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

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

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?

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?

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

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?

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

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?

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.

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?

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

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

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

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?

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

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

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

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

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

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?

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.

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

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?

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

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?

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

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.

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?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

Can you make square numbers by adding two prime numbers together?

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

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

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?

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?

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?

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?

Number problems at primary level that may require resilience.

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

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

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

Number problems at primary level to work on with others.

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