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

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?

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?

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.

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

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

Can you use the information to find out which cards I have used?

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?

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

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.

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

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?

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. . . .

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

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

Investigate this balance which is marked in halves. If you had a weight on the left-hand 7, where could you hang two weights on the right to make it balance?

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

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?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?

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?

Use these head, body and leg pieces to make Robot Monsters which are different heights.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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

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?

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Are these statements always true, sometimes true or never true?

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Investigate the different distances of these car journeys and find out how long they take.

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?