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?

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

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 when this piece of paper is folded up using the crease pattern shown?

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

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

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?

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

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

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

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

Can you make the birds from the egg tangram?

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

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

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

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?

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

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

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?

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?

Can you put these shapes in order of size? Start with the smallest.

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?

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

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

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

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

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

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

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

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

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

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

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

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?

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.

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

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?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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

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 ...

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

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

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

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