Geoboards can be used to explore various concepts in geometry such as area and perimeter and the characteristics of triangles and other polygons.
The TI-Nspire document provides virtual geoboards that can be used either by students on the handheld device or by a teacher using the software projected onto a screen.
There are two types of geoboard in the file - a square board and a circular board. Each contains a slider that can be used to adjust the size of the grid.
a) The derivation of Pick's Theorem is a popular investigation that can be carried out on the square geoboard. For various polygons the enclosed area, the number of points on the boundary and the number inside, can be tabulated on a Lists & Spreadsheets page.
b) For the circular geoboard you could challenge students to create a right-angled triangle. Under what conditions is this possible?