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?
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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!
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you complete this jigsaw of the multiplication square?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you explain the strategy for winning this game with any target?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
An environment which simulates working with Cuisenaire rods.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Here is a chance to play a version of the classic Countdown Game.
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 1 to 8 into the circles so that the four
calculations are correct?
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
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Choose a symbol to put into the number sentence.
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
What can you say about the values of n that make $7^n + 3^n$ a multiple of 10? Are there other pairs of integers between 1 and 10 which have similar properties?
A card pairing game involving knowledge of simple ratio.
A generic circular pegboard resource.
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?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Our 2008 Advent Calendar has a 'Making Maths' activity for every
day in the run-up to Christmas.
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 make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
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 game for 2 people that everybody knows. You can play with a
friend or online. If you play correctly you never lose!
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?
Work out how to light up the single light. What's the rule?
An interactive activity for one to experiment with a tricky tessellation
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Work out the fractions to match the cards with the same amount of
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 find all the different ways of lining up these Cuisenaire
NRICH December 2006 advent calendar - a new tangram for each 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.
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.
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
Train game for an adult and child. Who will be the first to make the train?