Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

What is the greatest number of squares you can make by overlapping three squares?

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

Can you visualise what shape this piece of paper will make when it is folded?

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Exploring and predicting folding, cutting and punching holes and making spirals.

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Make a cube out of straws and have a go at this practical challenge.

Can you fit the tangram pieces into the outline of this teacup?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Can you fit the tangram pieces into the outline of the house?

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Make a flower design using the same shape made out of different sizes of paper.

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

What shape is made when you fold using this crease pattern? Can you make a ring design?

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Can you fit the tangram pieces into the outlines of the convex shapes?

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Can you cut up a square in the way shown and make the pieces into a triangle?

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Can you fit the tangram pieces into the outlines of the people?

Can you fit the tangram pieces into the outline of Mah Ling?

Can you fit the tangram pieces into the outline of the butterfly?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the clock?

Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Can you fit the tangram pieces into the outline of the dragon?

Can you fit the tangram pieces into the outlines of the chairs?

Can you fit the tangram pieces into the outlines of the rabbits?

Can you fit the tangram pieces into the outline of Granma T?

Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Can you fit the tangram pieces into the outline of the playing piece?

Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Can you fit the tangram pieces into the outline of the child walking home from school?