An environment which simulates working with Cuisenaire rods.

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

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

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

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

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....?

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

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

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

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?

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?

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!

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

Can you complete this jigsaw of the multiplication square?

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

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?

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?

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?

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?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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

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

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

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

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

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

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

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

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

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

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

An interactive activity for one to experiment with a tricky tessellation

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.

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

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

Can you find all the different triangles on these peg boards, and find their angles?

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