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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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

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

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

There are exactly 3 ways to add 4 odd numbers to get 10. Find all the ways of adding 8 odd numbers to get 20. To be sure of getting all the solutions you will need to be systematic. What about. . . .

Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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?

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

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

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to do. . . .

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.

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

This Sudoku requires you to do some working backwards before working forwards.

Find out about Magic Squares in this article written for students. Why are they magic?!

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

By selecting digits for an addition grid, what targets can you make?

This dice train has been made using specific rules. How many different trains can you make?

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?

Try out some calculations. Are you surprised by the results?

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?

What happens when you add a three digit number to its reverse?

Play this game to learn about adding and subtracting positive and negative numbers

Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.

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?

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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?

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

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.

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?

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.

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, 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?

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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.

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.

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

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