Ask me anything...

I started volunteering at the Auroville ITI in Aug (2013) to work on delivery of Electronics curriculum. There is also concern about the standard of Math the youth come with. A glance at a math exam reveals familiar gaps in fractions, decimals, negative numbers, algebra, geometry from the 7th grade. Wish as we may, these doubts don't go away, it may become difficult to identify issues given everyone whips out a calculator and half the time get things right. Of course, to err is human and if you really want to screw up get a computer (but a calculator in the right hands is not to be trifled with :)).

The youth had come over one weekend for a Math class and I wondered how I should go about teaching 7th grade Math to kids in ITI. Why would they think its worth learning now when they haven't for the last 4-5 yrs. I have marked the replies from the students in italics

Electronics Class

1) Initial connection? - what would you like to do, what do you have difficulty in?

- Nothing. Everything is ok.

2) What is math?

Calculations - addition, subtractions, multiplication, division

probing

there is also geometry

more probing

ok, there is also algebra and all that other stuff in the book

How about puzzles?

What is that?

A man has to cross a stream with a goat, tiger and grass. The boat can only accommodate him and one of these. How does he get them across without leaving the goat with the grass or the tiger with the goat (as they will get eaten)? What puzzles do you know?

Never heard of these.

probing

No, really, this is the first we are hearing of these.

Puzzles are useful to help us exercise our brains for logical thinking, say you are building a torch and you need to figure out the order in which you do things. Lets try to solve this puzzle then

Can he tie the goat far away from the grass?

Generally, yes, but not for this puzzle, no rope.

Why doesn't the tiger just eat him?

Its a puzzle. Ok, its somewhat trained, it listens to him when he is around.

Can he ask the tiger to swim across?

No, not so well trained that it will do something on its own or not eat the goat when he is not around.

Can he swim across?

and have the tiger row the boat? (I got laughs for that one) No.

How do you write these things? Go (Goat), T(Tiger), Gr(Grass). How do you write out the steps so another person understands?

He can take a goat (Go) across first.

Ok. The T and Gr can coexist.

He can also take the T first.

Really, what happens to the Gr?

Oh, ok the Go eats Gr.

What next?

He take the T and leave it with the Go.

No, that's a problem.

He takes Gr and leaves it with Go.

time, time, time....

Can he sell the goat and get on with his life?

No.

Ok, fine we don't get it, tell us the answer.

Well, moving on

what is the answer?

I'm sure you will figure it out

He doesn't know the answer.

That is entirely possible depending on the puzzle, but in this case I do and so will you. This is your homework.

3) 

We talked algebra, it didn't go far so we settled down with

3x5=15

Tell me a story about it. [It took a little time to warm up, but once they got going pretty much everyone told stories.] 

We used the following as a template to go further:

We got into a bus and bought 3 tickets, each ticket was Rs.5. The total was Rs.15.

I followed up on Ohms law

V = I x R

(they didn't get confused though I did not write it as IxR=V.)

If 'I' is like tickets and 'R' is like the amount per ticket what if you know the total and amount per ticket, can you find the number of tickets i.e. V and resistance can you find the current?

Ok. Lets pick it up a notch and talk about something we could not address before. Same equation different context:

P = I x V (I left out the PF)

Watt = Amphere x Voltage

What is the Wattage of the ceiling fan? 60 W

What is the voltage applied to it? Its the AC mains? 230 V

I know yesterday you said that the current was 5A because you think of 5 A and 15 A fuses. But this only means that the current is smaller than 5 A.

60 W = I x 230V

Wait the total is smaller than one of two things being multiplied. Is this confusing? What will we get? Decimal. Yes, you need a number smaller than one.

[

Diversion:

The kids said that the mains was 230 W. W as we just discussed is the unit of power. What is power? Boy shows his biceps. Ok capacity to do work. But, what is energy? Hmm...

]

How much is the current then? Around 0.25 A. In 5 A you can then run 19 fans!

What is energy? Do you get electricity bill?

Yes, whether they give power or not they don't forget giving us a bill.

Do you understand the bill?

No, they just tell us some '200 units' and tell us how much to pay.

One of the kids looks in his wallet and pulls out the receipt.

But, this is a receipt, what about the bill that tells you how much power you used?

They don't tell us clearly. We are not able to understand what they say.

Being qualified in electricity for the outside world is ok, but don't you want to know what goes on at home? Do you really use so much power or are they putting any number they want?

This we want to know!

Ok. Energy is just how much power you use for how much time.

E = P x t

Again t is like tickets and P is like amount per ticket.

and 1 unit = 1 kWhr i.e. 1 kW for 1 hour.

What is 1 kW? 1000 W. Ok, great we are good to go.

Lets start with the energy required for the fans in this room for the time of the morning classes today

4 x 60 W  x 3 hr = 720 Whr

How many units is this? 720 units

Careful here we have Whr. How many Whr in one unit?

1000 Whr. Is this more than or less than 1000 Wh? Less.

So its less than one unit. How much?

0.72 units

Yes. How about the lights?

4 x 40 W x 3 hr = 480 Whr = 0.48 units

Together its more than one unit.

What if we now ask a different question how many How many fans can you run for one hour in 1 unit?

How do we do it....1000Whr/60W/1hr = 16.67

Yes, you need to run 16 fans to consume 1 unit of power in an hour. That's a lot isn't it?

How do you consume 200 units of power in a month? You should find out. If you can work out what appliance is on for how long you should be able to get a ball park estimate and then have a discussion with numbers with your electricity man.

That's the second homework.

One of the stories was about the 'efficiency' of 150 cc engine for 1 L of petrol. I think he just wanted to say fuel x fuel economy = distance. But, he had hit upon 'cc' which most people don't relate to ml so I talked about this further. It then turned into an IC engines class with talking about the volume of the cylinder and how you only put a bit of the fuel and how in a petrol engine you have a spark plug to ignite the mixture of fuel and air, an exhaust value.

Even the teacher got into the act now and was asking questions about how and why the choke works.

I realized it had become a sort of ask me anything class, but I guess if we want them to be engaged and learn democratic classroom needs to be part of the process.