Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

A game in which players take it in turns to choose a number. Can you block your opponent?

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?

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

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?

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.

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

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?

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?

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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

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 make dice stairs using the rules stated? How do you know you have all the possible stairs?

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

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?

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?

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?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

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?

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

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

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

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

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

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?

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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

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?

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?

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?

Explore the triangles that can be made with seven sticks of the same length.

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

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

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?

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

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?

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

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

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

Can you make the birds from the egg tangram?

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

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

A brief video looking at how you can sometimes use symmetry to distinguish knots. Can you use this idea to investigate the differences between the granny knot and the reef knot?

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

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?