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

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

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.

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

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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

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?

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?

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 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?

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

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?

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

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

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

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?

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?

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

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Can you help the children in Mrs Trimmer's class make different shapes out of a loop of string?

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

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.

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?

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

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?

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?

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?

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?

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

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?

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

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?

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?

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?

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

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

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

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

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?

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

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?

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