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?

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

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

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

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

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

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

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

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

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.

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.

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?

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

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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.

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

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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

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

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

Delight your friends with this cunning trick! Can you explain how it works?

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

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

What is the sum of all the digits in all the integers from one to one million?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

You have four jugs of 9, 7, 4 and 2 litres capacity. The 9 litre jug is full of wine, the others are empty. Can you divide the wine into three equal quantities?

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?

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

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

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?

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n $ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

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

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

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

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

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

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.

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

Choose any three by three square of dates on a calendar page...