Problem to Ponder

Geoboard figures area 2
Geoboard figures area 2

The March 2012 installment of NCTM's "Problem to Ponder" raises the question:

How many different polygons of area 2 can you construct on a 5 x 5 geoboard?

To make the problem accessible to a larger variety of grade levels, teachers might adapt the problem by first limiting the options to triangles; then to quadrilaterals, etc. Something to consider is how to determine whether two shapes are "different".

Visit the website below to see how NCTM poses the problem. Suggestions are provided for defining "different" but determining the number of possibilities is up to you and your students!