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

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?

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

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

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

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

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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

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

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

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?

Here's a simple way to make a Tangram without any measuring or ruling lines.

Can you fit the tangram pieces into the outline of Little Ming?

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

Can you fit the tangram pieces into the outline of these rabbits?

Can you fit the tangram pieces into the outline of this plaque design?

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

Can you fit the tangram pieces into the outlines of these clocks?

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

Can you fit the tangram pieces into the outline of this goat and giraffe?

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

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

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

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

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

Can you fit the tangram pieces into the outlines of the candle and sundial?

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?

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

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

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

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 ...

Can you fit the tangram pieces into the outline of the telescope and microscope?

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

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

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

Can you fit the tangram pieces into the outline of this sports car?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

Can you fit the tangram pieces into the outline of Little Fung at the table?

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

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

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

Reasoning about the number of matches needed to build squares that share their sides.

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 this telephone?

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Can you use the interactive to complete the tangrams in the shape of butterflies?

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?