The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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 arrange 5 different digits (from 0 - 9) in the cross in the way described?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Here is a chance to play a version of the classic Countdown Game.

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

Number problems at primary level that require careful consideration.

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

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

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?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

This number has 903 digits. What is the sum of all 903 digits?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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?

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.