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

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

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

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?

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

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

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?

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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?

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

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

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

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

In this activity focusing on capacity, you will need a collection of different jars and bottles.

For this activity which explores capacity, you will need to collect some bottles and jars.

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

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

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

These pictures show squares split into halves. Can you find other ways?

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

You have a set of the digits from 0 – 9. Can you arrange these in the 5 boxes to make two-digit numbers as close to the targets as possible?

Did you know mazes tell stories? Find out more about mazes and make one of your own.

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

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

Can you make five differently sized squares from the tangram pieces?

Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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

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?

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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?

The class were playing a maths game using interlocking cubes. Can you help them record what happened?

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

What do these two triangles have in common? How are they related?

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!

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?

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

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

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

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

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

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?

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

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

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?

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