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?

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

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

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

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

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

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.

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?

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

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

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?

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

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.

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

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. . . .

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.

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

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.

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

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?

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

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

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?

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 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.

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.

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

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

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

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

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

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

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

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

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

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

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. . . .

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.

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?

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

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. . . .

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?