It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
A metal puzzle which led to some mathematical questions.
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 group of interactive resources to support work on percentages Key
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Use an interactive Excel spreadsheet to explore number in this
Show that for any triangle it is always possible to construct 3
touching circles with centres at the vertices. Is it possible to
construct touching circles centred at the vertices of any polygon?
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.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
An animation that helps you understand the game of Nim.
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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
There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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?
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
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.
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.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Match the cards of the same value.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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
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
Use an Excel spreadsheet to explore long multiplication.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
Use Excel to explore multiplication of fractions.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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?
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.
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.
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.
Use Excel to practise adding and subtracting fractions.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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.
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. . . .
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
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.
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. . . .