This is an interactivity in which you have to sort the steps in the
completion of the square into the correct order to prove the
formula for the solutions of quadratic equations.
Can you discover whether this is a fair game?
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?
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
How good are you at finding the formula for a number pattern ?
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
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
A collection of resources to support work on Factors and Multiples at Secondary level.
Prove Pythagoras' Theorem using enlargements and scale factors.
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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?
P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
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.
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?
Place a red counter in the top left corner of a 4x4 array, which is
covered by 14 other smaller counters, leaving a gap in the bottom
right hand corner (HOME). What is the smallest number of moves. . . .
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
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.
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
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .
A and B are two interlocking cogwheels having p teeth and q teeth respectively. One tooth on B is painted red. Find the values of p and q for which the red tooth on B contacts every gap on the. . . .
Find all the ways of placing the numbers 1 to 9 on a W shape, with
3 numbers on each leg, so that each set of 3 numbers has the same
in how many ways can you place the numbers 1, 2, 3 … 9 in the
nine regions of the Olympic Emblem (5 overlapping circles) so that
the amount in each ring is the same?
Use Excel to explore multiplication of fractions.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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...
Have you seen this way of doing multiplication ?
A collection of our favourite pictorial problems, one for each day
A tool for generating random integers.
Here is a chance to play a fractions version of the classic
Here is a chance to play a version of the classic Countdown Game.
Cellular is an animation that helps you make geometric sequences composed of square cells.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Work out how to light up the single light. What's the rule?
Square It game for an adult and child. Can you come up with a way of always winning this game?
A game in which players take it in turns to choose a number. Can you block your opponent?