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.
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.
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?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
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.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Can you complete this jigsaw of the multiplication square?
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 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. . . .
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
A card pairing game involving knowledge of simple ratio.
Can you be the first to complete a row of three?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
What are the coordinates of the coloured dots that mark out the
tangram? Try changing the position of the origin. What happens to
the coordinates now?
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?
Ahmed has some wooden planks to use for three sides of a rabbit run
against the shed. What quadrilaterals would he be able to make with
the planks of different lengths?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Work out the fractions to match the cards with the same amount of
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
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?
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?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
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.
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
How many different triangles can you make on a circular pegboard that has nine pegs?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
A generic circular pegboard resource.
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.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
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.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you find all the different triangles on these peg boards, and
find their angles?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
What shaped overlaps can you make with two circles which are the
same size? What shapes are 'left over'? What shapes can you make
when the circles are different sizes?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Match pairs of cards so that they have equivalent ratios.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?