In a middle school math class, the teacher broke some rules. I was confused at first. It was like she wasn’t following her own instructions to us. She acted like certain mathematical details in the problem didn’t matter… What? How can that be?
The lesson she showed us in this casual yet powerful moment of class, I still use almost every day. It was about more than just basic math. It’s an important thing to know that we don’t HAVE to always stick to the rules… I liked that!
This example happened a long time ago, so I may not have it all perfectly recollected, but it went something like this:
Mrs. Mackie issued the class a handful of multiplication problems.
What’s 49 times 61?
How about 24 times 11?
Or 93 times 5?
I can recall trying to write down my numbers and start to work the problems as we’d been shown before. (I always had instant anxiety at these moments, not wanting to be slow to figure it out.)
She stopped us in the middle of scribbling and said something like: “Don’t make these harder than they are. Just get close. C’mon, somebody give me an answer.”
Huh? Just get close?? What? I thought this was MATHEMATICS and specific answers with numbers were like IMPORTANT! In fact, that’s the only way I’d experienced math. I was given a problem and had to report my work as an exactly correct numerical expression. In math, it’s either exactly right, or exactly WRONG… right?
Well on this occasion, my mind was stretched and opened up. I clearly remember the specific feeling of that. Mrs. Mackie said it was okay to just get close by rounding things off. You know, make it a quick and simple thing in your mind to just get in the ballpark. She was rattling off some answers within seconds.
But the solutions weren’t like we were used to hearing in math class. Instead of the number itself, she spoke in sentences and stories.
“Well 49 is close enough to 50, so lets’ just use that. 61 is close to 60. Break that down to 5 times 6 and then add the zeros back in. So 5 times 6 is 30, with a couple zeros more it’s 3000. And that is a ballpark answer to what is 49 x 61.”
“Same thing for the other two problems. 24 x 11 would be close to 24 x 10 which is really easy, then add another 24 to it. So 240 plus 24 is 264. She said that 93 x 5 is going to be between 450 and 500 because 90 x 5 is an easy calculation of 9 x 5 (45) plus a zero and 100 x 5 is 500.”
What?? Umm… Wow. These were not the kinds of answers I was used to hearing when it came to this anxiety-inducing specifically detail-oriented subject!
Teaching Estimation and Rounding isn’t the cutting edge of complex mathematics. It’s probably common for lots of middle-schoolers. The impact came from the way she presented the material. It really crystallized the concept for me. I could see the bigger picture utility, and it was about more than just math. It was a method to deal with life itself.
Her point was that it’s okay to generalize sometimes. She showed me that problems can be tackled from different perspectives. We can deconstruct things, round off and choose easier more familiar methods to work on them. In fact, there isn’t just one exactly correct way to handle an obstacle before you. There are several options and it depends how exact the answer needs to be.
This is real education. It’s something I’ve used almost every day since I learned it. It’s a mental tool passed down from a mentor. She taught me a way to use my own mind that I didn’t know existed before. I received transformation, not just information.
Thanks Mrs. Mackie. I appreciate to this day, the mind-stretching moments you delivered many years ago.
Until later this week my friends, go back to middle school if you have to. Don’t get stuck too deep into exact details. It’s okay to round it off and call it good. Estimate a generality of your goals, at least that’s better than skipping them altogether. Get yourself in the ballpark. It’s probably easier than you think.