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!
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
If you have only four weights, where could you place them in order
to balance this equaliser?
Choose a symbol to put into the number sentence.
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. . . .
An interactive activity for one to experiment with a tricky tessellation
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.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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?
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?
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?
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?
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
A train building game for 2 players.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
A generic circular pegboard resource.
Train game for an adult and child. Who will be the first to make the train?
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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
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.
Can you complete this jigsaw of the multiplication square?
A card pairing game involving knowledge of simple ratio.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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
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!
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
Use the Cuisenaire rods environment to investigate ratio. Can you
find pairs of rods in the ratio 3:2? How about 9:6?
Here is a chance to play a version of the classic Countdown Game.
Use the interactivities to complete these Venn diagrams.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Use the interactivity or play this dice game yourself. How could
you make it fair?
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?
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.