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.

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.?

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?

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?

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.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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....?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a 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?

This challenge extends the Plants investigation so now four or more children are involved.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

Find out what a "fault-free" rectangle is and try to make some of your own.

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

How many trains can you make which are the same length as Matt's, using rods that are identical?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

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

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?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

How many different triangles can you make on a circular pegboard that has nine pegs?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

Can you find all the different triangles on these peg boards, and find their angles?

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

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

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?

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?

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

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?

A challenging activity focusing on finding all possible ways of stacking rods.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?