What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
Match pairs of cards so that they have equivalent ratios.
A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
Prove Pythagoras Theorem using enlargements and scale factors.
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. . . .
Use Excel to explore multiplication of fractions.
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
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.
A simple spinner that is equally likely to land on Red or Black. Useful if tossing a coin, dropping it, and rummaging about on the floor have lost their appeal. Needs a modern browser; if IE then at. . . .
An environment that enables you to investigate tessellations of
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Square It game for an adult and child. Can you come up with a way of always winning this game?
Discover a handy way to describe reorderings and solve our anagram
in the process.
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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.
What is the relationship between the angle at the centre and the
angles at the circumference, for angles which stand on the same
arc? Can you prove it?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
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?
A metal puzzle which led to some mathematical questions.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
Match the cards of the same value.
How good are you at finding the formula for a number pattern ?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
A collection of our favourite pictorial problems, one for each day
Here is a chance to play a fractions version of the classic
Which exact dilution ratios can you make using only 2 dilutions?
Can you beat the computer in the challenging strategy game?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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
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.
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. . . .
The classic vector racing game brought to a screen near you.
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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
A tool for generating random integers.
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 investigate the effect of translations around a number
Use an interactive Excel spreadsheet to explore number in this
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.