hard for me to understand, and since I had two mathletes in my table I wouldn't really try to attempt the problem because I knew I wasn't as smart as them. I let my negative attitude get the best of me and in other words gave up easily, but during this problem that mind set changed. I knew that if I really wanted to figure out the question that I could and this mindset helped me a lot and is something I am going to continue to do.
Edits
Overall I received pretty positive feedback from my CFF group. The only piece of advice they gave me was to add another picture so that its easier to understand. This feedback was very important and helped me make my write up better. I decided to add a picture of my work so you can see my thought process and what I did to get my answer. I also added one of my growths in the 6 qualities of a mathmatician "While working on this problem I feel like I grew a lot in the growth mindset quality. Last year wast my best year of math because one of the math units we focused on was very hard for me to understand, and since I had two mathletes in my table I wouldn't really try to attempt the problem because I knew I wasn't as smart as them. I let my negative attitude get the best of me and in other words gave up easily, but during this problem that mind set changed. I knew that if I really wanted to figure out the question that I could and this mindset helped me a lot and is something I am going to continue to do" to the self evaluation part of my write up.