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?

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?

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?

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

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

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?

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?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

This package will help introduce children to, and encourage a deep exploration of, multiples.

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 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?

Number problems at primary level that may require determination.

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?

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?

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?

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?

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?

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?

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

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

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

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

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?

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

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?

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?

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

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.

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

Number problems at primary level to work on with others.

These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

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.

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?

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?

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

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?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.