Gifted Issues Discussion homepage Forums General Discussion Math Trick Question

DS showed me a trick he said he made up for subtracting seven from double digit numbers. I don't know if he actually made this up or saw it someplace, but he insists he was the one who thought of it.

Can anyone tell me if they've seen this type of computation before and what it's called?

He will take an equation like 15-7= and add three to the seven making it a ten then cross out the one in the fifteen, making it a zero, and add three to the five to get the answer of 8.

I didn't understand what he was doing as he was muttering under his breath all this. I said, "What are you doing?" He explained and being the math dunce I am, I didn't understand his first three explanations. Finally I wrote down equations ranging from 10-7 through 19-7 and he showed me on paper. It works for all of them. When I asked DS about an equation like 23-7, he said he'd add three to the 7 and cross off the two, make it a one and add three to the three in 23 to make a six. So then bring down the one next to the six and the answer is 16.

What is this?

He also has tricks for subtracting 8's and 6's. He just adds either a 2 or 4 respectively and completes the equation just as he does for the 7's.

He is basically adding to each part of the equation to make multiples of 10 - 15-7 becomes 18-10. It is a neat trick.and should work for any number (and lots of people use similar things for mental maths).

BUT - how old is your son? A trick shouldn't really be needed for the examples you gave, by the time the child's maths is good enough to manage the trick the basic facts should be pretty anutomatic. AND does he know what he is doing and why? The details you gave of his explanations sound like he doesn't understand well enough to explain well. If he is just doing it because it is his latest neat trick and he is that kind of person fine, if he is just doing rote manipulations on basic maths not fine.

It looks like a more robust illustration of borrowing. Rather than borrowing the ten onto the ones digit, he pulls it to the side and subtracts off the seven before bringing that result back. Orperhqps you could say it is associative property or such... Like:
23 - 7
(10 + 13) - 7
(10 - 7) + 13
3 + 13
16

It may represent a good handle on what they call algebraic thinking.

I think it might be what's called chunking here, but don't quote me! Very sensible way to do subtraction - see how far it is from the number being subtracted to the nearest convenient number in the right direction, e.g. multiple of 10, add that to how far it is from the convenient number to the thing being subtracted from.

Playing around with number patterns, finding quick or just different ways to do sums, and working out whether they always work, is good stuff - encourage!

I agree that it's cool! DD9 is really into math tricks and trying to invent them. BUT I would also wonder a bit, like puffin said, if it is a little odd that he is needing to do this for "to 20" facts like 15-7? Like maybe he is compensating for an issue with facts? For 23-7, it seems okay.

No. You should not be worrying. It's good.

Don't remember a specific name used but I first came across it a decade ago when my oldest DS' first grade teacher taught the class that strategy and a bunch of other ones to help them learn their basic addition/subtraction math facts (1 to 20).

Is this the complements method of subtraction (subtraction by addition)?
The examples above look like tens complements.
(Math is fun link- http://www.mathsisfun.com/numbers/subtraction-by-addition.html)

He's 6.7 years old and in first grade. He's in a class that expects kids to learn to answer 100, 11-18 equations in five minutes. So far, he's done three of those timed tests and is at 83% correct.

I know he's using some of these tricks to get the answer instead of using strictly memory, but I also know it only takes him around three to four seconds to do the equations in his head in this manner. So...is it preliminary memorization?

I've heard of this. Thanks for the term! Maybe he learned it on his Mathtacular videos and doesn't recall that is where it came from? Seems strange that he thinks he "invented" the trick.

(rolls eyes) Kids.