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

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?

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.

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

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

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 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.

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

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 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.

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

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. . . .

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

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

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

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

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

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?

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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?

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

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?

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.

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

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

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

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?

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

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

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.

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

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

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

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?

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

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

The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .

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

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

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. . . .

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. . . .