What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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. . . .
Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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.
Match pairs of cards so that they have equivalent ratios.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Triangle numbers can be represented by a triangular array of
squares. What do you notice about the sum of identical triangle
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
A metal puzzle which led to some mathematical questions.
This resource contains interactive problems to support work on
number sequences at Key Stage 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. . . .
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 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.
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.
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 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?
How good are you at finding the formula for a number pattern ?
Prove Pythagoras Theorem using enlargements and scale factors.
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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?
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.
Use Excel to explore multiplication of fractions.
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. . . .
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.
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
Can you beat the computer in the challenging strategy game?
An environment that enables you to investigate tessellations of
Which exact dilution ratios can you make using only 2 dilutions?
Match the cards of the same value.
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. . . .
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?
Discover a handy way to describe reorderings and solve our anagram
in the process.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
To avoid losing think of another very well known game where the
patterns of play are similar.
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. . . .
A java applet that takes you through the steps needed to solve a
Diophantine equation of the form Px+Qy=1 using Euclid's algorithm.
How many different triangles can you make which consist of the
centre point and two of the points on the edge? Can you work out
each of their angles?
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?
Here is a chance to play a fractions version of the classic
A point P is selected anywhere inside an equilateral triangle. What
can you say about the sum of the perpendicular distances from P to
the sides of the triangle? Can you prove your conjecture?
The classic vector racing game brought to a screen near you.
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. . . .
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
A collection of our favourite pictorial problems, one for each day