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?

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

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

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?

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?

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?

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

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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

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 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?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

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

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

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

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

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

Can you make the birds from the egg tangram?

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?

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?

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

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 practical challenges are all about making a 'tray' and covering it with paper.

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

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

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

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

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

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

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

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

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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

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

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

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

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.

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