Vertical multiplication-how does your child do it?

[Clumsymum]

DS has just brought home some maths homework. He in year 6, and has just been taught how to do "vertical multiplication".

Now, aside from the usual fuss he makes over doing homework, he does seem to be making heavy weather of this, but I'm struggling myself to see how he has been taught to do this.

811
x46
----
4800
60
6
32000
400
40
---
37306 (sorry, it won't right justify the numbers for me)

Now, Back in 1900 and ekky-thump, I was taught to do this differently, which would have taken me 2 lines, and much less struggle.

811
x46
----
4866
32440
----
37306

Now, has DS got the wrong end of the stick, or are they really teaching this way?

DS said to me "how can I work out what 40 X 800 is?"
Doing it the way I was taught, you don't have to !!

[Clumsymum]

?

[spanieleyes]

This is a combination of vertical multiplication and place value! If you look at the multiplicand ( the 46) this has been split into 40 and 6 then each of these has been multiplied by the digits in the first number, so 6x1,6x10 and 6x800 ( this 6x811) and then 40x1,40x10 and 40x800 (so 40x811). If he has been taught place value correctly, he should know 40x800 because he knows 4x8! He just then adds all the answers together. I would guess the reason it is taught like this is so he knows each step in the calculation (rather than the way I was taught which ended up a litany of 6times1 is1,6 times1 is 1 6times 8is 48, write these down etc! ) Understanding what you are doing, rather thanjust how to do it is meant to make things easier!

[Clumsymum]

but he doesn't understand what he is doing any better this way.

He does know 4X8 (cos of our efforts chanting times table over and over), but got very confused over the number of zeros that result from 40X800 - I'll admit I had to think hard about that.

Doing the multiplication the old way, the magnitude of the number (or place value, if you must) falls correctly.

[Whitevanmam]

It doesn't matter - as long as he understands what he is doing and why he is doing it. No one really needs to do long multiplication efficently - we all have calculators now that do the job much quicker.

[spanieleyes]

Well, if there are 3 zeros in the question, there will be 3 zeros in the answer!( unless you have something like 40x500 where 4x5 is 20 and then the 3 zeros!) This is because each of the zeros means you have moved one place to the left in place value from the original numbers.

We stick to grid method!

[emptyshell]

Looks like an intermediate method between grid and the "normal" way of doing it (ie how we were taught at school). Not one I'd personally be using mind you - I'd just take him back to grid method for the moment if he's getting in knots with that method (and there's a heck of a lot of numbers there to go wrong with!), then go straight onto the traditonal method, linking it up with how the grid one works each step of the way when he's solid on what's going on with grids.

[CloudsAway]

yes this is definitely a method they are taught.

I think it's supposed to help them line things up to add them more easily than the grid method.

I find that it confuses them if/when they ever move to the traditional way. But they do tend to understand it as a method, and why it works, perhaps better than the traditional way.

What I find that they don't do is spend enough time when/if they do eventually teach the traditional way, so that they children don't get extremely practiced and comfortable with exactly which numbers you multiply by which, when you add the carried numbers, and when/where you put the placeholder zeroes. They understand it at the time they are taught (often not til Year 6), do a few practice examples to show it, and then move on to other things.

The result is GCSE pupils who can't do a long multiplication without using the grid method or some other similar method (Napier's bones, is the name they sometimes refer to one method; though I've also heard it called lattice method). Nothing wrong with the methods, but it takes them forever!

[swill72]

But emptyshell even with the grid method, he's still got to be able to do 40 x 800, it's just laid out differently! However, you're right that this is a stepping stone to the quick method known and loved by parents!

clumsymum - is he confident multiplying by 10? If he is, then 40 x 800 is no problem:

4 x 8 = 32
40 x 8 = 320 (4 x 8 x 10)
40 x 80 = 3200 (40 x 8 x 10)
40 x 800 = 32000 (40 x 80 x 10)

He should know by y6 that when multiplying and dividing by 10, 100, 1000 etc. the digits don't change, but the place value does. If he understands that, none of this should be too tricky!

[swill72]

Sorry - looks like I've given you a maths lesson you don't need! My point was: that's how he's probably been taught at school!

[MovingMom]

My son's teacher suggested the book "maths for mums and dads" to understand how they teach at school

[MovingMom]

Sorry clumsymum, ignore my message. I am not sure if it is followed in year6. Ignore my message.

[DrZeus]

That book - Maths for Mums and Dads is a great read, I would recommend it.

[DrZeus]

Have a look here Grid Multiplication. This may help.