This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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

Can you hang weights in the right place to make the equaliser balance?

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

This challenge is about finding the difference between numbers which have the same tens digit.

These caterpillars have 16 parts. What different shapes do they make if each part lies in the small squares of a 4 by 4 square?

Jack's mum bought some candles to use on his birthday cakes and when his sister was born, she used them on her cakes too. Can you use the information to find out when Kate was born?

Sam got into an elevator. He went down five floors, up six floors, down seven floors, then got out on the second floor. On what floor did he get on?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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

Fill in the numbers to make the sum of each row, column and diagonal equal to 15.

This activity is best done with a whole class or in a large group. Can you match the cards? What happens when you add pairs of the numbers together?

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.

On Planet Plex, there are only 6 hours in the day. Can you answer these questions about how Arog the Alien spends his day?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Use these four dominoes to make a square that has the same number of dots on each side.

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. . . .

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

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

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!

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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

These two group activities use mathematical reasoning - one is numerical, one geometric.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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?

Investigate what happens when you add house numbers along a street in different ways.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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 task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

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!

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Find all the numbers that can be made by adding the dots on two dice.

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?