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.
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?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Match pairs of cards so that they have equivalent ratios.
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 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 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 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?
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.
Use Excel to explore multiplication of fractions.
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.
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"
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?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
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. . . .
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?
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.
Prove Pythagoras Theorem using enlargements and scale factors.
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
A tool for generating random integers.
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?
This game challenges you to locate hidden triangles in The White
Box by firing rays and observing where the rays exit the Box.
The classic vector racing game brought to a screen near you.
Square It game for an adult and child. Can you come up with a way of always winning this game?
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.
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. . . .
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
A metal puzzle which led to some mathematical questions.
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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. . . .
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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.
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.
Can you beat the computer in the challenging strategy game?
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.
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
A group of interactive resources to support work on percentages Key
Use Excel to investigate the effect of translations around a number
Use an interactive Excel spreadsheet to explore number in this
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?