Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
Can you work out which spinners were used to generate the frequency charts?
This interactivity invites you to make conjectures and explore probabilities of outcomes related to two independent events.
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?
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?
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over... You win if all your cards end up in the trays before you run out of cards in. . . .
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
A counter is placed in the bottom right hand corner of a grid. You toss a coin and move the star according to the following rules: ... What is the probability that you end up in the top left-hand. . . .
Use this animation to experiment with lotteries. Choose how many balls to match, how many are in the carousel, and how many draws to make at once.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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.
Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are 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.
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.
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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
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...
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
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.
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
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?
How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?
Work out how to light up the single light. What's the rule?
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
To avoid losing think of another very well known game where the patterns of play are similar.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
A collection of our favourite pictorial problems, one for each day of Advent.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
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. . . .
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.
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.
Here is a chance to play a fractions version of the classic Countdown Game.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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.
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. . . .
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 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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
The classic vector racing game brought to a screen near you.
A tool for generating random integers.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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 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.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.