Math Is Fun Forum

paulb203

Member

Registered: 2023-02-24

Posts: 261

Subtracting in Columns

I was taught the “add one ten to the top, one ten to the bottom,” method.

I just discovered another method on MathsGenie. When necessary you borrow 1 from the column to your left, e.g, you're subtracting in the units column but the answer would be negative so you borrow one of the tens from the column to your left which gives you ten units for your units column number.

Which did/do you use, and why?

And in either did/do you understand what's going on, or were/are you just following the method?

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Subtracting in Columns

hi paulb203

That's what I was taught too.  It was 'explained' as borrow ten for the top and pay it back at the bottom.

eg.  42 - 17 = = (40 + 10 + 2) - (17 + 10)= (40 - 10 - 10) + (12 - 7)

It was only when I came to teach it that I realised I had never questioned it and worked out for myself why it works.

I think it is technically known as subtraction by equal addition. (ie add ten top and bottom)

Primary schools at that time were encouraged to teach the decomposition method because it was argued it makes more sense and so pupils would be more likely to remember it.

eg.  42 - 17 = 30 + (10 + 2 ) - (10 + 7) = (30 - 10) + (12 - 7)

If, at secondary level, a pupil was struggling with subtraction, my first task was to find out which method they had been taught and then stick with it, explaining it properly so the pupil could work it out for themselves.

That principle of 'don't try to change their method' but 'make sure they can understand it' underpins most of my teaching philosophy.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 261

Re: Subtracting in Columns

Thanks, Bob.

I agree that understanding the method is so important, for both enjoyment, and for remembering how to do it when you've forgotten the rote method.

I also get the approach; stick to the method you know. But, if a student has time, and the inclination, to learn a different method can be enlightening, as certain pennies can drop in various ways.

P.S. I tried the MathsGenie way. It was interesting, but could be messy, sometimes crossing out and replacing several numbers in several coloumns

P.P.S. I think some students are not taught, or not reminded enough after they are taught, that with the add one ten to the top, one ten to the bottom method, they are adding, for example, ten UNITS to the top in the units column, which amounts to one TEN for the tens column. Some think, 'Why does adding 1 to the top, and 1 to the bottom work? (1 as in 1 unit).

woodturner550

Member

Registered: 2024-06-08

Posts: 24

Re: Subtracting in Columns

Bob,

Any idea why deductive logic is not taught at the very beginning of a child's education? Then proofs make sense as well as creating clear thinking. Once the early proofs are understood then upper mathematics is easier to conceptualize concepts.

One problem with people with deductive logic understanding, they are harder to lead.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,524

Re: Subtracting in Columns

I don't think young children would understand what is going on.  It's very abstract and learning starts with 'concrete' experiences.  eg. Children learn to count by counting objects.  They learn about subtraction by having some objects (eg. beads) and taking some away.

One problem with people with deductive logic understanding, they are harder to lead.

Isn't that a good thing rather than a problem.

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

woodturner550

Member

Registered: 2024-06-08

Posts: 24

Re: Subtracting in Columns

Bob,
I was taught deductive logic and has served me well, but I am not in the teaching field.
"One problem with people with deductive logic understanding, they are harder to lead. Isn't that a good thing rather than a problem." That depends on the government. Do they just want people who will work as a cog in their wealth and power generating system or do they want clear thinking people to be able to live their best lives.