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?

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

Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

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.

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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

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

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

Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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

What is the relationship between the angle at the centre and the angles at the circumference, for angles which stand on the same arc? Can you prove it?

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

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?

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

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

An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.

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

Match the cards of the same value.

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.

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Can you find triangles on a 9-point circle? Can you work out their angles?

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. . . .

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

Find the frequency distribution for ordinary English, and use it to help you crack the code.

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.

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?

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

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...

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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

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

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.

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

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?

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?

Show how this pentagonal tile can be used to tile the plane and describe the transformations which map this pentagon to its images in the tiling.

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

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

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 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. . . .

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Start with any number of counters in any number of piles. 2 players take it in turns to remove any number of counters from a single pile. The winner is the player to take the last counter.

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.