Can you recreate this Indian screen pattern? Can you make up similar patterns of your own?

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!

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?

Follow these instructions to make a five-pointed snowflake from a square of paper.

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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!

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

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

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.

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 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?

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

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

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

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

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

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

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?

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

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

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

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 ...

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?

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

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 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?

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

Here is a chance to create some Celtic knots and explore the mathematics behind them.

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.

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

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

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

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?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

How many models can you find which obey these rules?

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?

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