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.
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.
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?
Use Excel to explore multiplication of fractions.
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?
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?
Can you discover whether this is a fair game?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 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.
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.
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.
To avoid losing think of another very well known game where the patterns of play are similar.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
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. . . .
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. . . .
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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. . . .
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?
Can you explain the strategy for winning this game with any target?
How good are you at finding the formula for a number pattern ?
An Excel spreadsheet with an investigation.
Use Excel to practise adding and subtracting fractions.
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...
Use an interactive Excel spreadsheet to investigate factors and multiples.
Use an Excel to investigate division. Explore the relationships between the process elements using an interactive spreadsheet.
Use Excel to investigate the effect of translations around a number 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.
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 explore number in this exciting game!
Here is a chance to play a version of the classic Countdown Game.
How good are you at estimating angles?
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?
This game challenges you to locate hidden triangles in The White Box by firing rays and observing where the rays exit the Box.
Here is a chance to play a fractions version of the classic Countdown 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?
An animation that helps you understand the game of Nim.
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.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
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 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. . . .
Can you beat the computer in the challenging strategy game?
A game in which players take it in turns to choose a number. Can you block your opponent?