Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
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. . . .
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Triangle ABC has equilateral triangles drawn on its edges. Points P, Q and R are the centres of the equilateral triangles. What can you prove about the triangle PQR?
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?
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.
A group of interactive resources to support work on percentages Key Stage 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.
Show that for any triangle it is always possible to construct 3 touching circles with centres at the vertices. Is it possible to construct touching circles centred at the vertices of any polygon?
To avoid losing think of another very well known game where the patterns of play are similar.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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 give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Use Excel to explore multiplication of fractions.
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.
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Match pairs of cards so that they have equivalent ratios.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
An environment that enables you to investigate tessellations of regular polygons
Use Excel to investigate the effect of translations around a number grid.
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
A tool for generating random integers.
Use an interactive Excel spreadsheet to explore number in this exciting game!
Can you find all the 4-ball shuffles?
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.
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
A collection of our favourite pictorial problems, one for each day of Advent.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
An animation that helps you understand the game of Nim.
How good are you at finding the formula for a number pattern ?
A java applet that takes you through the steps needed to solve a Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Use an interactive Excel spreadsheet to investigate factors and multiples.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
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?
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.
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.
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.
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.