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

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

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

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.

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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!

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?

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.

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.

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

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

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

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?

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

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?

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

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?

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

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

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?

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

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?

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 complete this jigsaw of the multiplication square?

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?

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

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

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

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

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?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

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?

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

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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

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?

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

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

Use the interactivities to complete these Venn diagrams.

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?