Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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.

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?

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.

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?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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?

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

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

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

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

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.?

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.

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.

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

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?

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

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

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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.

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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?

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!

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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

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?

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?

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

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?