In one of our problems, we proved that 2 \(=\) \(-\)2.
No, actually, we examined a sequence of equations that seemed to show that 2 \(=\) \(-\)2, but of course we figured out that something wasn’t quite right with the argument!
This was a problem about arithmetic (among other things), which got me thinking about when people do arithmetic in their heads, which, in the teacher world, is an example of what is known as “mental math”.
Recently I was talking to a friend about mental math, and she said something like “Well, I don’t really do a lot of math in my head.” If you’ve been reading our blogs, you might know what kind of response I had. To me, she might as well have been saying 2 \(=\) \(-\)2! Of course she does math in her head, and you do too. And very likely, you do it well, without even thinking about it, all the time.
My first question back to my friend was about what she made for dinner last night. She has a big family, and loves to cook. She almost always makes 150% of a recipe (because 100% just won’t be enough), so she does mental math to figure out how much of each ingredient to use. She calculates how long things will need to cook when she’s making extra, and also exactly when food needs to go into the oven if dinner is at 6 pm. And that’s just the beginning. She’s also an amazing comparison shopper. When she comparison shops, what is she doing? Mental math! She’s not comparing quantities and prices with her calculator in hand; she’s estimating unit rates (price per ounce, or pound, or per container…) and then uses these estimates to compare brands and prices from store to store, in her head. Mental math is practical math. It’s the math we do every day, to figure out how long, how far, how much, how many, when. It’s simple, and awesome.
And do you want to know something amazing? There are lots of different ways we’ve learned to calculate in our heads. Sometimes we round numbers, other times we take them apart and put them together (and we all do that differently), sometimes we work left to right, other times we think right to left. My husband provides a great example of the wide variety of ways in which people calculate. Being the giant dork that I am, I often ask him to explain to me how he figured out a tip, or a bill, or some other amount, because I know he thinks about it in a totally different way than I do, which I think is really interesting. Sometimes I ask my dad similar questions, because I know he’s got a totally different approach, rooted in his many years of thinking about quantities large and small (when he ran a group of cemeteries!).
Okay. Now for the most fabulous part. Yes, you are good at mental math. And you, yes, you, can help your kids to become fantastic at mental math too. How? Easy!
Talk about it.
Seriously. That’s it. When you calculate a tip, tell them how you figured it out. Ask other adults around your table how they would have figured it out. Ask your kids if they can think of another way that would have worked, or better yet, would have worked faster. Challenge them to double, or halve (or make 150%!) of a recipe. Pay in cash in a store, and ask them to figure out how much change you should get back.
Why? Because mental math is a life skill. We all calculate tips, modify recipes, make change. Helping your kids to be better at mental math prepares them to function in society, get a job (since lots of jobs that a teenager might get could involve getting tips or making change!), be fiscally responsible, and so much more.
Yes, you do mental math. And you should share it. Your kids will benefit (and you might learn some new strategies too!).
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