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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
How good are you at finding the formula for a number pattern ?
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
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
To avoid losing think of another very well known game where the
patterns of play are similar.
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
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you discover whether this is a fair game?
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.
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Have you seen this way of doing multiplication ?
Find the vertices of a pentagon given the midpoints of its sides.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Work out how to light up the single light. What's the rule?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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.
Use Excel to explore multiplication of fractions.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
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
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?
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. . . .
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. . . .
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.
Prove Pythagoras' Theorem using enlargements and scale factors.
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.
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?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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?
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?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you beat the computer in the challenging strategy game?
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.
Use this animation to experiment with lotteries. Choose how many
balls to match, how many are in the carousel, and how many draws to
make at once.
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?
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.