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.
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.
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
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
How good are you at finding the formula for a number pattern ?
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
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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.
Here is a chance to play a version of the classic Countdown Game.
Can you discover whether this is a fair game?
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
To avoid losing think of another very well known game where the
patterns of play are similar.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Have you seen this way of doing multiplication ?
Find the vertices of a pentagon given the midpoints of its sides.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
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?
You can move the 4 pieces of the jigsaw and fit them into both
outlines. Explain what has happened to the missing one unit of
Use Excel to explore multiplication of fractions.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Prove Pythagoras Theorem using enlargements and scale factors.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Match the cards of the same value.
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.
Practise your skills of proportional reasoning with this interactive haemocytometer.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Cellular is an animation that helps you make geometric sequences
composed of square cells.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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?
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Can you beat the computer in the challenging strategy game?
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
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?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
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.
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.
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.
Investigate how logic gates work in circuits.
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?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .