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.

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?

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?

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?

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.

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 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,. . . .

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

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

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!

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

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

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?

Number problems at primary level that require careful consideration.

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?

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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.

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

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. . . .

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

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

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

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

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?

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?

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

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

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.

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 task combines spatial awareness with addition and multiplication.

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

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?

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

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

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

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?

A game that tests your understanding of remainders.

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

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?

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?