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.

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?

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

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 complete this jigsaw of the multiplication square?

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

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!

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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

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

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

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

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

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

"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 ...?

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

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

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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?

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?

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?

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

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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

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

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

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?

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

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

Number problems at primary level to work on with others.

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?

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?

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

Use the interactivity to sort these numbers into sets. Can you give each set a name?

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

Number problems at primary level that may require determination.

An environment which simulates working with Cuisenaire rods.