Are these statements always true, sometimes true or never true?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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!

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

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?

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

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?

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!

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.

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

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?

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

Here is a chance to play a version of the classic Countdown Game.

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?

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

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge combines addition, multiplication, perseverance and even proof.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

Can you find all the ways to get 15 at the top of this triangle of numbers?

This task follows on from Build it Up and takes the ideas into three dimensions!

This task combines spatial awareness with addition and multiplication.

Find a great variety of ways of asking questions which make 8.

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?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

This challenge is about finding the difference between numbers which have the same tens digit.

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.

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

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

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

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?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

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?

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?

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

There were 22 legs creeping across the web. How many flies? How many spiders?