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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
An animation that helps you understand the game of Nim.
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?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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 Excel to investigate the effect of translations around a number
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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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.
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?
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?
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
Match the cards of the same value.
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?
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. . . .
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Use an interactive Excel spreadsheet to explore number in this
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Work out how to light up the single light. What's the rule?
Use Excel to explore multiplication of fractions.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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
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
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
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 spreadsheet to explore long multiplication.
Use Excel to practise adding and subtracting fractions.
An Excel spreadsheet with an investigation.
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
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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?
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 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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
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.
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.