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

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

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

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

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

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.

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

Can you sort numbers into sets? Can you give each set a name?

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

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?

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?

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

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

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.

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

How will you work out which numbers have been used to create this multiplication square?

Can you complete this jigsaw of the multiplication square?

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

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?

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?

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 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 find different ways of creating paths using these paving slabs?

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?

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

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?

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

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

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

"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 ...?

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?

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?

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?

How many different rectangles can you make using this set of rods?

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

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

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

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

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

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?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. 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?