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

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

Here is a chance to play a version of the classic Countdown Game.

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

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?

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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

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

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

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

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.

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?

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

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?

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?

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

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

This task combines spatial awareness with addition and multiplication.

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

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

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?

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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

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?

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

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

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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?

The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

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

56 406 is the product of two consecutive numbers. What are these two numbers?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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?

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?