Monday, March 17, 2008

Squares and stuff



This video shows Sean working out 34x34 using a method I taught him this morning. Although he's not doing it at lightning-quick speed like kids from abacus/kumon classes, I think something's clicking in there. Slowly and steadily.

I'm pretty excited about him understanding the concept, cos when I tried teaching this to Brian years ago, he didn't get it, in fact, as recently as last year, Brian still said he didn't get it. Granted, I've streamlined my method somewhat and it's lots clearer now than before.

I suspected Sean might be be ready for the method when I saw he's got his multiplication (and simple division) pretty much down to pat, not by memorising but through a combination of skip-counting, adding, subtracting, I dunno, just different ways.



The Method. Sean knows 10x10 right? So I showed him what 10x10 actually means, 10 squares by 10 squares (see top drawing in picture above), total 100 squares. Then I showed him what 15x15 looked like. First add 5 more columns of 10s, and 5 rows of 10s, this makes 50+50 which is 100, add that to the initial 10x10 square, so we have 200, and finally the small square of 5x5, altogether 225.

He was excited to 'see' this and insisted on doing 16x16 through to 40x40.

Here is 17x17.



And 19x19.



When he did 20x20 and got 4 squares of 100, somehow that got him jumping with delight. I told him from then on, the 20x20 square would form the basic square now. But that each additional row would be an extra 20 squares. Get it?

So here's 26x26....Okay, I'll go slowwwwwww....the basic box is now 20x20=400 right? 6 more twenties make 120, another 6 twenties make another 120...and you have the 6x6 box at the bottom which is 36. Altogether add that in your head, you get 676.



After 30, the basic square would be 30x30=900 and this is how 32x32 is worked out.



38x38.....



How do you like The Method? Of course, doing this by vertical multiplication with the carrying and all may be faster, but if you do The Method often enough, you're able to picture the diagram in your head and come up with the answers pretty quickly and accurately, without pen and paper.

Also, without realising it, Sean learnt to add in hundreds pretty niftily too today.

11 comments:

bACk in GERMANY said...

You are a genius!
Are you opening up a Math enrichment class? Can I send my children over now??? :)

Lilian said...

So you get what I wrote? I wasn't sure if I was clear enough...Wendy said she was still processing my "magic squares" lol!

bACk in GERMANY said...

Heehee... I'll suggest she gets a piece of square-grid paper.

What I like is that you've broken it up into "tangible" squares for Sean. And that's the concept of squaring!

Is there a book that you read to make you so smart? I don't have those grey matters to think in that graphical representation!

Lilian said...

Hehe no book, just years of discussing Math with Brian I guess, and doing Singapore Math, makes you think of different ways to 'see' numbers.

You are obviously much more linguistically-abled than I, so I guess different pp have different strengths, that's all :)

Hsien Lei said...

Way cool! I'm usually no good at these kinds of math shortcuts but your method is definitely clear.

bACk in GERMANY said...

Now since there's no book in the market yet, I suggest you write one, my friend. It's such a waste to have to sit around in Moscow and "rot"!!!! Just pen down your discussions with Brian on Math and Science!

Kowtow... Math GURU, you!

Lilian said...

Oi Oi, who says I'm rotting! I'm very much alive and kicking, catching all the American Idol updates as they get uploaded on the net!

bACk in GERMANY said...

Just testing... :p

So, Jason Castro's still in? He's got your vote, right? I like his hippy look!

Lilian said...

Of course Jason's still in. The winner has got to be in till the end! Whoooooop!

Hsien Lei said...

'It's such a waste to have to sit around in Moscow and "rot"!!!!'

Ohhh. I so agree!!!!! I would buy the book for sure.

tealeafs said...

WHOA! Smarty-pants!

I am starting to p-a-n-i-c ...