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?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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?
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!
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Here is a chance to play a version of the classic Countdown Game.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
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.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
An environment which simulates working with Cuisenaire rods.
Choose a symbol to put into the number sentence.
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
A card pairing game involving knowledge of simple ratio.
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?
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.
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 can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
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.
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 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!
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 which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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.
Use the interactivities to complete these Venn diagrams.
Use the sightings of the lion to guess the location of its lair.
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?
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?
Using angular.js to bind inputs to outputs
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
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....?
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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 hit?