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

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

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.

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

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?

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?

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?

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

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?

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?

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?

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

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

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

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

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

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?

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?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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?

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

How many models can you find which obey these rules?

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

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.

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

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?

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

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?

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

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?

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

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

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?

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Can you make the birds from the egg tangram?

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.

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?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

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?

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

If you'd like to know more about Primary Maths Masterclasses, this is the package to read! Find out about current groups in your region or how to set up your own.

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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