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.

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

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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

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?

Can you explain the strategy for winning this game with any target?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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!

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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?

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

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

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?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

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?

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

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

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?

Exchange the positions of the two sets of counters in the least possible number of moves

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

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

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

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

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

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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 locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.

Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.

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

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

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

An interactive activity for one to experiment with a tricky tessellation

A game for 2 players. Can be played online. One player has 1 red counter, the other has 4 blue. The red counter needs to reach the other side, and the blue needs to trap the red.

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?

Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?