
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.

Which spinners were used to generate these frequency charts?

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

Identical discs are flipped in the air. You win if all of the faces show the same colour. Can you calculate the probability of winning with n discs?

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?

Which of these sets of numbered balls will give the most even totals when two balls are chosen from them?

Players all start with zero points, they take turns to throw the dice as many times as they like, adding the total at each throw to their cumulative total.

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

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

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?

Place the ten odd numbers less than 20 in the grid so that at least four rectangles can be drawn around groups of four odd numbers whose sum is 34.

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the chairs?

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.

Can you fit the tangram pieces into the outlines of these clocks?

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.

Fifteen is a game for two players that you can play anywhere, anytime. Players take it in turns to select a number from 1 to 9. The aim is to choose 3 numbers that total 15.

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. . . .

Can you fit the tangram pieces into the outline of Little Fung at the table?

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?

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

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 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?

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

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.

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

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.

Can you fit the tangram pieces into the outline of this telephone?

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.

Can you fit the tangram pieces into the outlines of these people?

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.

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?

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

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

A game for two or more players that uses a knowledge of measuring tools. Spin the spinner and identify which jobs can be done with the measuring tool shown.

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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

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 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?

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?

An interactive activity for one to experiment with a tricky tessellation

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

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.

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 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

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

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?

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.