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 with exactly four pegs on the boundary. All you do is tell her how many pegs are on the inside. Using her formula, she can give you the area immediately. Using these two formulas for reference, we have to find a formula that anyone can use to find the area of any polygon by knowing the number of pegs on the boundary and interior.

Process-
The first two equations by Freddie and Sally were a preparation for the final, building up the information in order to find the "superformula".

For Freddie's equation, I drew an In-Out table, with the number of pegs on the boundary for the In/x value, and the area of the polygon for the Out/y value. With this table set up, I made some different polygons on geo-paper (attached), and plugged them into the table. I found the area for all of them by looking at the figure. However, just looking at the figure was not very accurate, so I looked for a pattern between the in and the out, and quickly found a formula that made sense, and I worked with it until I got a formula. This formula was x/2-1=y. This works in all shapes with no interior pegs, as the problem said. (In-Out table attached)

For Sally, I saw that another In-Out table would work the best, and drew one with the same guidelines. With this set up, I made some polygons on geo-paper (attached). I found that the In/x value is the number of pegs on the interior, and the Out/y value is the area. I then filled the table with a few values from the geo-paper, and saw a pattern that soon led to a...

...Problem Statement
My task was to find 3 equations, that would give me an answer, if I had certain information. The first was to find one that if you knew that there were four pegs on the boundary, and none on the interior, you could get the area. The second was if you knew that there were 4 pegs on the boundary, and you knew how many were on the interior, you could get the area. And last, if you had the number on the interior, and the number on the boundary, you...

...Justcount the Pegs
Freddie Short has a new shortcut to find the area of any polygon on the geoboard that has no pegs on the interior. His formula is like a rule for an In-Out in which the In is the number of pegs on the boundary and out is the area of the figure.
Sally Shorter has a shortcut for any geoboard polygon with exactly four pegs on the boundary. All you have to tell her is how many...

...Jordan Hunt P.3
POW Write Up; JustCount the Pegs
Problem Statement:
For the POW: JustCount the Pegs, I had to try and find the best formula possible for finding the area of any polygon on a geoboard. There are 3 different formulas you have to find. The first two are formulas that will combine together and help you find the best or “superformula”. In order to find the first...

...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...

...POW 17- Cutting the Pie
Problem Statement-
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-...

...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...

...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...

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