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

Can you complete this jigsaw of the multiplication square?

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?

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

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

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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

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?

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

Twizzle, a female giraffe, needs transporting to another zoo. Which route will give the fastest journey?

Can you replace the letters with numbers? Is there only one solution in each case?

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?

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,. . . .

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.

Number problems at primary level that require careful consideration.

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.

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

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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?

There were 22 legs creeping across the web. How many flies? How many spiders?

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

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

This problem is designed to help children to learn, and to use, the two and three times tables.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Claire thinks she has the most sports cards in her album. "I have 12 pages with 2 cards on each page", says Claire. Ross counts his cards. "No! I have 3 cards on each of my pages and there are. . . .

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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?

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

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.

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

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?

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. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

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

Resources to support understanding of multiplication and division through playing with number.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.