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?

Which times on a digital clock have a line of symmetry? Which look the same upside-down? You might like to try this investigation and find out!

This article for teachers suggests ideas for activities built around 10 and 2010.

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

Investigate the different distances of these car journeys and find out how long they take.

Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

Where can you draw a line on a clock face so that the numbers on both sides have the same total?

Investigate what happens when you add house numbers along a street in different ways.

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?

In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?

Number problems at primary level that require careful consideration.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Max and Mandy put their number lines together to make a graph. How far had each of them moved along and up from 0 to get the counter to the place marked?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?

Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.

The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

There are nasty versions of this dice game but we'll start with the nice ones...

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

This group activity will encourage you to share calculation strategies and to think about which strategy might be the most efficient.

Complete these two jigsaws then put one on top of the other. What happens when you add the 'touching' numbers? What happens when you change the position of the jigsaws?

Generate large numbers then give the values of each digit.

Investigate the different distances of these car journeys and find out how long they take.

This article suggests some ways of making sense of calculations involving positive and negative numbers.

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

If you have only four weights, where could you place them in order to balance this equaliser?

Number problems at primary level to work on with others.

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?