Problem Statement
Kyle gave us this sheet and told us to number each shape, then told us to ask ourselves the following:
What patterns do you see?
What shapes do you see?
What will 36 look like?
Kyle gave us this sheet and told us to number each shape, then told us to ask ourselves the following:
What patterns do you see?
What shapes do you see?
What will 36 look like?
My Process
After a minute or so I discovered a constant a pattern that made sense. The first six shapes that are boxed (above) are what I referred to as the "key" to rest of the shapes. I noticed each shape was made out of one of the first six. All shapes are made from multiples of the number. For example, #8 is made out of 2 groups of 4. Another thing I noticed immediately was that all prime numbers were just circles, beginning with #7.
Other Peers' Process
The group I discussed the pattern with disagreed with my idea. They didn't notice a pattern yet, but they had an answer for what #36 might look like. They saw that starting from #4 they just add two groups of 4 diagonally, coming to the conclusion that #36 is going to be 9 groups of 4 (below). It made sense but I disagreed with their idea this time. That pattern occurs because those numbers are all divisible by 4, so of course there is going to be a pattern. I am still unsure on what the actual answer for what #36 may look like. I saw that the numbers like #9, #16, and #25 have similarities. #9 is made from 3 groups of 3, #16 is made from 4 groups of 4, #25 is made from 5 groups of 5, It's only common sense #36 would be made from 6 groups of 6 (below).
After a minute or so I discovered a constant a pattern that made sense. The first six shapes that are boxed (above) are what I referred to as the "key" to rest of the shapes. I noticed each shape was made out of one of the first six. All shapes are made from multiples of the number. For example, #8 is made out of 2 groups of 4. Another thing I noticed immediately was that all prime numbers were just circles, beginning with #7.
Other Peers' Process
The group I discussed the pattern with disagreed with my idea. They didn't notice a pattern yet, but they had an answer for what #36 might look like. They saw that starting from #4 they just add two groups of 4 diagonally, coming to the conclusion that #36 is going to be 9 groups of 4 (below). It made sense but I disagreed with their idea this time. That pattern occurs because those numbers are all divisible by 4, so of course there is going to be a pattern. I am still unsure on what the actual answer for what #36 may look like. I saw that the numbers like #9, #16, and #25 have similarities. #9 is made from 3 groups of 3, #16 is made from 4 groups of 4, #25 is made from 5 groups of 5, It's only common sense #36 would be made from 6 groups of 6 (below).
Assessment of Problem & Self Evaluation
I enjoyed this problem, it really made me pay attention to little details and focus on what I see. It was difficult to see the whole class' different predictions considering how quickly time goes by and how little we have. My group agreed to disagree so we didn't progress with new ideas. I'd give myself an A-, if I could change something I would have shared and elaborated on my ideas. Like I explained above, I am still unsure on what the actual answer for what #36 may look like. I saw that the numbers like #9, #16, and #25 have similarities. #9 is made from 3 groups of 3, #16 is made from 4 groups of 4, #25 is made from 5 groups of 5, It's only common sense #36 would be made from 6 groups of 6, (#36) I think the quality of a mathematician I used the most was explaining/justifying. When I first identified the patterns my peers didn't notice, I had to explain in detail my observation. Teaching others always gives you a better understanding and gives you the opportunity you learn more. It helps me grow as a student when I share my thought with others as well as explaining my ideas to them.
I enjoyed this problem, it really made me pay attention to little details and focus on what I see. It was difficult to see the whole class' different predictions considering how quickly time goes by and how little we have. My group agreed to disagree so we didn't progress with new ideas. I'd give myself an A-, if I could change something I would have shared and elaborated on my ideas. Like I explained above, I am still unsure on what the actual answer for what #36 may look like. I saw that the numbers like #9, #16, and #25 have similarities. #9 is made from 3 groups of 3, #16 is made from 4 groups of 4, #25 is made from 5 groups of 5, It's only common sense #36 would be made from 6 groups of 6, (#36) I think the quality of a mathematician I used the most was explaining/justifying. When I first identified the patterns my peers didn't notice, I had to explain in detail my observation. Teaching others always gives you a better understanding and gives you the opportunity you learn more. It helps me grow as a student when I share my thought with others as well as explaining my ideas to them.