Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

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?

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.

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?

Number problems at primary level to work on with others.

Number problems at primary level that may require determination.

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?

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?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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.

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

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

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.

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

Number problems at primary level that require careful consideration.

Can you score 100 by throwing rings on this board? Is there more than way to do it?

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

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.

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

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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?

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

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

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?

Use the information to work out how many gifts there are in each pile.

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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?

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

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?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

This task combines spatial awareness with addition and multiplication.

Got It game for an adult and child. How can you play so that you know you will always win?

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

This number has 903 digits. What is the sum of all 903 digits?

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.