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

The problem was posed this way to prompt students to ask, “Are they different if they are the same shape but in a different position on the geoboard?” Let us then define different to mean non-congruent. Any quadrilateral that is a translation, rotation, reflection, or glide reflection of another quadrilateral will not be considered different for the purpose of this problem.

Then the problem becomes, “How many different non-congruent quadrilaterals can be constructed on a 5 x 5 geoboard?” There are many. Just how many is for your students to determine. Below are some examples of types of quadrilaterals that a class of middle school students found.