Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?
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.
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.
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?
Practise your diamond mining skills and your x,y coordination in this homage to Pacman.
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 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?
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?
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.
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 find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
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.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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 reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?
Work out how to light up the single light. What's the rule?
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?
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.
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?
An animation that helps you understand the game of Nim.
A game for 1 person to play on screen. Practise your number bonds
whilst improving your memory
A game in which players take it in turns to choose a number. Can you block your opponent?
Square It game for an adult and child. Can you come up with a way of always winning this game?
Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.
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.
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
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.
To avoid losing think of another very well known game where the
patterns of play are similar.
Use Excel to explore multiplication of fractions.
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?
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. . . .
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. . . .
Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?
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.
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?
Start with any number of counters in any number of piles. 2 players
take it in turns to remove any number of counters from a single
pile. The winner is the player to take the last counter.
If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.
Can you beat Piggy in this simple dice game? Can you figure out
Piggy's strategy, and is there a better one?
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. . . .
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?
Investigate how logic gates work in circuits.
A metal puzzle which led to some mathematical questions.
This set of resources for teachers offers interactive environments
to support work on loci at Key Stage 4.