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 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?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you find all the different ways of lining up these Cuisenaire
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Find out what a "fault-free" rectangle is and try to make some of
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Can you find all the different triangles on these peg boards, and
find their angles?
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....?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you explain the strategy for winning this game with any target?
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.
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...
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
Can you find all the 4-ball shuffles?
An environment which simulates working with Cuisenaire rods.
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?
Work out the fractions to match the cards with the same amount of
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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.
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.
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. . . .
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?
Learn how to use the Shuffles interactivity by running through these tutorial demonstrations.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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!
A generic circular pegboard resource.
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?
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.
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!
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 card pairing game involving knowledge of simple ratio.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?