Teaching Children to Subtract

Date: 08/30/2005 at 09:20:33
From: Christopher
Subject: Teach subtraction between 10 and 20

Dear Dr. Math:

I am having a hard time trying to teach my 7 year old how to subtract 
any number between 10 and 20, such as 14 - 7 or 17 - 9 or 15 - 8, 
without having to tell him to remember the results by heart.

I know I could say 7 + 7 = 14 so 14 - 7 should be 7.  But to be able 
to do it quickly the only way seems to be to remember the calculation.

Is there an easier way?

Date: 08/30/2005 at 18:16:06
From: Doctor Achilles
Subject: Re: Teach subtraction between 10 and 20

Hi Christopher,

Thanks for writing to Dr. Math.

Everyone learns a little differently.  Here's one trick that I find
useful for doing this kind of subtraction.

For any subtraction problem: x - y is equal to (x+1) - (y+1).

So 14 - 7 = 15 - 8 = 16 - 9 = 17 - 10.

The reason this is helpful is 17 - 10 is an easy subtraction problem
to do.

So try teaching your child to take a problem like 14 - 7 and add 3 to
both numbers to get 17 - 10.

Or, for 17 - 9, you add 1 to both numbers and get 18 - 10.

Note:  This only works for subtraction.  You cannot add 1 to both 
parts of an addition, multiplication, or division problem or you will
get the wrong answer.  But for subtraction I think it's useful.

Hope this helps.  If you have other questions or you'd like to talk
about this some more, please write back.  I will leave your problem
where other members of the Dr. Math team can read it in case any one
else has another suggestion.

- Doctor Achilles, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 08/30/2005 at 20:43:45
From: Doctor Greenie
Subject: Re: Teach subtraction between 10 and 20

Hi Christopher --

Doctor Achilles has suggested one way a child might learn to find the 
answer for subtraction problems like these.  He also opens his 
response by noting that different people learn differently.  So let me 
present another option which I find useful for subtraction problems 
like this.

When we have a subtraction problem like 14-7, we are being asked what
the difference is between the two numbers; that is, we are being asked 
how far it is between the two numbers.

My approach to the problem is to pick a "nice" number between the two
numbers--a "nice" number being one which is easy to work with.  The
"nice" number between 7 and 14 is 10.  Then my approach is to say that
the difference (distance) between 7 and 14 is the difference between 7
and 10, plus the difference between 10 and 14.

Without quite so many words, my thought process when I perform the 
subtraction 14-7 is the following:  "from 7 to 10 is 3; and from 10 to 
14 is 4--so from 7 to 14 is 3 + 4 = 7."  Or, a slightly different way 
of putting the same picture into words is "10 is 3 more than 7 and 4 
less than 14, so the difference between 14 and 7 is 3 + 4 = 7."

For your other specific example, 17-9, my thought process, with a 
minimum of explanatory words, is "17-9 equals 7 + 1 = 8, because 17 is
7 more than 10 and 9 is 1 less than 10."

This approach extends easily to numbers which are farther apart.  For
example, 53-17 is 3 + 30 + 3 = 36, because 53 is 3 more than 50, 50 is 
30 more than 20, and 20 is 3 more than 17.

This method is sometimes called "counting up", because it can also 
work by thinking, "How do I get from 17 to 53?"  I add 3 to get to 20,
then 30 to get to 50, then 3 more to get to 53, so I get a total of 3
+ 30 + 3 = 36 as I "count up" from 17 to 53.

I hope you find this approach useful.  Try both this approach and the 
one proposed by Doctor Achilles and see if one or the other works 
better for your son.

- Doctor Greenie, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 08/31/2005 at 05:42:30
From: Christopher
Subject: Thank you (Teach subtraction between 10 and 20)

Thanks so much for your suggestions.  I will try them out this week.  
They appear much more logical and intuitive than rote memorization.

Thanks again.