7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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 find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
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?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
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
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...
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.
An animation that helps you understand the game of Nim.
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.
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?
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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.
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.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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
Work out how to light up the single light. What's the rule?
Find the frequency distribution for ordinary English, and use it to help you crack the code.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you fit the tangram pieces into the outlines of the chairs?
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
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Square It game for an adult and child. Can you come up with a way of always winning this game?
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. . . .
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of this telephone?
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
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.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
An interactive activity for one to experiment with a tricky tessellation