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?

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!

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.

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

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?

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

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?

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

Find the next number in this pattern: 3, 7, 19, 55 ...

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?

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

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

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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.

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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.

Number problems at primary level that may require resilience.

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?

Number problems at primary level that require careful consideration.

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?

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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?

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.

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!

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

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

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.

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?

Number problems at primary level to work on with others.

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?

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.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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?

Can you substitute numbers for the letters in these sums?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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.

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?

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?

Tell your friends that you have a strange calculator that turns numbers backwards. What secret number do you have to enter to make 141 414 turn around?

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

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

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.

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.

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?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?