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 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?
Here is a chance to play a version of the classic Countdown Game.
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!
If you have only four weights, where could you place them in order
to balance this equaliser?
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
Choose a symbol to put into the number sentence.
An environment which simulates working with Cuisenaire rods.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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 complete this jigsaw of the multiplication square?
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. . . .
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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.
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!
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. . . .
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
A card pairing game involving knowledge of simple ratio.
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Interactive game. Set your own level of challenge, practise your table skills and beat your previous best score.
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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 activity for one to experiment with a tricky tessellation
A game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
Find out what a "fault-free" rectangle is and try to make some of
NRICH December 2006 advent calendar - a new tangram for each day in
the run-up to Christmas.
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
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 find all the different ways of lining up these Cuisenaire
A generic circular pegboard resource.
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?