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 could get the area.

Process
The first two equations, were a preparation for the final, building up towards the complete idea. This helped, because I could complete the first two pretty 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 with the same guidelines. The figure, the interior pegs (in), and the area (out). After I filled in a few figures, and their properties, I noticed a pattern, and not long after, a formula, which worked for them. It was X+1=Y. This T-Table is also attached.

Now...the next was not so easy. Frashy's required a long thought process, and several hours thinking it over, logically. I thought that this next equation would be a combination of the two, it would have to incorporate what I had found out from both of the above. Especially the first. So I thought to myself what this equation, or formula, would have to include. And realized there wasn't 1 variable, but 2. Because it has the variable from the first, and the second problem. 1: The number of pegs on the border, and 2: The number of pegs on the interior. So this means that there are 2 IN's....

...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...

...“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...

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