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?
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. . . .
How good are you at finding the formula for a number pattern ?
Prove Pythagoras' Theorem using enlargements and scale factors.
Can you discover whether this is a fair game?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This is an interactivity in which you have to sort the steps in the completion of the square into the correct order to prove the formula for the solutions of quadratic equations.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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. . . .
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.
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
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.
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 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. . . .
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?
To avoid losing think of another very well known game where the patterns of play are similar.
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?
Can you explain the strategy for winning this game with any 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.
An animation that helps you understand the game of Nim.
7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
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.
Can you find a way to turn a rectangle into a square?
This set of resources for teachers offers interactive environments to support work on graphical interpretation at Key Stage 4.
An environment that simulates a protractor carrying a right- angled triangle of unit hypotenuse.
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?
Six balls of various colours are randomly shaken into a trianglular arrangement. What is the probability of having at least one red in the corner?
Mo has left, but Meg is still experimenting. Use the interactivity to help you find out how she can alter her pouch of marbles and still keep the two pouches balanced.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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 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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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.
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?
Meg and Mo still need to hang their marbles so that they balance, but this time the constraints are different. Use the interactivity to experiment and find out what they need to do.
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?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.
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?