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.
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?
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.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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?
An Excel spreadsheet with an investigation.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Use Excel to investigate the effect of translations around a number
Use an Excel spreadsheet to explore long multiplication.
Use an interactive Excel spreadsheet to investigate factors and
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 practise adding and subtracting fractions.
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?
Use Excel to explore multiplication of fractions.
Match the cards of the same value.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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.
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.
An animation that helps you understand the game of Nim.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
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. . . .
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?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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?
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.
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?
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
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. . . .
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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?
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Use the blue spot to help you move the yellow spot from one star to
the other. How are the trails of the blue and yellow spots related?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
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...