Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

In this simulation of a balance, you can drag numbers and parts of number sentences on to the trays. Have a play!

Can you find different ways of creating paths using these paving slabs?

This problem looks at how one example of your choice can show something about the general structure of multiplication.

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?

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

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?

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

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.

This challenge combines addition, multiplication, perseverance and even proof.

What is the smallest number of answers you need to reveal in order to work out the missing headers?

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

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?

This task combines spatial awareness with addition and multiplication.

Play this game and see if you can figure out the computer's chosen number.

Number problems at primary level that require careful consideration.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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

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

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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

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!

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

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?

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?

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

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

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?

Find the next number in this pattern: 3, 7, 19, 55 ...

Number problems at primary level that may require resilience.

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

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

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

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

How would you count the number of fingers in these pictures?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Use the information to work out how many gifts there are in each pile.

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.