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.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this
Use Excel to investigate the effect of translations around a number
Use an Excel spreadsheet to explore long multiplication.
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.
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?
An Excel spreadsheet with an investigation.
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.
Use Excel to practise adding and subtracting fractions.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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?
Use an interactive Excel spreadsheet to investigate factors and
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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
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?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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
An animation that helps you understand the game of Nim.
Match the cards of the same value.
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.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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 Excel to explore multiplication of fractions.
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.
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?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
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 an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Work out how to light up the single light. What's the rule?
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. . . .
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.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Can you fit the tangram pieces into the outlines of these clocks?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?