Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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.

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

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?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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?

This article suggests some ways of making sense of calculations involving positive and negative numbers.

Investigate the different distances of these car journeys and find out how long they take.

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?

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?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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?

How can we help students make sense of addition and subtraction of negative numbers?

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

Find a great variety of ways of asking questions which make 8.

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.

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?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

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?

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Find the next number in this pattern: 3, 7, 19, 55 ...

Here is a chance to play a version of the classic Countdown Game.

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Number problems at primary level that require careful consideration.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

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?

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?

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.

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.