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

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

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

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

Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?

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.

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?

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

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

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 complete this jigsaw of the multiplication square?

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

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?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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

An interactive activity for one to experiment with a tricky tessellation

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. . . .

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

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

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

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

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

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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.

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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

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

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

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....?

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.

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.

Two engines, at opposite ends of a single track railway line, set off towards one another just as a fly, sitting on the front of one of the engines, sets off flying along the railway line...

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

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?

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?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

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

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?

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

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

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?

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 and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .

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?

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