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

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?

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

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

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

Use the interactivities to complete these Venn diagrams.

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!

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

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.

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

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

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?

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

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

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

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

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.

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

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?

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 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?

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?

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

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

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

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

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

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

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?

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

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?

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?

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

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

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

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

Can you work out some different ways to balance this equation?

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?