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?

This resources contains a series of interactivities designed to support work on transformations 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?

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?

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

7 balls are shaken in a container. You win if the two blue balls touch. What is the probability of winning?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

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?

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?

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?

Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.

This set of resources for teachers offers interactive environments to support work on loci at Key Stage 4.

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.

Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.

Can you give the coordinates of the vertices of the fifth point in the patterm on this 3D grid?

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.

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.

How many different triangles can you make which consist of the centre point and two of the points on the edge? Can you work out each of their angles?

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

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?

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...

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.

Practise your diamond mining skills and your x,y coordination in this homage to Pacman.

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?

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?

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

The interactive diagram has two labelled points, A and B. It is designed to be used with the problem "Cushion Ball"

Help the bee to build a stack of blocks far enough to save his friend trapped in the tower.

Use Excel to explore multiplication of fractions.

This resource contains a range of problems and interactivities on the theme of coordinates in two and three dimensions.

Match pairs of cards so that they have equivalent ratios.

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

This resource contains interactive problems to support work on number sequences at Key Stage 4.

A tool for generating random integers.

Imagine picking up a bow and some arrows and attempting to hit the target a few times. Can you work out the settings for the sight that give you the best chance of gaining a high score?

A collection of our favourite pictorial problems, one for each day of Advent.

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.

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.

Rotate a copy of the trapezium about the centre of the longest side of the blue triangle to make a square. Find the area of the square and then derive a formula for the area of the trapezium.

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

The classic vector racing game brought to a screen near you.

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.

A game for 1 person to play on screen. Practise your number bonds whilst improving your memory

Here is a chance to play a fractions version of the classic Countdown Game.