Rotate a copy of the trapezium about the centre of the longest side
of the blue triangle to make a square. Find the area of the square
and then derive a formula for the area of the trapezium.
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?
Can you beat the computer in the challenging strategy game?
How good are you at finding the formula for a number pattern ?
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?
A collection of resources to support work on Factors and Multiples at Secondary level.
Cellular is an animation that helps you make geometric sequences
composed of square cells.
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.
Find the vertices of a pentagon given the midpoints of its sides.
Have you seen this way of doing multiplication ?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
Balancing interactivity with springs and weights.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
On the 3D grid a strange (and deadly) animal is lurking. Using the tracking system can you locate this creature as quickly as possible?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Match pairs of cards so that they have equivalent ratios.
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 metal puzzle which led to some mathematical questions.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
An environment that enables you to investigate tessellations of
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
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.
Discover a handy way to describe reorderings and solve our anagram
in the process.
Investigate how logic gates work in circuits.
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. . . .
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
Match the cards of the same value.
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.
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?
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
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. . . .
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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?
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
Use Excel to explore multiplication of fractions.
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.
Experiment with the interactivity of "rolling" regular polygons, and explore how the different positions of the red dot affects the distance it travels at each stage.
Prove Pythagoras Theorem using enlargements and scale factors.
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?
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?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.