Maths Write-Up
Problem Statement: (Restate the problem using words, pictures, and/or a diagram)
I saw the problem asking about how many cuts you could make on a Pie. There was different requirements for each Pie, for example for one of the Pies you can only make 3 lines and you have to see how many sections you can make. You must see the most you can make not the least so you have to move your lines around to get more sections.
When you are working on it is almost like making a pie chart but you can cross other lines which makes it a bit more difficult. When I was working on the Problem I it really reminded me of Pie Charts.
Process Description: (How did you try to solve the problem? You may also consider how others in your group tried)
At my first attempt to solve this problem I tried to see a pattern in the lines that were already given to us. If there was a way that I use lines in one of the Pies that let me get the maximum amount I tried to see if using the same lines in the same place help me get the same result as I did in the previous Pie. My pattern worked for some of the Pie Charts but for the greater numbers I had to rearrange some of the lines. I look at how other groups tried to solve the problem and they had a very similar strategy to what I did.Instead of using the same lines in the same place they used the same spots the previously on there Pie Chart. I think Collaborating with other groups helped me get a different perspective of the problem.
Extensions: Invent some extensions or variations to the problem; that is, write down some related problems.They can be easier, harder, or about the same level of difficulty as the original problem. (You don't have to solve these additional problems.)
Actually when my peers and I were solving the problem we came up with some extensions of our own. One of them was trying to create our own In-n-Out Table and trying to find our pattern that worked for that specific problem. Solving our own In-n-Out Table would help us a lot when trying to understand the problem.
Extension- How many pieces can you make with 0 cuts. This was a very difficult Extension but I think the answer is 0 as well.
Solution: (The end result, wrong or right, it doesn’t matter! Include one or many solutions as long as they make sense to you!)
One solution that my peers and I came up was y=(x+1)÷ 2+1 for the question that you had to come up with an equation. For Number 1 the greatest number of cuts for 4 and 5 you can get was 11 & 16. For Number 2 a pattern that seem to me very interesting. Example-
For Part 2-b My answer was 55 Pieces with 10 lines.
Self-Assessment: Reflect on two Habits of a Mathematician you used when solving this problem
Two Habits of Mathematician That I used when working on this problem was Looking for Patterns & Conjecture and Test. I used a lot of trying to find a pattern especially when I first started as I said I tried to put the same lines I put into my previous Pie into the next one. I think this really help me out a lot through the process of solving this problem. Then Conjecture and test I used for every Pie that I was trying to figure out. For example I had to Test out if this set of lines worked or if this was the most sections it can have so I had to Conjecture and test a lot especially on this problem of the week.
Problem Statement: (Restate the problem using words, pictures, and/or a diagram)
I saw the problem asking about how many cuts you could make on a Pie. There was different requirements for each Pie, for example for one of the Pies you can only make 3 lines and you have to see how many sections you can make. You must see the most you can make not the least so you have to move your lines around to get more sections.
When you are working on it is almost like making a pie chart but you can cross other lines which makes it a bit more difficult. When I was working on the Problem I it really reminded me of Pie Charts.
Process Description: (How did you try to solve the problem? You may also consider how others in your group tried)
At my first attempt to solve this problem I tried to see a pattern in the lines that were already given to us. If there was a way that I use lines in one of the Pies that let me get the maximum amount I tried to see if using the same lines in the same place help me get the same result as I did in the previous Pie. My pattern worked for some of the Pie Charts but for the greater numbers I had to rearrange some of the lines. I look at how other groups tried to solve the problem and they had a very similar strategy to what I did.Instead of using the same lines in the same place they used the same spots the previously on there Pie Chart. I think Collaborating with other groups helped me get a different perspective of the problem.
Extensions: Invent some extensions or variations to the problem; that is, write down some related problems.They can be easier, harder, or about the same level of difficulty as the original problem. (You don't have to solve these additional problems.)
Actually when my peers and I were solving the problem we came up with some extensions of our own. One of them was trying to create our own In-n-Out Table and trying to find our pattern that worked for that specific problem. Solving our own In-n-Out Table would help us a lot when trying to understand the problem.
Extension- How many pieces can you make with 0 cuts. This was a very difficult Extension but I think the answer is 0 as well.
Solution: (The end result, wrong or right, it doesn’t matter! Include one or many solutions as long as they make sense to you!)
One solution that my peers and I came up was y=(x+1)÷ 2+1 for the question that you had to come up with an equation. For Number 1 the greatest number of cuts for 4 and 5 you can get was 11 & 16. For Number 2 a pattern that seem to me very interesting. Example-
For Part 2-b My answer was 55 Pieces with 10 lines.
Self-Assessment: Reflect on two Habits of a Mathematician you used when solving this problem
Two Habits of Mathematician That I used when working on this problem was Looking for Patterns & Conjecture and Test. I used a lot of trying to find a pattern especially when I first started as I said I tried to put the same lines I put into my previous Pie into the next one. I think this really help me out a lot through the process of solving this problem. Then Conjecture and test I used for every Pie that I was trying to figure out. For example I had to Test out if this set of lines worked or if this was the most sections it can have so I had to Conjecture and test a lot especially on this problem of the week.