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

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

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

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

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?

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?

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

Can you complete this jigsaw of the multiplication square?

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

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 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?

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

Number problems at primary level that require careful consideration.

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

Throw the dice and decide whether to double or halve the number. Will you be the first to reach the target?

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.

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

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?

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. . . .

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

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

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

On Friday the magic plant was only 2 centimetres tall. Every day it doubled its height. How tall was it on Monday?

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.

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

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?

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?

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

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

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?

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

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

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

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

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?

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

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?

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

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

Can you work out some different ways to balance this equation?