a. Making a geoboard

Method of construction:

Make a template or a master copy which you can use to make your geoboard. Leave about 3 cm between each nail:

b. Making triangles on your geoboard

Note about different triangles: The dotted triangle (above) is not different. It is the same, but rotated!

c. Making quadrilaterals on your geoboard

Different quadrilaterals: The dotted quadrilateral (opposite) is not different. It is the same, but rotated.

You don’t need elastic bands – you can draw your shapes on the geoboards (below) with a pencil.

All the different triangles possible on a 9-pin geoboard are recorded below. Now try to see how many different quadrilaterals you can make (some are done for you):

**Note:** What do we mean when we say, *different?*

Triangles are not different if they have been rotated or reflected. If two shapes are congruent they are not different; if two shapes are different they are not congruent.

c. Making quadrilaterals on the geoboard

Make many **different** quadrilaterals as you can on your geoboard? As before, record you quadrilaterals as you make them.

**Clue:** You can make 16 different quadrilaterals on the 9-pin geoboard.

**d. Looking at the shapes you have recorded**

After recording all the different triangles and quadrilaterals, it is time for you to look at some of the shapes you have made and look at their properties. Here are a few questions for you to ask yourself or your friends:

**Questions:**

**e. Look at the area of the shapes**

You can find out the area of the various shapes you have made on the geoboard. The square unit is shown and this can be the base unit for working out the area of other shapes:

f. Artistic shapes

You can learn a lot about mathematics through your artwork. The geoboard can become a great artistic experimental ‘drawing board’! Use several elastic bands to make artistic patterns on the geoboard. You can draw geoboard art on dotted paper without actually using a geoboard:

A Tangram is an ancient Chinese puzzle made from a square. The Tangram is also called *‘The Seven Pieces of Cleverness’, ‘The Wisdom Board’, ‘Chinese Puzzle’* or *‘The Seven-Board of Cunning’*.

a. Making a Tangram

Find out about: The differences between; the same, different, similar and congruent.

b. Are you cleverer? Beat the seven ‘Pieces of Cleverness’

c. Making pictures

Try making your own pictures with the tangram shapes: