Here is a solitaire type environment for you to experiment with. Which targets can you reach?
A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?
A game for 2 players. Can be played online. One player has 1 red
counter, the other has 4 blue. The red counter needs to reach the
other side, and the blue needs to trap the red.
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 the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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. . . .
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.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
A collection of our favourite pictorial problems, one for each day
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.
An environment that enables you to investigate tessellations of
Match pairs of cards so that they have equivalent ratios.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Can you discover whether this is a fair game?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you find all the 4-ball shuffles?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
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
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
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
Do you know how to find the area of a triangle? You can count the
squares. What happens if we turn the triangle on end? Press the
button and see. Try counting the number of units in the triangle
now. . . .
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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.
Use Excel to explore multiplication of fractions.
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. . . .
Use Excel to investigate the effect of translations around a number
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to explore number in this
An Excel spreadsheet with an investigation.
Use an Excel spreadsheet to explore long multiplication.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Use an interactive Excel spreadsheet to investigate factors and
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
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. . . .
A metal puzzle which led to some mathematical questions.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Match the cards of the same value.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?