This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

How would you move the bands on the pegboard to alter these shapes?

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

Take it in turns to make a triangle on the pegboard. Can you block your opponent?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Can you find all the different triangles on these peg boards, and find their angles?

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

How many different triangles can you make on a circular pegboard that has nine pegs?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Can you split each of the shapes below in half so that the two parts are exactly the same?

This article for teachers explains why geoboards are such an invaluable resource and introduces several tasks which make use of them.