Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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 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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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.
Here is a chance to play a version of the classic Countdown Game.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a 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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
Try out the lottery that is played in a far-away land. What is the chance of winning?
An environment which simulates working with Cuisenaire rods.
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Can you find all the different ways of lining up these Cuisenaire rods?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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?
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!
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?
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.
Choose a symbol to put into the number sentence.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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 many different triangles can you make on a circular pegboard that has nine pegs?
Can you find all the different triangles on these peg boards, and find their angles?
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?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Can you complete this jigsaw of the multiplication square?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
A train building game for 2 players.
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?
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. . . .
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?
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!
Carry out some time trials and gather some data to help you decide on the best training regime for your rowing crew.
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory