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?
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?
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. . . .
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?
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?
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.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Use Excel to investigate the effect of translations around a number grid.
A group of interactive resources to support work on percentages Key Stage 4.
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.
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"
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 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. . . .
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.
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.
To avoid losing think of another very well known game where the patterns of play are similar.
An environment that enables you to investigate tessellations of regular polygons
Use an interactive Excel spreadsheet to explore number in this exciting game!
A tool for generating random integers.
A simple file for the Interactive whiteboard or PC screen, demonstrating equivalent fractions.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Use Excel to explore multiplication of fractions.
How good are you at finding the formula for a number pattern ?
An animation that helps you understand the game of Nim.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Here is a chance to play a fractions version of the classic Countdown Game.
A collection of our favourite pictorial problems, one for each day of Advent.
Can you find all the 4-ball shuffles?
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
An Excel spreadsheet with an investigation.
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to investigate factors and multiples.
Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?
Use an Excel spreadsheet to explore long multiplication.
Can you explain the strategy for winning this game with any target?
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 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.
How good are you at estimating angles?
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?
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?