Regrouping Subtraction

Math is hard.

That’s what I learned Tuesday night. It didn’t seem that hard. Basic subtraction. What’s 56 minus 7? Easy, right?

But what I was reminded of is that it’s easy only because I’ve been doing it for the better part of three decades until it’s second nature. I no longer think about why 56 minus 7 is 49; I no longer mentally work the problem, at least not slowly enough that I recognize what I’m doing. I see the problem, I know the answer.

If that weren’t the case, it turns out, it would be tougher. If, for example you were a second-grader learning these things for the first time. If the only way you could do it was to know why it works the way it does, if there was no second nature.

It’s very fun to me how good it has been for me getting to know Heather’s boys and becoming closer to them. They, quite literally, make the world a different place. They remind me constantly that even though it seems like we’re in the same places, doing the same things, they live in a world that is entirely different than mine. And it makes me realize how much my own world is really just what I make of it.

They live in a world in which much less is taken for granted. If something happens today, that doesn’t mean it will happen tomorrow. And you can’t just assume that something will happen a certain way the first time. They haven’t seen that, they haven’t experienced it, they haven’t built those expectations. They also haven’t seen things thousands of times until the wonder has worn off. They live in a world that’s much fresher, much more exciting, at times much scarier, but much more colorful. They also, ironically, in some ways, live in a world that’s much more matter of fact. Things that adults wouldn’t know how to make sense of they take in without breaking stride. When you don’t have expectations, a dozen surprising things might happen to you in a day, so what’s one more? Something that’s a big deal to an adult might be no more or less unusual to them than the fact that you don’t go to school on Veterans Day. “What? Why not? What does that mean? But why are we off school for that?”

It’s good to be reminded of the wonder of Veterans Day. It’s good to be reminded that things that seem like big deals to me really aren’t. It’s good to be reminded not to take things for granted. It’s good to be forced to stop expecting to see the things I always have, and start looking at what’s really there.

On the other hand, it’s not necessarily as much fun having to relearn math.

It’s simple. Like I said, I don’t have to think about 56 minus 7. I just know it. Even the basic explanation is easy; if I have 56 of something, and take away 7, I have 49 left. But that’s too time-consuming, to count down every time. And it’s not what the teacher wanted. She wanted regrouping tens. You don’t have enough ones in the ones column to subtract the larger number, so you take some from the tens column. Again, simple. But only because it makes perfect sense. It involves making sure there’s an understanding of the relationship between the ones column and the tens column. It involves making sure there’s an understanding of what happens when you “regroup” from one to the other. It involves making sure there’s an understanding of how many ones you have if you regroup some ones from the tens. It involves making sure there’s an understanding of how many tens you have if you regroup some tens into ones. And it involves making sure there’s an understanding of how you put all of that back together to get the final answer. Like I said, math is hard.

We used scratch paper. We got out the pennies and dimes. We worked the problems; talked about what we were doing. I think he got it. Mostly. Enough to get through the night’s problems. I suspect he’ll need a refresher before it’s all over. But that’s OK. He doesn’t have to master it in one night. There’s time. Step by step.

But, you know, I suspect I learned as much about subtraction that night as he did.

4 Responses

  1. We had school on Veteran’s Day. (Well, I didn’t, I was taking a personal day.) My school obviously is unpatriotic.

  2. Ah, the irony.

  3. I learned an awesome model today at an interview, of all places. The “as compared to” model for subtraction. Take “7 – 2”. This can be read as “7 as compared to 2”, which leads to an answer of “they are comparably 5 apart”.

    It also works for subtracting negatives! “7 – -2” can be read as “7 as compared to -2”, which leads to an answer of 9 since 7 and -2 are comparably 9 spaces apart!

    So awesome!

  4. Ah, cool. I suspect that’s probably a bit too advanced still for him (I know negative numbers are), but it’s a good explanation for me to file away.

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