John McCormick
11/4/14
Count The Pegs
Problem Statement:
3 students are attempting to find out formulas for polygons, Freddie has come up with one. Sally has also found an equation. Freddie’s only works on squares, rectangles. Sally’s only works on squares rectangles and diamonds. Frashy has come up with a super formula that works for all simple polygons.
Process:
Freddie :
The way I came up with freddies formula was. When I noticed we could just do
(L x W) x B. Because we were looking at squares and rectangles. The B stands for boards or rather the number of squares freddie has. EX: Square with a side of 4 and there is 3 of them. 4x4=16x3=48.
Sally:
If you know sally only has 4 pegs to work with then you know she can only create a square, rectangle or a diamond. Which would mean the area can only be 1 every time. Unless she has multiple different shapes but to solve in that case all you have to do is add how many shapes she has. EX: 3 shapes = 1 + 1 + 1 = 3 units.
Frashy:
First off to use this equation (Pick’s theorem) you need to know two definitions. The number of pegs on the boundary (the number of pegs on the outside) and the interior number of pegs. You can use this equation (A = i + B/2 - 1) to solve find the area of any simple polygon no matter size or shape.
People
Polygons
Formula
Freddie
Squares and Rectangles
(L x w) x B = A
Sally
Squares Rectangles and
diamonds
1
Frashy
Everything
A= i + B/2 - 1
Solution:
Here are my final formulas
People
Polygons
Formula
Freddie
Squares and Rectangles
(L x w) x B = A
Sally
Squares Rectangles and
diamonds
1
Frashy
Everything
A= i + B/2 - 1
Reflection:
I used persistence for most of this write up / lab. Finding frashy's formula was the one that took me quite a while to find (Along with help from friends and classmates)
11/4/14
Count The Pegs
Problem Statement:
3 students are attempting to find out formulas for polygons, Freddie has come up with one. Sally has also found an equation. Freddie’s only works on squares, rectangles. Sally’s only works on squares rectangles and diamonds. Frashy has come up with a super formula that works for all simple polygons.
Process:
Freddie :
The way I came up with freddies formula was. When I noticed we could just do
(L x W) x B. Because we were looking at squares and rectangles. The B stands for boards or rather the number of squares freddie has. EX: Square with a side of 4 and there is 3 of them. 4x4=16x3=48.
Sally:
If you know sally only has 4 pegs to work with then you know she can only create a square, rectangle or a diamond. Which would mean the area can only be 1 every time. Unless she has multiple different shapes but to solve in that case all you have to do is add how many shapes she has. EX: 3 shapes = 1 + 1 + 1 = 3 units.
Frashy:
First off to use this equation (Pick’s theorem) you need to know two definitions. The number of pegs on the boundary (the number of pegs on the outside) and the interior number of pegs. You can use this equation (A = i + B/2 - 1) to solve find the area of any simple polygon no matter size or shape.
People
Polygons
Formula
Freddie
Squares and Rectangles
(L x w) x B = A
Sally
Squares Rectangles and
diamonds
1
Frashy
Everything
A= i + B/2 - 1
Solution:
Here are my final formulas
People
Polygons
Formula
Freddie
Squares and Rectangles
(L x w) x B = A
Sally
Squares Rectangles and
diamonds
1
Frashy
Everything
A= i + B/2 - 1
Reflection:
I used persistence for most of this write up / lab. Finding frashy's formula was the one that took me quite a while to find (Along with help from friends and classmates)