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?

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?

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

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

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

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

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?

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

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

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.

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

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

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?

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

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?

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

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

If you have only four weights, where could you place them in order to balance this equaliser?

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

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

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

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?

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?

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?

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?

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?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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?

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?

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?

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

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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

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?