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 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.
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?
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?
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.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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.
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?
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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. . . .
Match the cards of the same value.
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
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
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Use Excel to explore multiplication of fractions.
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.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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 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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
An animation that helps you understand the game of Nim.
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?
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.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Use Excel to practise adding and subtracting fractions.
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?
Work out how to light up the single light. What's the rule?
An Excel spreadsheet with an investigation.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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.
Use an interactive Excel spreadsheet to investigate factors and
Use an interactive Excel spreadsheet to explore number in this
Use Excel to investigate the effect of translations around a number
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
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.
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an Excel spreadsheet to explore long multiplication.
A counter is placed in the bottom right hand corner of a grid. You
toss a coin and move the star according to the following rules: ...
What is the probability that you end up in the top left-hand. . . .
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.
To avoid losing think of another very well known game where the
patterns of play are similar.