We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?

Can you make the birds from the egg tangram?

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

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

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

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

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?

Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?

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

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

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

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?

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

Can you deduce the pattern that has been used to lay out these bottle tops?

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

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?

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!

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

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

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

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

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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 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?

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

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

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

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

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

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?

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.

This practical activity challenges you to create symmetrical designs by cutting a square into strips.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

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?

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

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?

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

Can you split each of the shapes below in half so that the two parts are exactly the same?

A game in which players take it in turns to choose a number. Can you block your opponent?

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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

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 ...