Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
Here is a chance to play a version of the classic Countdown Game.
Can you explain the strategy for winning this game with any 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?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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!
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?
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.
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?
Can you complete this jigsaw of the multiplication square?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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.
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
If you have only four weights, where could you place them in order to balance this equaliser?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Use the interactivity to create some steady rhythms. How could you create a rhythm which sounds the same forwards as it does backwards?
Try out the lottery that is played in a far-away land. What is the chance of winning?
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!
Train game for an adult and child. Who will be the first to make the train?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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 find all the different ways of lining up these Cuisenaire rods?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
Find out what a "fault-free" rectangle is and try to make some of your own.
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?
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Choose a symbol to put into the number sentence.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
A train building game for 2 players.
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. . . .
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?
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
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 make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
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?
Work out the fractions to match the cards with the same amount of money.
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?
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?
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?
Exchange the positions of the two sets of counters in the least possible number of moves