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?

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

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

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

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?

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

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.

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?

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?

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?

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

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?

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 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?

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

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

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

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

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?

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

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

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

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?

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

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?

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?

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?

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!

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?

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

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?

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

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.

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?

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

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?

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?