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 use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you be the first to complete a row of three?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
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?
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.
A game in which players take it in turns to choose a number. Can you block your opponent?
How good are you at estimating angles?
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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.
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 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. . . .
To avoid losing think of another very well known game where the patterns of play are similar.
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 about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
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. . . .
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.
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. . . .
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
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. . . .
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
Use Excel to explore multiplication of fractions.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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?
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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.
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
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.
Investigate how logic gates work in circuits.
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?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
Can you coach your rowing eight to win?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
An animation that helps you understand the game of Nim.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Can you explain the strategy for winning this game with any target?
A tool for generating random integers.
A collection of our favourite pictorial problems, one for each day of Advent.
Here is a chance to play a version of the classic Countdown Game.
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?