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?

In this matching game, you have to decide how long different events take.

Try this matching game which will help you recognise different ways of saying the same time interval.

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you find all the different ways of lining up these Cuisenaire rods?

What happens when you try and fit the triomino pieces into these two grids?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

The pages of my calendar have got mixed up. Can you sort them out?

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

This challenge is about finding the difference between numbers which have the same tens digit.

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

An activity making various patterns with 2 x 1 rectangular tiles.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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 practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?