This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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?
How many triangles can you make on the 3 by 3 pegboard?
This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.
Can you find all the different triangles on these peg boards, and
find their angles?
How many different triangles can you make on a circular pegboard that has nine pegs?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
A generic circular pegboard resource.
How would you move the bands on the pegboard to alter these shapes?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the interactivity to investigate what kinds of triangles can be
drawn on peg boards with different numbers of pegs.
Polygons drawn on square dotty paper have dots on their perimeter
(p) and often internal (i) ones as well. Find a relationship
between p, i and the area of the polygons.
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
The diagram shows a 5 by 5 geoboard with 25 pins set out in a square array. Squares are made by stretching rubber bands round specific pins. What is the total number of squares that can be made on a. . . .
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
This article for teachers explains why geoboards are such an invaluable resource and introduces several tasks which make use of them.
Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?