The idle ramblings of a Jack of some trades, Master of none

May 20, 2011

Math Tales #7

Last weekend, the boy and I sat down to do some homework. It dealt with paying for purchases and calculating the change due. This tied in neatly with the boy's inability to collect change from his weekly 'Tuck Shop' purchases.

'But the Tuck Shop is free,' he protested.

'Why do you say that?' I said.

'Because they don't give me any money back,' he said.

At this point, we needed to established definitions.

'If you give money for something, then it is not free,' I said. 'Do you give money at the Tuck Shop?'

'Yes,' he said.

'Well then, it's not free,' I said.

We then looked at his exercise sheet.

'Okay,' I said. 'Suppose I am a shopkeeper and you come into my shop to buy an apple.'

'I want to be the shopkeeper,' said the boy.

'All right,' I said, being an agreeable sort. 'I come to your shop to buy an apple.'

'What shop is it?' asked the boy. 'Is it Marks, or is it Tesco, or is it Sainsbury's?'

'It doesn't matter,' I said.

'I like Sainsbury's,' said the boy, with some relish.

'The apple's price is 5p,' I said. 'How much should I pay you for it?'

The boy looked at me, puzzled. I had a vivid recollection of Swami from Malgudi Days asking his father how big the fruit was when asked to work out its price.

'I should pay you the price of the apple, shouldn't I?' I urged.

He nodded.

'I can't pay you less than 5p, can I?' I asked.

He shrugged in a noncommittal way.

'If I paid only 3p and took the apple, that would be stealing, wouldn't it?' I said.

He sat up, interested.

'You must not steal,' he intoned. 'Otherwise, the police will come.'

'Yes,' I said.

'Let them come,' he said, seized with a sudden fit of bravado. 'I'll punch them on the nose.'

I sighed.

'Try to focus,' I said. 'Do you agree that if something costs 5p, you should not pay less than that?'

He yawned. He nodded.

'Okay,' I continued. 'Now what if I pay you more than 5p? Suppose I paid you 10p? What will you do?'

He stared.

'You should give me some money back, shouldn't you?' I said.

'I don't have any money,' he said.

'You are a shopkeeper. Of course you have some money,' I said.

'Did I get it from the bank?' he said.

'And from the other customers who came to buy things before me,' I said.

'Did they buy oranges, or did they buy sweets, or did they buy a Munch Bunch?' he said.

'It doesn't matter,' I said, feeling as though I had walked into a cloud. 'Let us worry about the apple I'm trying to buy, shall we?'

'I don't like apples,' whispered the boy in my ear.

'I know,' I said. 'So, anyway. The apple costs 5p, and I paid you 10p. I paid you more than I should have, so you should give me some change back. How do we work out the change?'

'Suppose you gave me 1 pound?' said the boy, his eyes as round as a pound.

'We'll worry about pounds later,' I said. 'Shall we stick to pence for now?'

'Pens?' said the boy, completely confused.

'Pence,' I said. 'You know, pennies.'

'Okay,' said the boy.

We looked at each other.

'I don't know,' he said, agonised. 'It's too hard.'

'Don't worry,' I said. 'I'll explain. If I pay you 10p for something that costs 5p, you should give me some money back. How much money? Well, you should return to me what I paid you minus the price.'

'What is minus?' said the boy.

'I meant 'take-away',' I said, correcting myself.

'Take-away' is the modern English method of teaching subtraction.

We looked at each other again.

'Did you get that?' I said. 'You give me back what I paid you take away the price.'

'Okay,' he said.

'So - what did I pay you?'

His eyes glazed over.

'I forgot,' he said.

'I paid you 10p. Please pay attention,' I said. 'How much did the apple cost?'

'5p,' said the boy.

'So what do you do?' I said.

After some more to-ing and fro-ing, the boy finally said, 'Ten take-away five.'

It took him several seconds to work this out in his head and on his fingers.

'I will give you 5p,' he said.

'Excellent,' I said.

I don't think he has quite got it yet. Even when he does, it will probably strike him as some kind of magic formula. How do I explain it to him so it appears natural and reasonable? I have no idea.

Exhausting stuff.


Space Bar said...

I am loving the kid's adventures in mathland and I feel deep sympathy for him.

Have I ever told youabout my dad trying to teach my cousin some math when he was a kid? The fellow was a total blank until it was put it in terms of money. Then he got the answer before the question could be completed.

km said...

Chuckles and sympathy.

This is exactly how I tried to make sense of so-called "commercial maths" and it was my least favorite part of mathematics.

Anonymous said...

You're very patient. Alas, my father never taught me maths but instead got me a tutor. I think it's probably because he wasn't very good at it.

Gurusharan said...

Reminds me of our own attempts with Simran at Chandigarh - we used graphic bunch of toffees or coins to explain plus's and minuses....

Fëanor said...

SB, KM: I kinda hoped that crass commercialism would help, but the evidence thus far is mixed.

CB: Me, patient? At first I constantly lost my temper, until I remembered that's how my dad's teaching was, so I quickly stopped. Now I drink lots of water instead of clutching at my head and yelling.

Guru: do you have any recollection of how you learned basic arithmetic? I don't remember at all...

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