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?

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.

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?

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.

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

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.?

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

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

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

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

Can you draw a square in which the perimeter is numerically equal to the area?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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!

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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?

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Can you make square numbers by adding two prime numbers together?

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Can you use the information to find out which cards I have used?

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!

How many models can you find which obey these rules?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?