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
To avoid losing think of another very well known game where the
patterns of play are similar.
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?
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
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Can you discover whether this is a fair game?
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
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.
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?
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.
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.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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 make a right-angled triangle on this peg-board by joining up three points round the edge?
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...
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.
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. . . .
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?
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
An environment that enables you to investigate tessellations of
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.
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Use Excel to explore multiplication of fractions.
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Work out how to light up the single light. What's the rule?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
A collection of our favourite pictorial problems, one for each day
A tool for generating random integers.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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. . . .
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.