If you have only four weights, where could you place them in order
to balance this equaliser?
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!
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Choose a symbol to put into the number sentence.
Can you complete this jigsaw of the multiplication square?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Here is a chance to play a version of the classic Countdown Game.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Can you find all the different ways of lining up these Cuisenaire
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 make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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 1 to 8 into the circles so that the four
calculations are correct?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
A simulation of target archery practice
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?
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?
Use the blue spot to help you move the yellow spot from one star to
the other. How are the trails of the blue and yellow spots related?
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
A card pairing game involving knowledge of simple ratio.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
An environment which simulates working with Cuisenaire rods.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Work out the fractions to match the cards with the same amount of
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Board Block game for two. Can you stop your partner from being able to make a shape on the board?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
A generic circular pegboard resource.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A train building game for 2 players.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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!