Can you make a right-angled triangle on this peg-board by joining
up three points round the edge?
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
How good are you at finding the formula for a number pattern ?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
Which exact dilution ratios can you make using only 2 dilutions?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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. . . .
Can you work out which spinners were used to generate the frequency charts?
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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 the cards of the same value.
Can you beat the computer in the challenging strategy game?
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.
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 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. . . .
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?
Can you give the coordinates of the vertices of the fifth point in
the patterm on this 3D grid?
Discover a handy way to describe reorderings and solve our anagram
in the process.
An environment that enables you to investigate tessellations of
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?
A metal puzzle which led to some mathematical questions.
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?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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. . . .
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 tool for generating random integers.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
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
Here is a chance to play a fractions version of the classic
Use Excel to explore multiplication of fractions.
To avoid losing think of another very well known game where the
patterns of play are similar.
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 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. . . .
Find the vertices of a pentagon given the midpoints of its sides.
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?