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

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?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?

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?

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

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

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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

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 are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?

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

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?

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!

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

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

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

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?

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?

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

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?

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

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

I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

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?

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

This task combines spatial awareness with addition and multiplication.

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

Shut the Box game for an adult and child. Can you turn over the cards which match the numbers on the dice?

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

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?

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

Number problems at primary level that may require resilience.

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

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

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

Number problems at primary level that require careful consideration.

During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?