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

Number problems at primary level to work on with others.

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?

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?

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?

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

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?

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

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

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

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

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?

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?

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?

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

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?

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

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

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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.

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Are these statements always true, sometimes true or never true?

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

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?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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?

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?

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

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

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

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 a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

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?