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A more natural answer

Q The concept of even numbers appears simple and easily understood by quite young pupils. However, I'd like your comments on these questions which occurred when subtracting dice scores in a probability study.

1. Are negative numbers, - 2, - 4, - 6, even?

2. Similarly, are - 3, - 6, - 9 multiples of 3?

3. Is 0 even?

4. Is 0 a multiple of 3, 4, 5?

A Your question is reliant on the definitions we use. This can be used to stress the importance in mathematics of making clear, concise definitions.

If we define an even number as an integer that is exactly divisible by 2, the general form being n = 2k where n is an integer, then your questions 1 and 3 are answered together: - 2, - 4, - 6 and 0 are even numbers.

However, if we define an even number as a natural number that is exactly divisible by 2 (the general form being n = 2k where n is a natural number), we also have to define our natural numbers, as sometimes 0 is included as a natural number. (It is more convenient to exclude 0 in number theory but include it in computer science.) The set of numbers which includes 0 is called the set of whole numbers. So the answers to your questions depend on how you define "even number" or "multiples of three". For further help visit http:mathworld.wolfram.comevennumber.html

Q Can you suggest a fun activity based on percentages as a lesson starter that encourages pupils to use a calculator?

A A lesson starter I like is one involving test scores. For pupils who need it, the session might start with a quick refresher on how to turn "marks out of an amount" into a percentage. For example: An English paper is marked out of 40. Zoya got 36 out of 40 correct. What is this as a percentage?

This should be written as a fraction, 36Z40, as this is generally how a score would be written on a test paper.

To change into a percentage this is multiplied by 100. So we have 36Z40 x 100.

Invite pupils to suggest ways that this sum could be entered into the calculator.

36 V 40 x 100 36 x 100 V 40 36 abZc 40 x 100or in two steps: 36 V 40 = 0.9 and 0.9 x 100 = 90%.

Let pupils have a go with a second paper, marked out of 70.

This time, say, Zoya scored 64Z70. Which was Zoya's best paper? (64Z70 is approximately 91.4%.) Now set up some challenges on the board such as:27Z35 for paper 1, 8Z12 for paper 2. Which is the highest percentage?

Before they use the calculators ask them to make rough estimates. Write four of these on the board and ask pupils to vote for which they think is correct. Then ask pupils to use calculators to find out the answer.

The kind of estimates they might use are: 27Z35 is roughly 30Z40 or 3Z4 (about 75%).

For 8Z12 this cancels to 2Z3 (roughly 67%).

For further examples, try these (23Z60, 45Z112 and 59Z130, 14Z30).

Q I am an English teacher. I have been reading your column and like your poetry. Have you any suggestions for topics we could explore with poetry?

A I have included this poem about creating a shape. Perhaps pupils could think of the maths in everyday objects and create a poetic puzzle for the reader to guess the object - for example, the geometry of a pencil, made up of a cone and a cylinder. The maths department could then use the most effective in lessons.


To play this game You need to name The shape.

Drawing pins are placed Three pins so equal spaced From each other.

Take a six-centimetre tape.

To help create this shape Imagine!

Now watch as it twines Around the pins in lines.

The perimeter.

Straight sides are created.

The shape now ideated.

By you.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses. your questions to Mathagony Aunt at

Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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