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
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
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.
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.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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?
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?
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. . . .
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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?
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 spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
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.
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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.
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
A collection of resources to support work on Factors and Multiples at Secondary level.
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?
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?
An animation that helps you understand the game of Nim.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
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?
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?
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...
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?
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.
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.
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?
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
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. . . .
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
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.
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Square It game for an adult and child. Can you come up with a way of always winning this game?
Can you work out which spinners were used to generate the frequency charts?
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.
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