Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its speed at each stage.
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 opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
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...
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects its vertical and horizontal movement at each stage.
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 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. . . .
Can you find a way to turn a rectangle into a square?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
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?
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.
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Use Excel to explore multiplication of fractions.
The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
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.
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.
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.
To avoid losing think of another very well known game where the patterns of play are similar.
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.
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. . . .
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
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. . . .
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
Prove Pythagoras' Theorem using enlargements and scale factors.
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?
Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?
A tool for generating random integers.
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 Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
Seven balls are shaken. You win if the two blue balls end up touching. What is the probability of winning?
Here is a chance to play a version of the classic Countdown Game.
Here is a chance to play a fractions version of the classic Countdown Game.
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
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?
Six balls are shaken. You win if at least one red ball ends in a corner. What is the probability of winning?
The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
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.