Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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.
Can you discover whether this is a fair game?
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.
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
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Match pairs of cards so that they have equivalent ratios.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Use Excel to practise adding and subtracting fractions.
Use Excel to investigate the effect of translations around a number grid.
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 be the first to complete a row of three?
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 simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
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?
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?
Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?
Use an Excel spreadsheet to explore long multiplication.
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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. . . .
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.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Match the cards of the same value.
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?
An environment that enables you to investigate tessellations of regular polygons
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.
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.
An Excel spreadsheet with an investigation.
Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.
A collection of our favourite pictorial problems, one for each day of Advent.
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. . . .
Use Excel to explore multiplication of fractions.
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.
Use an interactive Excel spreadsheet to investigate factors and multiples.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Can you beat the computer in the challenging strategy game?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Can you find all the 4-ball shuffles?
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?
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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.
Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A train building game for 2 players.
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?
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?