For this POW we had to cut imaginary pizzas with a certain amount of cuts with the most pieces we could create possible. We had to have the cuts go straight through the pizza and the pieces do not have to be equal. We were given a table with the number of cuts and the maximum number of pieces per cut. 1-3 cuts and the maximum pieces were given. For the first scenario we had to find the largest number of pieces we could achieve with 4 cuts. We then had to find the scenario for 5 cuts and try to find a pattern with all the maximum cuts we have found. We also had to explain why we thought the pattern was occurring and try to find a rule that pertains to the problem.
I began by experimenting on the 4-cut pizza and I found out that the more intersections I create, the more pieces I receive. I experimented 4 times and I got 11 pieces at most multiple times. I began to start on 5 and I used the same tactic of producing more intersections. I then plugged what I thought was the maximum into the table and began to find patterns. Once I found my pattern I used that pattern in order to find the most pieces I could receive from 10 cuts. I also explained why I believed the pattern was occurring in the table. I also created a rule for the table in order to better understand the table and how many pieces you can receive from a certain amount of cuts.
I began by experimenting on the 4-cut pizza and I found out that the more intersections I create, the more pieces I receive. I experimented 4 times and I got 11 pieces at most multiple times. I began to start on 5 and I used the same tactic of producing more intersections. I then plugged what I thought was the maximum into the table and began to find patterns. Once I found my pattern I used that pattern in order to find the most pieces I could receive from 10 cuts. I also explained why I believed the pattern was occurring in the table. I also created a rule for the table in order to better understand the table and how many pieces you can receive from a certain amount of cuts.
# of cuts Maximum # of cuts 1 2 24 37 411 516
1.) 4 cuts: 11 pieces
5 cuts: 16 pieces
2. The pattern I found was when you add the maximum number of cuts to the next number of cuts in the table you get the maximum cuts for the nex number of cuts. For example 2 cuts has a maximum number of 4 pieces so if you add the pieces to the next # of cuts (3) you get 7 which is the maximum # of cuts for 3.
10 cuts: 56 pieces
I believe this pattern is occurring because each cut affects every single other cut but at a non-exponential pace which explains why my pattern doesn't have anything to do with multiplication.
3. My rule for this table is the maximum # of cuts plus the next number on the table's # of cuts equals the maximum number of cuts for the # of cuts on the table.
I definitely learned how to use visualization and a table at the same time through this POW because we had to use the pizzas and insert the data into a table. Then through the use of that I had to find patterns within the table. I believe I deserve a 10/10 with his POW because I fully understood this problem and worked with others to ensure that my maximum pieces were similar to theirs. I used the habit finding patterns because with this problem in particular I had to find a pattern which actually took a while because I couldn't find any relevance at first.
1.) 4 cuts: 11 pieces
5 cuts: 16 pieces
2. The pattern I found was when you add the maximum number of cuts to the next number of cuts in the table you get the maximum cuts for the nex number of cuts. For example 2 cuts has a maximum number of 4 pieces so if you add the pieces to the next # of cuts (3) you get 7 which is the maximum # of cuts for 3.
10 cuts: 56 pieces
I believe this pattern is occurring because each cut affects every single other cut but at a non-exponential pace which explains why my pattern doesn't have anything to do with multiplication.
3. My rule for this table is the maximum # of cuts plus the next number on the table's # of cuts equals the maximum number of cuts for the # of cuts on the table.
I definitely learned how to use visualization and a table at the same time through this POW because we had to use the pizzas and insert the data into a table. Then through the use of that I had to find patterns within the table. I believe I deserve a 10/10 with his POW because I fully understood this problem and worked with others to ensure that my maximum pieces were similar to theirs. I used the habit finding patterns because with this problem in particular I had to find a pattern which actually took a while because I couldn't find any relevance at first.