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

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

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?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

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

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.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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

An interactive activity for one to experiment with a tricky tessellation

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

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. . . .

Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Train game for an adult and child. Who will be the first to make the train?

Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.

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

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

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?

Use the interactivity or play this dice game yourself. How could you make it fair?

Work out the fractions to match the cards with the same amount of money.

Meg and Mo need to hang their marbles so that they balance. Use the interactivity to experiment and find out what they need to do.

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?

Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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?