Subtracting Without Borrowing

Get ready for a subtraction method that will blow the marks off your number line, have your Cuisenaire rods in a jumbled mess, and fry your calculator buttons before you can even insert the batteries. 

Well that may be a bit of an exaggeration, but it is pretty cool.

Yes, we’ve seen all kinds of math tricks and tips. Most seem harder to learn than the traditional way of doing things - like ones that only work if all the figures end in a digit that isn’t 2, 3 or 7, or something like that.

But most teachers like to stick with a tried-and-true curriculum that they are sure will teach the kids what they’ll need to know in a standard way, usually based on workbooks or copying problems from the textbook of a mainstream publisher. Nothin’ wrong with that. 

There’s also nothing wrong with a few alternatives, shortcuts, or things that are just plain fun - if they really are easier and they work all the time. For example, if all the digits in a number add up to a number that is divisible by 3, then the number itself will be divisible by three too. I’m sure there’s a use for that somewhere, but if you are looking at a pizza that’s cut into eight pieces and there are three of you it’s pretty obvious that rock-paper-scissors will be the most important division strategy at the time. But I like knowing it. 

I also like the thing with the 9’s times tables where if you hold down the fourth finger of your left hand, there will be three fingers on the left and six on the right, etc. Just think where we’d be if God had ordered the English language - we might be spelling “often” as “offen” and there’d be no messing with that “t” that is either silent or not.

Now to the one that is the subject of this post. I’ve only heard of this from one source - my sixth grade teacher, Mr. Bober.  I’ve used it ever since, taught my kids, and they use it too. I haven’t searched the web to see if anyone else teaches this, or asked my smart speaker, because I like to keep it in my mind as a kind of homage to Mr. B who endured the antics of 12 year olds for a whole career and deserves some kind of immortality, however small.

Consider the usual way of ‘borrowing’ a ‘ten’ from one column in order to subtract a number in another column.  It works.  But it can get a bit messy lining out a number and inserting a little number next to it to represent the reduced figure. And don’t forget to add a tiny ‘one’ that will change the value of the number in the column on the right to a teen.

Here’s what Mr. Bober taught us: Instead, add a ten to the column that needs it and add a one to the bottom number in the column that you would have borrowed from. So, 425 minus 236 will look like this: The 5 becomes 15 and the 3 becomes 4; the top 2 becomes 12 and the bottom 2 becomes 3. So you get 15-6=9, 12-4=8 and 4-3=1.

The third example looks a little wonky because of the spacing with subscript and superscript, but I think the idea comes through.

It still involves having some of those mini ‘ones’ running around, and you have to be sure that commas look like commas and not stray ‘ones’ but it’s easier and faster than drawing lines through numbers and noting new ones. For the comma situation, consider using a colored pencil to write out the problem and a regular pencil to work it until Junior gets the hang of it.

You have my sworn statement that this is the only way I’ve subtracted since 6th grade, which was 50 years ago, and it’s never let me down.  Even with figures that end in 2, 5 or 7.  :)  Thanks, Mr. B!