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

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

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?

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?

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?

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

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

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

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.

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

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?

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?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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?

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

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

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?

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

Can you find the chosen number from the grid using the clues?

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

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?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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?

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?

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?

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.

How many trains can you make which are the same length as Matt's, using rods that are identical?

Number problems at primary level that may require resilience.

An investigation that gives you the opportunity to make and justify predictions.

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

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?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

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