Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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!

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

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?

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.

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Can you replace the letters with numbers? Is there only one solution in each case?

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

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?

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?

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

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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

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

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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!

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

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?

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?

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

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

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?

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?

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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

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

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?

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

At the beginning of May Tom put his tomato plant outside. On the same day he sowed a bean in another pot. When will the two be the same height?

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. . . .

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?

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,. . . .

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

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?

Can you work out how many flowers there will be on the Amazing Splitting Plant after it has been growing for six weeks?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

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

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

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?

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

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

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?