Can you make a 3x3 cube with these shapes made from small cubes?

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?

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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 outlines of the chairs?

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 outlines of the lobster, yacht and cyclist?

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!

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

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

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

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

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

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

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

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

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

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

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

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

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?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Exchange the positions of the two sets of counters in the least possible number of moves

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 this brazier for roasting chestnuts?

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

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

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

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

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?

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

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

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

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?

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

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

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

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

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

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

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

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

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

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

Can you find a way of counting the spheres in these arrangements?