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

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

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

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?

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

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?

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?

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?

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

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

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

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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.

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?

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?

Number problems at primary level to work on with others.

Play this game and see if you can figure out the computer's chosen number.

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.

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

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

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

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

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?

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.

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

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?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

Can you complete this jigsaw of the multiplication square?

Number problems at primary level that may require resilience.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

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

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 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?

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?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?