Sort the houses in my street into different groups. Can you do it in any other ways?

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

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

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!

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

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

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?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

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

Can you complete this jigsaw of the multiplication square?

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

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

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

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

An environment which simulates working with Cuisenaire rods.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

If you have only four weights, where could you place them in order to balance this equaliser?

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?

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation

Try out the lottery that is played in a far-away land. What is the chance of winning?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

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?

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

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

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

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?

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. . . .

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Here is a chance to play a version of the classic Countdown Game.

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

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?