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

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?

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

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

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

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?

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?

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?

Can you complete this jigsaw of the multiplication square?

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 find any perfect numbers? Read this article to find out more...

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

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?

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?

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

Have a go at balancing this equation. Can you find different ways of doing it?

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

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?

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

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

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?

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

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

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?

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

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

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?

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

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?

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?

Number problems at primary level to work on with others.

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

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

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

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?

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?

Number problems at primary level that may require determination.

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?