Problem Statement:
Freddie Short has a formula to find the area of any polygon on a geoboard that has no pegs on the inside. His formula is like a rule for an in-out table in which the In is the number of pegs on the boundary and the Out is the area of the figure. Sally Shorter says she has a shortcut for any geoboard polygon with exactly four pegs on the boundary. All you have to tell her is how many pegs it has in the interior, and she can use her formula to find the area immediately. Frashy Shortest says she has the best formula yet. If you make any polygon on the geoboard and tell her both the number of pegs on the interior and the number of pegs on the boundary, her formula will give you the area.
Process:
To come up with the three different formulas for Freddie, Sally, and Frashy I drew polygons based on each one of their requirements. Freddie wanted no pegs in the interior, Sally wanted 4 pegs on the outside, and Frashy wanted any number of pegs on the interior and exterior. Then I put the values the different people requested into in and out tables, looked at the results and came up with Freddie and Sally's formulas.
Solution:
The formulas that I started out with were y = x/2 -1 for Freddie, and y = x + 1 for Sally. I got these because I compared in and out tables and started to come up with different equations. After a lot of trial and error I ended up getting to the equation of A = (Y/2) - 1 + X
Evaluation:
What did you learn from it? I learned how to combine formulas to create one “super formula”Describe one Habit of a Mathematician that you used? Patterns
Did you enjoy working on it? I didn’t really like working on this problem.
Was it too hard or too easy? I personally found this problem challenging. I understood what I was supposed to be doing but I still thought it was hard and I ended up getting help from my peers to figure it out.
Freddie Short has a formula to find the area of any polygon on a geoboard that has no pegs on the inside. His formula is like a rule for an in-out table in which the In is the number of pegs on the boundary and the Out is the area of the figure. Sally Shorter says she has a shortcut for any geoboard polygon with exactly four pegs on the boundary. All you have to tell her is how many pegs it has in the interior, and she can use her formula to find the area immediately. Frashy Shortest says she has the best formula yet. If you make any polygon on the geoboard and tell her both the number of pegs on the interior and the number of pegs on the boundary, her formula will give you the area.
Process:
To come up with the three different formulas for Freddie, Sally, and Frashy I drew polygons based on each one of their requirements. Freddie wanted no pegs in the interior, Sally wanted 4 pegs on the outside, and Frashy wanted any number of pegs on the interior and exterior. Then I put the values the different people requested into in and out tables, looked at the results and came up with Freddie and Sally's formulas.
Solution:
The formulas that I started out with were y = x/2 -1 for Freddie, and y = x + 1 for Sally. I got these because I compared in and out tables and started to come up with different equations. After a lot of trial and error I ended up getting to the equation of A = (Y/2) - 1 + X
Evaluation:
What did you learn from it? I learned how to combine formulas to create one “super formula”Describe one Habit of a Mathematician that you used? Patterns
Did you enjoy working on it? I didn’t really like working on this problem.
Was it too hard or too easy? I personally found this problem challenging. I understood what I was supposed to be doing but I still thought it was hard and I ended up getting help from my peers to figure it out.