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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Choose a symbol to put into the number sentence.
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....?
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!
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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 make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
A generic circular pegboard resource.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Here is a chance to play a version of the classic Countdown Game.
Can you complete this jigsaw of the multiplication square?
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?
Watch this film carefully. Can you find a general rule for
explaining when the dot will be this same distance from the
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!
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?
Using angular.js to bind inputs to outputs
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.
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. . . .
Train game for an adult and child. Who will be the first to make the train?
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
A train building game for 2 players.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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!
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.
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
A card pairing game involving knowledge of simple ratio.
Can you find all the different ways of lining up these Cuisenaire
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Investigate how the four L-shapes fit together to make an enlarged
L-shape. You could explore this idea with other shapes too.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
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?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?