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?

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

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

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

Annie and Ben are playing a game with a calculator. What was Annie's secret number?

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

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

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

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

Can you score 100 by throwing rings on this board? Is there more than way to do it?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Number problems at primary level that may require resilience.

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

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

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.

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

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?

How will you work out which numbers have been used to create this multiplication square?

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

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?

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

Use the information to work out how many gifts there are in each pile.

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?

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

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

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?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

This task combines spatial awareness with addition and multiplication.

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

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

Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?

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

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

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?

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Number problems at primary level that require careful consideration.

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

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?

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