It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
A metal puzzle which led to some mathematical questions.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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...
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
Use Excel to investigate the effect of translations around a number
Use an interactive Excel spreadsheet to explore number in this
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
An environment which simulates working with Cuisenaire rods.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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?
Match the cards of the same value.
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.
Work out the fractions to match the cards with the same amount of
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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. . . .
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. . . .
Use Excel to explore multiplication of fractions.
Can you spot the similarities between this game and other games you
know? The aim is to choose 3 numbers that total 15.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
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
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
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.
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?
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
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?
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
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. . . .
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
Use an Excel spreadsheet to explore long multiplication.
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
What shape is the overlap when you slide one of these shapes half
way across another? Can you picture it in your head? Use the
interactivity to check your visualisation.
Use Excel to practise adding and subtracting fractions.
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
An Excel spreadsheet with an investigation.
Here is a chance to play a version of the classic Countdown Game.