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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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
Can you beat the computer in the challenging strategy game?
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
How good are you at finding the formula for a number pattern ?
Can you discover whether this is a fair game?
To avoid losing think of another very well known game where the
patterns of play are similar.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Use the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
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?
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?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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 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?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
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?
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
Use Excel to explore multiplication of fractions.
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?
Can you work out which spinners were used to generate the frequency charts?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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. . . .
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
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.
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
An animation that helps you understand the game of Nim.
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. . . .
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.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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?
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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. . . .