Cutting the Pie
For this POW we were required to find the different amount of pieces in a pie when you cut into it a certain amount of times. This is the problem statement:
1. Find the largest number of pieces you can get from four cuts and from five cuts. Put those numbers into the table.
2.a. Try to find ta pattern describing what is happening in the table.
b. Use your pattern to find the largest possible number of pieces from ten cuts.
c. Try to explain why this pattern is occurring.
3. Try to find a rule for the In an Out table. If you used a variable for that input, how could you write the output as a formula in terms of that variable?
During the process of creating pies with a certain amount of cuts was hard, specially trying to put all your data together and trying to find a pattern within a table was pretty difficult. In my In an Out Table I started from 1 and went all the way up to 6. Below is my data table.
1. Find the largest number of pieces you can get from four cuts and from five cuts. Put those numbers into the table.
2.a. Try to find ta pattern describing what is happening in the table.
b. Use your pattern to find the largest possible number of pieces from ten cuts.
c. Try to explain why this pattern is occurring.
3. Try to find a rule for the In an Out table. If you used a variable for that input, how could you write the output as a formula in terms of that variable?
During the process of creating pies with a certain amount of cuts was hard, specially trying to put all your data together and trying to find a pattern within a table was pretty difficult. In my In an Out Table I started from 1 and went all the way up to 6. Below is my data table.
With this data table I found a pattern. I found that starting from the beginning, every time a cut goes up, the difference of each pieces goes up by one. An example of this is from 4-2=2, 7-4=3, 11-7=4 so the pattern there is that it keeps going up by one and if your creating these pies and cutting them you can rely on this table and it'll give you the most amount of pieces possible for each cut given. This table was what I used through out the entire problem. For each answer I got throughout each piece I checked with my table group to see if they got anything higher and if they did I would go over and try again until I got the most of what I knew of. I think throughout this POW I did good because I kept trying to figure out what the highest possibility of each cut/pieces was. The most I got for 10 cuts was 41 pieces. I attempted this twice so that I can see if I get something different but each time I got 41 pieces. The formula I found with my data table information I found that..=