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

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?

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?

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.

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?

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?

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?

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.

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

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?

Number problems at primary level that may require determination.

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?

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?

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

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

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?

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?

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?

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?

Number problems at primary level to work on with others.

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

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?

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

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

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?

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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

An environment which simulates working with Cuisenaire rods.

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

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 student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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?

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.

Given the products of adjacent cells, can you complete this Sudoku?

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?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Can you complete this jigsaw of the multiplication square?

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