Can you make the birds from the egg tangram?

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

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

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

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?

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.

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

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?

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

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

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?

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

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 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?

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?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

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.

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

How many models can you find which obey these rules?

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

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

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

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?

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

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?

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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

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 ...

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

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

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?

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?

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

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

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?

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?

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?

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

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

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?

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?