If you were given a pie what is the maximum number of pieces you can produce from 4, 5, and 10 cuts? Keep in mind, that the slices do not have to be the same size and the cuts do not necessarily have to go through the center of the pie, but the cuts do have to be straight and go all the way across the pie. Include any diagrams you used to find the solution such as an In-Out table, or any patterns you found.

Process-

The first thing I did to try to find my solution was to finish the In-Out table given, which already told us the maximum number of pieces that could be made with 1, 2 and 3 cuts. So I drew two circles, and drew in four cuts in one and five cuts in another to find the maximum number of pieces that could be produced. After several circles for each I found that the maximum number of pieces you can produce from four cuts is 11, and the maximum number of pieces for five cuts is 15. In-Out Table

In-X (Number of cuts)Out-Y (Maximum # of pieces)
12
24
37
411
516

So instead of trying to do the same thing t find out the maximum number of pieces for 10 cuts, I started looking for a pattern. I found that the difference between four and two is 2, the difference between seven and four is 3, the difference between eleven and seven is 4, and finally the difference between sixteen and eleven is 5. Based, on these results from my In-Out table I found out that one more value is added to the previous addend to come up with the next value. However, this wouldn't work that well because if I was to find the maximum number of pieces that can be produced from 50 cuts I would have to do a lot of tedious work to finally reach 50 cuts. This is because the independent variable is the number of cuts, not the maximum number of pieces. Finding the pattern was easy, but the challenging part was finding the formula. I tried finding something that had to do with the way the actual pie was cut, like how...

...five bales of hay. When the bales of hay are weighed, they are weighed in pairs of two. When weighed, they were weighed in all possible pairs of two, like so: bales 1 &2, bales 1 &3, bales 1 & When weighed, they were weighed in all possible pairs of two, like so: bales 1&2, bales 1&3, bales 1&4, bales 1&5, bales 2&3, bales 2&4, bales 2&5, bales 3&4, bales 3&5, and bales 4&5. There are also 10 different weights and they are:...

...POW 8
Problem Statement-
For this POW, our task was to find the best formula for finding the area of any polygon that is formed on a geoboard. In order to do this, there are two formulas given to help you. One tells how to get the area of a polygon based on the number of pegs on the boundary. This works as an In-Out table, where In is the amount of pegs on the boundary, and Out is the area. The other formula tells how to get the area by having a polygon...

...quickly.
For Freddie I drew a 3 column T-Table, with a drawing of the figure, the number of Pegs (in), and the Area (out). I looked for a pattern between the in and the out, and quickly found one that made sense, and I worked it into a formula. I got X/2-1=Y. Where X is IN (number of pegs) and Y is OUT (Area). This works in all shapes with no interior pegs, like Freddie described. I attached this T-Table.
For Sally I followed my luck of the 3 column T-Table, and drew another...

...IMP2POW 3: Divisor Counting.
I. Problem statement:
This POW is all about finding information and patterns about the way divisors of certain numbers are found and expressed. In this POW when we talk about divisors we usually are counting the number of divisors that a number has. The divisor is a number that a number can be divided by, of course every number is divisible by every other number but in these problems we are...

...Pow2
Problem Statement:
There’s a standard 8 x 8 checkerboard made up by 64 small squares. Each square is able to combine with others squares to make other squares of different sizes. Our job is to find out how many squares there’s in total. Once you get all the number of squares get all the number of squares and feel confident with your answer you next explain how to find the...

...each part of the problem. When you know that one thing means you go on to the next part. When you figure out what that means you have to see how the two statements are related. If they are related then you can deduce a conclusion that makes sense.
2. Here are my conclusions for the 6 problems on page 7.
1. a. No medicine is nice
b. Senna is a medicine
Here I deduced that Senna is not a nice medicine. I think this because the first statement says that “no...

...“A Sticky Gum Problem” POW 4
Problem statement:
The next scenario is very similar. In this one, Ms. Hernandez passed a different gumball machine the next day with three different colors Once again her twins each want a gumball of the same color, and each gumball is still one cent. What is the most amount of money that Ms. Hernandez would have to spend in order to get each of her daughters the same color gumball?
In the last scenario, Mr. Hodges and his triplets pass...