Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

What happens when you try and fit the triomino pieces into these two grids?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

How many different rhythms can you make by putting two drums on the wheel?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

You'll need two dice to play this game against a partner. Will Incey Wincey make it to the top of the drain pipe or the bottom of the drain pipe first?

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.

An interactive activity for one to experiment with a tricky tessellation

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you find all the different ways of lining up these Cuisenaire rods?

Complete the squares - but be warned some are trickier than they look!

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

Move just three of the circles so that the triangle faces in the opposite direction.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Investigate the different sounds you can make by putting the owls and donkeys on the wheel.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

How many different triangles can you make on a circular pegboard that has nine pegs?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.