Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
Here is a chance to play a version of the classic Countdown Game.
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?
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. . . .
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?
Work out how to light up the single light. What's the rule?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
A collection of resources to support work on Factors and Multiples at Secondary level.
Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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 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 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?
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.
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?
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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.
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.
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.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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. . . .
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.
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 beat the computer in the challenging strategy game?
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...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you find all the 4-ball shuffles?
Match the cards of the same value.
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?
Could games evolve by natural selection? Take part in this web experiment to find out!
Can you coach your rowing eight to win?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Place a red counter in the top left corner of a 4x4 array, which is covered by 14 other smaller counters, leaving a gap in the bottom right hand corner (HOME). What is the smallest number of moves. . . .
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 locate the lost giraffe? Input coordinates to help you search and find the giraffe in the fewest guesses.
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. . . .
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.
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?