It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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
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.
Can you make a right-angled triangle on this peg-board by joining up three points round the edge?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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. . . .
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
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?
This resource contains interactive problems to support work on
number sequences at Key Stage 4.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
This resource contains a range of problems and interactivities on
the theme of coordinates in two and three dimensions.
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. . . .
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Can you work out which spinners were used to generate the frequency charts?
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
Which exact dilution ratios can you make using only 2 dilutions?
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 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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
A metal puzzle which led to some mathematical questions.
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?
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.
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.
Match the cards of the same value.
The interactive diagram has two labelled points, A and B. It is
designed to be used with the problem "Cushion Ball"
Can you beat the computer in the challenging strategy game?
Prove Pythagoras' Theorem using enlargements and scale factors.
An environment that enables you to investigate tessellations of
Use Excel to explore multiplication of fractions.
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 collection of our favourite pictorial problems, one for each day
A tool for generating random integers.
An environment that simulates a protractor carrying a right- angled
triangle of unit hypotenuse.
Here is a chance to play a fractions version of the classic
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?
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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.
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.
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. . . .
Use an Excel to investigate division. Explore the relationships
between the process elements using an interactive spreadsheet.
Square It game for an adult and child. Can you come up with a way of always winning this game?