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

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?

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?

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

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

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

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

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?

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

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?

Make an equilateral triangle by folding paper and use it to make patterns of your own.

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

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?

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?

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?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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.

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

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?

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

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

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?

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?

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

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

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?

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

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

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?

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.

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?

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

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?

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?

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.

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 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?

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?

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

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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?

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