Q What is the difference between whole numbers, integers and natural numbers?
A Whole numbers are without fractions. Natural numbers are our positive counting numbers. Integers include all the negative numbers, as well as zero and the positive numbers.
Q So much emphasis is put on pupils being able to do calculations without a calculator. Wouldn't it be better to teach them how to use a calculator properly? When I want to calculate something I use my calculator in preference to a pencil and paper.
A Calculators are a wonderful invention, but it is dangerous to let pupils become over-reliant on them. They do, however, allow us to investigate concepts much more easily. I can remember with great pain doing statistics and having to hand-calculate everything. On the other hand, I have found that, when allowed, pupils will use a calculator for the simplest calculations. Problems can also occur when they key in an extra digit or miss one out and believe that the answer is correct (although some calculators will list on screen what has been keyed in). Pupils can lose confidence in their knowledge and ability to do calculations.The most important technique to be mastered when using a calulator is estimation, so that the size of the answer can be checked.
Shop tills are also calculators, which are relied upon to provide correct information. But machines can break down. I know of a restaurant which had to close because the waitresses did not know how to do the calculations by hand! A friend also told me of an incident where she bought some items for pound;7.20 and paid for them with a pound;20 note. The assistant accidently keyed in pound;10 and was convinced the change was pound;2.80, because it was written on the till's screen. When I'm in a hurry I don't always check receipts and this has inspired me to write a poem:
The machine can deceive When people believe it's infallible.
How important, mathematics
In the age of "techmatics".
There's a hustling, rustling, bustling Of Christmas in the store.
A light, bright, sight, Rolls of wrapping paper by the door.
Pauline picks up three, Full of Christmas glee!
Long queues that are stating, hating, Waiting today, she joins for a while
With a smile in the aisle to pay.
Three rolls clasped tight
A good price alright.
The whanging, twanging, clanging of The Christmas tills.
Assistants busy processing, assessing, Pressing for bills.
Harassed mum in front of her
Going mad, her face a blur!
A flurry of worry as they hurry to buy Their Christmas gifts.
They are snacking as they're packing, Yakking into the lifts.
Pauline hands the rolls to the assistant
Who really seems to be quite distant.
He enters on his till in a trice, thrice The price for a receipt.
"Thirty pounds, please madam." He's unaware of the deceit.
"But they're only a pound each
That's three pounds, it should reach!"
"But look", he says convinced. "Dear, I fear, it's clear!" He sniggers at
the rigour of the figures. "Do you hear?"
"You shouldn't get shirty. See here It's 30!"
"Forget the caper with that paper, This is mathematics," Pauline explains.
"Don't you see it's three times one? The total of the basket solely,
wholly, Three rolls, a total of three pounds All done."
"It's 30 written here," he says With a sneer.
"Perhaps a slip, a blip-of-a-slip, As you whipped in the amount For each
A few of the queue now grow restless, The argument beginning to blight'em!
When the floor manager arrives
The assistant she deprives of his till.
She says as she intervenes,
"Don't trust these machines
To do the maths".
Pauline felt sad at the sight of the lad.
The assistant sent packing told to do The stacking of the shelves.
He probably feels glum,
He couldn't do the sum
To check the receipt.
How much has it cost?
How much have you lost?
You should check very hard
And be on your guard.
A paper receipt shouldn't rule.
Use what you learnt in a school!
This is one example of why it is important to be able to do simple calculations without the use of a calculator and, most importantly, be able to estimate the correct size of the solution.
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. Email your questions to Mathagony Aunt at email@example.comOr write to TESTeacher, Admiral House, 66-68 East Smithfield, London E1W 1BX