This task combines spatial awareness with addition and multiplication.

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

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

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the 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?

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

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

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.

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

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

A game that tests your understanding of remainders.

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.

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?

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?

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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?

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

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

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

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?

Can you complete this jigsaw of the multiplication square?

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?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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

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?

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

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

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

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

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

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.

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?

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

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?

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?