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?

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

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

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?

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

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?

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

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?

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

Can you make the birds from the egg tangram?

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

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

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

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 fit the tangram pieces into the outline of Little Ming?

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?

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

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

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

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

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

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

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?

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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 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?

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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

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?

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

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.

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

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

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

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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

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?

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

Here's a simple way to make a Tangram without any measuring or ruling lines.

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?