Problem Statement: This problem stated that there was a lattice polygon (a polygon whose vertices lie on the points of a square lattice) and we were to find the formula to find the area of a lattice polygons regardless of how many interior or boundary points there are for that polygon.
Process/Solution: For this problem we simply started out with drawing three lattice polygons on a piece of paper. We then found the boundary points, interior points, and the area of each polygon. Then we got a little bit more complex and had to draw 20 lattice polygons and find the boundary points, area, and interior points. We did this as a class so we could compare and share our data. once we finished finding those three questions we compared our data with polygons that had no interior points. We wrote our data on a white board and we had to graph our data because wit only two pieces of information (boundary points and area) we could make an x and y graph. the y axis is area and the x axis is boundary points. After we graphed our data we had to find/estimate our line of best fit and I estimated my line of best fit. We did this step because once you find the line of best fit you can find a formula using Y=MX+B. My formula was 1/2x-1. After we found the formula for 0 interior points different groups got paired wit different amount of interior points. I got 1 interior point so I made a graph for 1 interior point. after I made my graph I once more estimated my line of best fit and used the Y=MX+B to find the formula for 1 interior point. I came up with the formula Y=1x+1 and all the other kids got the same answer except with their number of interior points. At the end of the day our final formula for finding the area of a lattice polygon regardless of how many interior points or boundary points there are is Y=1/2x-1.