You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?
What is the sum of all the three digit whole numbers?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Find the numbers in this sum
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
How can we help students make sense of addition and subtraction of negative numbers?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
You have 5 darts and your target score is 44. How many different ways could you score 44?
What is happening at each box in these machines?
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?
Replace each letter with a digit to make this addition correct.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
This task follows on from Build it Up and takes the ideas into three dimensions!
Got It game for an adult and child. How can you play so that you know you will always win?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Investigate the different distances of these car journeys and find out how long they take.