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

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

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!

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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!

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 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,. . . .

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?

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?

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

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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?

Number problems at primary level that require careful consideration.

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

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?

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?

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

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?

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

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?

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

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

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

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

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

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?

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?

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?

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?

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

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

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?

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

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?

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?

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?

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