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?

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

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?

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?

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?

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

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

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!

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

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?

There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.

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

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?

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?

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.

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!

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

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

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.

Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Susie took cherries out of a bowl by following a certain pattern. How many cherries had there been in the bowl to start with if she was left with 14 single ones?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?

Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.

Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

In this investigation, you are challenged to make mobile phone numbers which are easy to remember. What happens if you make a sequence adding 2 each time?

Can you score 100 by throwing rings on this board? Is there more than way to do it?

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?

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!

Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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?

I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?

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

Number problems at primary level that may require determination.

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?

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.