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?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
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
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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.
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.
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?
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.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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 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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Two engines, at opposite ends of a single track railway line, set
off towards one another just as a fly, sitting on the front of one
of the engines, sets off flying along the railway line...
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
An animation that helps you understand the game of Nim.
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.
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 game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Here is a chance to play a version of the classic Countdown Game.
Work out how to light up the single light. What's the rule?
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.
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
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
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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?
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?
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?
Here is a solitaire type environment for you to experiment with. Which targets can you reach?
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?
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.
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 the interactivity to play two of the bells in a pattern. How do
you know when it is your turn to ring, and how do you know which
bell to ring?
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.
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. . . .
Can you find all the 4-ball shuffles?