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

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Can you explain the strategy for winning this game with any target?

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

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?

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

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

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

How can we help students make sense of addition and subtraction of negative numbers?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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

This challenge extends the Plants investigation so now four or more children are involved.

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

Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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

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

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 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.

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

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 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!

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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?

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?

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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?

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

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

A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

An environment which simulates working with Cuisenaire rods.

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.

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?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

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!