During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

This article for teachers suggests ideas for activities built around 10 and 2010.

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

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?

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

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

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

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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

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,. . . .

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

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?

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

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!

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?

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?

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

This challenge is a game for two players. Choose two numbers from the grid and multiply or divide, then mark your answer on the number line. Can you get four in a row before your partner?

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?

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

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

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

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?

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?

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?

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?

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?

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?

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

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?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?

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!

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

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.