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
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
Can you work through these direct proofs, using our interactive
Can you discover whether this is a fair game?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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
Prove Pythagoras Theorem using enlargements and scale factors.
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
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.
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 ringing hand bells for yourself with interactive versions of
Diagram 2 (Plain Hunt Minimus) and Diagram 3 described in the
article 'Ding Dong Bell'.
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
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?
Investigate how logic gates work in circuits.
Find the vertices of a pentagon given the midpoints of its sides.
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.
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?
Match the cards of the same value.
Use Excel to explore multiplication of fractions.
Here is a chance to play a fractions version of the classic
Cellular is an animation that helps you make geometric sequences
composed of square cells.
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. . . .
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.
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.
Re-arrange the pieces of the puzzle to form a rectangle and then to
form an equilateral triangle. Calculate the angles and lengths.
A tool for generating random integers.
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?
How good are you at finding the formula for a number pattern ?
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 collection of our favourite pictorial problems, one for each day
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?
A metal puzzle which led to some mathematical questions.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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 loci at Key Stage 4.
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. . . .
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?
Practise your skills of proportional reasoning with this interactive haemocytometer.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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 locate these values on this interactive logarithmic scale?
Discover a handy way to describe reorderings and solve our anagram
in the process.
Use an interactive Excel spreadsheet to investigate factors and
Use Excel to practise adding and subtracting fractions.