Subtraction

[Kassee]

How do kids learn to subtract nowadays. Say take 600 - 426 = ?
When I was at school you added 10 to the top and one to the bottom (I still do today) but my granddaughter is having none of it. But cant remember how she was taught to do it. Just started senior school. Thanks.

[woofgang]

We were taught borrowing from the next largest column and I still do it that way...the add ten to the top thing makes no sense at all to me.

[EDDIE51]

I do it in my head no problem.

[Old_Geezer]

Aye. You need sometimes to use 1 from the column that represents digits 10 larger than the column you are presently working out, in order calculate that volumn's answer.

So you use, for example, 10×1 for now, and when you do the next column you have to subtract an extra 1×10 to cover (because you already used it in the last column).

[Jackdaw33]

Nowadays in this example you would borrow 1 from the 6 and add 10 to the tens column then borrow 1 ten and add it to the units column, leaving 59 10. I prefer the doorstep method I was taught over 6 years ago.

[Old_Geezer]

Ah but did you as a young kid Eddie ?

[Old_Geezer]

...in order calculate that column's answer...
Like I clearly $^^^/$$$/^^&&^ typed !!!

[fiction-factory]

> I prefer the doorstep method I was taught over 6 years ago

You're a lot younger than I thought, Jackdaw!

[Old_Geezer]

125 years is more than 6.

[fiction-factory]

The formal written method of borrowing ten seems unwieldy to me as we wouldn't do it that way in our heads if working out change from £6 if we spend £4.26.

600-400= 200. Then take 26 and you get 174. For those who don't feel comfortable subtracting the 26 then they can do it in two steps: subtract 20 then 6.
Some teachers will do it this way encouraging pupils to draw a number line

[Jackdaw33]

The method is essentially the same but you alter the top figures rather than pay back 'on the doorstep'. In the given example you have 60 tens so you cross out the 60 and write 59 then add the 10 to the units column. If the top number had been 6000 you would cross out 600 and write 599 above.

[Jackdaw33]

Of course I meant 60 years ago.

[Buenchico]

The 'old-fashioned' way of teaching subtraction was by 'equal addition'. By adding 10 (in the units column) and one (in the tens column) you were effectively changing the sum to one where both the numbers were ten bigger than you started with.

The 'new' way of doing it is by 'decomposition', whereby the numbers in the sum remain the same but are simply written differently. Consider, for example, the sum 62 - 35. In order to accomplish the calculation, 'six tens and two units' is rewritten as 'five tens and twelve units'. i.e. Ten is added to the units column and one is subtracted from the tens column. (Meanwhile the other number, 35, remains totally unchanged).

In the example you've chosen though (600 - 426) there's a bit of complication because when you add ten to the units column (of the number 600), to change it from '0' to '10', you can't knock one off the tens column (since it's already zero). Instead you need to look at the next digit to the left and realise that six hundreds is the same as sixty tens. So you then knock one off the 60 to change it to 59 tens.

Written out:
http://oi66.tinypic.com/s3erzk.jpg

It's not really a 'new' method though. I was brought up on 'equal addition' but I first encountered 'decomposition' on my first teaching practice in 1972!

[Prudie]

I was taught to pay back on the bottom but when i started teaching my pupils had been taught to pinch from the left hand top column. Whichever way we all get the right answer.
Wonder if someone will come along however and say there is one and only one correct way to do it.

[fiction-factory]

v is next to c so it's an easy mistake to make, O_G. Either that or your keyboard is faulty.

[fiction-factory]

Yes, divebuddy- counting up using a number line (or mentally) is another way of doing it.