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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
A metal puzzle which led to some mathematical questions.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .
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...
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
An Excel spreadsheet with an investigation.
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.
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
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Use an Excel spreadsheet to explore long multiplication.
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
Use Excel to practise adding and subtracting fractions.
Use an interactive Excel spreadsheet to explore number in this
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
An environment which simulates working with Cuisenaire rods.
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
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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?
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.
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?
Use Excel to investigate the effect of translations around a number
Use Excel to explore multiplication of fractions.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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?
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?
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
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. . . .
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
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.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
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?
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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.
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 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.
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. . . .
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.
Match the cards of the same value.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.