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?

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

How would you count the number of fingers in these pictures?

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

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Can you find different ways of creating paths using these paving slabs?

Number problems at primary level that require careful consideration.

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?

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Find the next number in this pattern: 3, 7, 19, 55 ...

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

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

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

This article for primary teachers encourages exploration of two fundamental ideas, exchange and 'unitising', which will help children become more fluent when calculating.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

This task offers an opportunity to explore all sorts of number relationships, but particularly multiplication.

How would you find out how many football cards Catrina has collected?

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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!

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Use this grid to shade the numbers in the way described. Which numbers do you have left? Do you know what they are called?

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

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

Resources to support understanding of multiplication and division through playing with number.

Are you resilient enough to solve these number problems?

This task combines spatial awareness with addition and multiplication.

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

In this article for primary teachers, Lynne McClure outlines what is meant by fluency in the context of number and explains how our selection of NRICH tasks can help.

In this article, Alf outlines six activities using the Gattegno chart, which help to develop understanding of place value, multiplication and division.

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

Related resources supporting pupils' understanding of multiplication and division through playing with numbers.

More resources to support understanding multiplication and division through playing with numbers

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

In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.

In this article for teachers, Elizabeth Carruthers and Maulfry Worthington explore the differences between 'recording mathematics' and 'representing mathematical thinking'.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Number problems at primary level that may require resilience.

This number has 903 digits. What is the sum of all 903 digits?

It's Sahila's birthday and she is having a party. How could you answer these questions using a picture, with things, with numbers or symbols?

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