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?
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?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
If you have only four weights, where could you place them in order to balance this equaliser?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
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....?
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?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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 work out how to balance this equaliser? You can put more than one weight on a hook.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
An environment which simulates working with Cuisenaire rods.
Can you hang weights in the right place to make the equaliser balance?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
An odd version of tic tac toe
A variant on the game Alquerque
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
What happens when you try and fit the triomino pieces into these two grids?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Can you complete this jigsaw of the multiplication square?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
Can you cover the camel with these pieces?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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?
Use the number weights to find different ways of balancing the equaliser.
Use the clues to colour each square.
Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Move just three of the circles so that the triangle faces in the opposite direction.
Here is a chance to play a version of the classic Countdown Game.
NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
Choose a symbol to put into the number sentence.
Try out the lottery that is played in a far-away land. What is the chance of winning?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Twenty four games for the run-up to Christmas.
Can you find all the different ways of lining up these Cuisenaire rods?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?