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.
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?
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Can you find all the 4-ball shuffles?
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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"
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?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
To avoid losing think of another very well known game where the
patterns of play are similar.
Can you discover whether this is a fair game?
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?
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
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
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?
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.
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.
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
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
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Use Excel to explore multiplication of fractions.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
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.
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. . . .
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. . . .
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.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
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 investigate the effect of translations around a number
Use an interactive Excel spreadsheet to explore number in this
Use an Excel spreadsheet to explore long multiplication.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to investigate factors and
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
An animation that helps you understand the game of Nim.
Here is a chance to play a version of the classic Countdown Game.
How good are you at finding the formula for a number pattern ?
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.