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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you complete this jigsaw of the multiplication square?
Choose a symbol to put into the number sentence.
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
An interactive activity for one to experiment with a tricky tessellation
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?
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. . . .
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Can you find all the different ways of lining up these Cuisenaire
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A generic circular pegboard resource.
Here is a chance to play a version of the classic Countdown Game.
A train building game for 2 players.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
A card pairing game involving knowledge of simple ratio.
Train game for an adult and child. Who will be the first to make the train?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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.
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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....?
Work out the fractions to match the cards with the same amount of
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?
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!
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?
Use the interactivity or play this dice game yourself. How could
you make it fair?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?