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?
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
The shortest path between any two points on a snooker table is the straight line between them but what if the ball must bounce off one wall, or 2 walls, or 3 walls?
Three equilateral triangles ABC, AYX and XZB are drawn with the
point X a moveable point on AB. The points P, Q and R are the
centres of the three triangles. What can you say about triangle
Take any parallelogram and draw squares on the sides of the
parallelogram. What can you prove about the quadrilateral formed by
joining the centres of these squares?
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?
With red and blue beads on a circular wire; 'put a red bead between
any two of the same colour and a blue between different colours
then remove the original beads'. Keep repeating this. What happens?
Six circles around a central circle make a flower. Watch the flower
as you change the radii in this circle packing. Prove that with the
given ratios of the radii the petals touch and fit perfectly.
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. . . .
A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?
Can you beat the computer in the challenging strategy game?
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.
Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
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. . . .
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Try this interactivity to familiarise yourself with the proof that the square root of 2 is irrational. Sort the steps of the proof into the correct order.
Make and prove a conjecture about the cyclic quadrilateral
inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
This is an interactivity in which you have to sort into the correct
order the steps in the proof of the formula for the sum of a
Use Excel to explore multiplication of fractions.
A metal puzzle which led to some mathematical questions.
Give your further pure mathematics skills a workout with this interactive and reusable set of activities.
A weekly challenge concerning prime numbers.
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Play a more cerebral countdown using complex numbers.
Play countdown with vectors.
Square It game for an adult and child. Can you come up with a way of always winning this game?
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
The classic vector racing game brought to a screen near you.
Play countdown with matrices
A tool for generating random integers.
A collection of our favourite pictorial problems, one for each day
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
How good are you at finding the formula for a number pattern ?
Can you set the logic gates so that the number of bulbs which are on is the same as the number of switches which are on?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Balancing interactivity with springs and weights.
Can you locate these values on this interactive logarithmic scale?