How will you work out which numbers have been used to create this multiplication square?

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Number problems at primary level that may require resilience.

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.

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

If there is a ring of six chairs and thirty children must either sit on a chair or stand behind one, how many children will be behind each chair?

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level to work on with others.

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?

56 406 is the product of two consecutive numbers. What are these two numbers?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Can you find different ways of creating paths using these paving slabs?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Can you complete this jigsaw of the multiplication square?

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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

This article for teachers describes how number arrays can be a useful representation for many number concepts.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Can you sort numbers into sets? Can you give each set a name?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?