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

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

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

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?

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

How many different sets of numbers with at least four members can you find in the numbers in this box?

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?

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?

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

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

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

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?

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?

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.

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.

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

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?

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.

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

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

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?

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 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 resilience.

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?

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?

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

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

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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?

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

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?

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?

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?

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

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

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?

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?

There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?

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?

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?

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

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