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...

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. . . .

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

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

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

Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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

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

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?

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.

Can you use the information to find out which cards I have used?

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

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. . . .

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?

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.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

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

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

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

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.

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

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.

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

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.

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?

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.

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

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?

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. . . .

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?

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

Are these statements always true, sometimes true or never true?

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

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

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.

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

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

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?

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.

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

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.