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?

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

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

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

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 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 the chosen number from the grid using the clues?

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

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?

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?

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

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

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 work out some different ways to balance this equation?

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

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

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

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

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.

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?

Can you complete this jigsaw of the multiplication square?

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.

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?

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?

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?

Ben’s class were making cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

This package will help introduce children to, and encourage a deep exploration of, multiples.

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.

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?

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

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?

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

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

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

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?

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

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?

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

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

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?

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

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.

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