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

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?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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?

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

Use the tangram pieces to make our pictures, or to design some of your own!

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

How can you make an angle of 60 degrees by folding a sheet of paper twice?

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 make the birds from the egg tangram?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

A game to make and play based on the number line.

Here is a version of the game 'Happy Families' for you to make and play.

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?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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 ...

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.

Can you each work out what shape you have part of on your card? What will the rest of it look like?

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

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?

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

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

Delight your friends with this cunning trick! Can you explain how it works?

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

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

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

An activity making various patterns with 2 x 1 rectangular tiles.

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?

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

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

These practical challenges are all about making a 'tray' and covering it with paper.

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.