For this problem we were provided a paper (as seen below) with different shapes made to represent numbers. Here we see up to the number 35 represented in these shapes made up from small circles. Our task was to find out what the number 36 would look like.We could do so by finding patterns using prime factorization, whatever we liked.
The technique that I chose was finding patterns and then seeing how 36 fit into said patterns. I decided that 36 would look like a slightly elongated 24. I came to this conclusion by looking at all the variables of 6. 12 is a triangle made of 4 circle squares, 18 is a shape made from 6 circle triangle like shapes. 24 is a triangle like shape made up from squares. and finally 30 is another shape made from triangle like shapes. From this pattern it is safe to assume that 36 will be some sort of shape made up from 4 circle squares. And by looking closer at the pattern I can also assume that it will look like 24 if 12 is a smaller version of 24. This Is only one of the multiple patterns that I used using variables of 36.
Other processes
One of the many other processes used by my fellow classmates was to use prime factorization to break down the 36 into smaller number. At that point people would use it to find out how many of each shape would be used in 36. This is just one of the many techniques used.
The Solution
In the end we came up with two possible solutions. One looked like a version of 30 with an extra shape, and the other was the shape I came up with. We are yet to know which is correct but we've been assured that both are possible.
Problem Assessment
This was a very interesting problem. I don't think I've ever done any problem like this one. I liked how many techniques could be used to reach a solution. It was pretty fun when the sparks finally connected in my head about how exactly I could find a solution. Then getting to present my findings on the board was also pretty fun. Anything where I get to present my solution is pretty cool, especially when there are so many different solutions that people have presented. I got a refresher course on prime factorization and I got to compare answers with my group.
Self Evaluation
I am pretty proud of how I worked during this project. I worked together with my team,I thought long and hard to present a solution I was proud and certain of. It's hard not to do good with a simple problem like this. The only thing I could've done better was showing off my solution in other words stepping up more. But I still believe that I deserve A+. I used the Patterns/Generalizing quality of a mathematician. The place where I used it is pretty obvious. My whole technique revolved around finding patterns instead of using prime factorization. Logical thinking in finding patterns that's how I solved the problem.
Journal Entry: 5
Think of a time in math class when you thought deeply about a concept or connected two ideas.
At the time I can't think of a specific concept in which I had to think very deeply or connected two ideas. However I can say that this is something that done on multiple occasions. Whenever I encounter a particularly difficult problem I need some time to think it through, and I could say that every mathematical process requires you to connect multiple ideas. For example, multiplication is just advanced addition.
Edits
Mr. Kirby recommended that I explain how I used my quality of a mathematician so I did so in my self evaluation section. He also recommended that I make a section to show the edits I've made based on feedback, and this is it. In addition to that some of my fellow classmates noted grammatical errors which I was able to correct. Also I've planned where I will put scanned pages from my journal as two of my critical friends and Mr. Kirby suggested.