Homeschool Memories…
Kitten (my daughter) and I sat on the couch sharing a whiteboard, passing it back and forth as we took turns working through our prealgebra book together.
The chapter on number theory began with some puzzles about multiples and divisibility rules.
The Problem Was…
“147 and 357 are both multiples of 7. Is 147+357 also a multiple of 7?”
Kitten: “Yes.”
Most of the time, she remembers to give her reasoning. After years of my asking, “How did you figure it out?”, she’s pretty well trained, but on occasion I have to remind her. This time, she answered so fast, perhaps she thought it was just too obvious to explain.
Me: “How do you know?”
Kitten: “Well, if 147 is a multiple of 7, then that means we could write it as 7+7+7+…, and if 357 is a multiple of 7, then it would also be 7+7+7+ a bunch more 7s. And when you put them together, you still have a whole lot of 7+7+7+… So the answer has to be a multiple of 7.”
A Bit Down the Page…
“If k and j are multiples of 7, will k+j be a multiple of 7?”
Kitten: “We just did that problem!”
Me: “Well, you did. Your answer would work here, too. But some students might have just added up 147 and 357 and tested the answer, dividing by seven.”
Kitten: “Oh. Well, if they did that, I feel sorry for them.”
She paused, perhaps thinking that she had spoken too harshly, then added: “But at least they could use long division, so that’s not too bad.”
Which left me wondering: How many middle-school students would view a chance to do long division as a consolation prize?
* * *
For more of Kitten’s adventures learning math, check out my earlier posts on Math for Middle School. Or take a look at the cutest math proof ever: Backwards Math.
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“Middle School Math Proof” copyright © 2023 by Denise Gaskins. Image at the top of the post copyright © ngvprod / Depositphotos.
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