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

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

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

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

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

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

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

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?

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

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

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 ...

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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?

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?

Can you arrange the shapes in a chain so that each one shares a face (or faces) that are the same shape as the one that follows it?

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.

Can you work out what is wrong with the cogs on a UK 2 pound coin?

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

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

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.

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

Which of these dice are right-handed and which are left-handed?

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

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.

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

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 outlines of Mah Ling and Chi Wing?

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?

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

Can you fit the tangram pieces into the silhouette of the junk?

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

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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

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 people?

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

Have a look at these photos of different fruit. How many do you see? How did you count?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

An activity centred around observations of dots and how we visualise number arrangement patterns.

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

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

Can you logically construct these silhouettes using the tangram pieces?

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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