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 numbers?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
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 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?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.
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.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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?
These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
An activity based on the game 'Pelmanism'. Set your own level of challenge and beat your own previous best score.
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. . . .
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Meg and Mo still need to hang their marbles so that they balance,
but this time the constraints are different. Use the interactivity
to experiment and find out what they need to do.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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 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. . . .
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
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 locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Experiment with the interactivity of "rolling" regular polygons,
and explore how the different positions of the red dot affects its
vertical and horizontal movement at each stage.
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
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.
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
Two circles of equal radius touch at P. One circle is fixed whilst the other moves, rolling without slipping, all the way round. How many times does the moving coin revolve before returning to P?
Mo has left, but Meg is still experimenting. Use the interactivity
to help you find out how she can alter her pouch of marbles and
still keep the two pouches balanced.
Meg and Mo need to hang their marbles so that they balance. Use the
interactivity to experiment and find out what they need to do.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
Identical discs are flipped in the air. You win if all of the faces
show the same colour. Can you calculate the probability of winning
with n discs?
An animation that helps you understand the game of Nim.
Here is a chance to play a version of the classic Countdown Game.
Square It game for an adult and child. Can you come up with a way of always winning this game?
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?
Use the interactivity to listen to the bells ringing a pattern. Now
it's your turn! Play one of the bells yourself. How do you know
when it is your turn to ring?
Work out how to light up the single light. What's the rule?
Can you set the logic gates so that the number of bulbs which are
on is the same as the number of switches which are on?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?