Can you work through these direct proofs, using our interactive proof sorters?

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.

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 geometric series.

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...

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?

Prove Pythagoras' Theorem using enlargements and scale factors.

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?

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.

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.

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 PQR?

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.

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with the solutions x and y being integers? Read this article to find out.

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.

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.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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 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?

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?

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.

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.

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

A tool for generating random integers.

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.

P is a point on the circumference of a circle radius r which rolls, without slipping, inside a circle of radius 2r. What is the locus of P?

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.

Use Excel to practise adding and subtracting fractions.

Use Excel to explore multiplication of fractions.

Use an interactive Excel spreadsheet to investigate factors and multiples.

Can you beat Piggy in this simple dice game? Can you figure out Piggy's strategy, and is there a better one?

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

An Excel spreadsheet with an investigation.

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. . . .

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

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

A metal puzzle which led to some mathematical questions.

Practise your skills of proportional reasoning with this interactive haemocytometer.

How good are you at finding the formula for a number pattern ?

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

Can you locate these values on this interactive logarithmic scale?

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

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?

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?