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.

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?

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

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

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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

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.?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

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.

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

What could the half time scores have been in these Olympic hockey matches?

What happens when you round these numbers to the nearest whole number?

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

What happens when you round these three-digit numbers to the nearest 100?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

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?

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

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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?

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?

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

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

In how many ways can you stack these rods, following the rules?