Using the 8 dominoes make a square where each of the columns and rows adds up to 8

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

Use these four dominoes to make a square that has the same number of dots on each side.

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

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. . . .

Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .

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. . . .

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.

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

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.

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.

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?

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

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.

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?

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

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

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.

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

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.

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

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?

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?

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

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

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

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?

An account of some magic squares and their properties and and how to construct them for yourself.

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

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

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

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

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

Fancy a game of cricket? Here is a mathematical version you can play indoors without breaking any windows.

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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.

This article suggests some ways of making sense of calculations involving positive and 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?

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?

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

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

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

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.