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.
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?
This resources contains a series of interactivities designed to
support work on transformations at Key Stage 4.
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?
Overlaying pentominoes can produce some effective patterns. Why not
use LOGO to try out some of the ideas suggested here?
Prove Pythagoras Theorem using enlargements and scale factors.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Triangle ABC has equilateral triangles drawn on its edges. Points
P, Q and R are the centres of the equilateral triangles. What can
you prove about the triangle PQR?
A simple file for the Interactive whiteboard or PC screen,
demonstrating equivalent fractions.
Use an interactive Excel spreadsheet to explore number in this
Use Excel to investigate the effect of translations around a number
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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.
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?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Match pairs of cards so that they have equivalent ratios.
To avoid losing think of another very well known game where the
patterns of play are similar.
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.
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 discover whether this is a fair game?
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
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?
Use an Excel spreadsheet to explore long multiplication.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Use an interactive Excel spreadsheet to investigate factors and
A tool for generating random integers.
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
The classic vector racing game brought to a screen near you.
Find the vertices of a pentagon given the midpoints of its sides.
Use Excel to explore multiplication of fractions.
A metal puzzle which led to some mathematical questions.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Use Excel to practise adding and subtracting fractions.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
An Excel spreadsheet with an investigation.
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?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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.
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. . . .
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. . . .
Four cards are shuffled and placed into two piles of two. Starting with the first pile of cards - turn a card over...
You win if all your cards end up in the trays before you run out of cards in. . . .
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. . . .
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.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?