Function compositions

Just before classes started today, I had an epiphany on how to teach function compositions:

Say the Apple Store is having a sale: $100 off AND 15% off each MacBook. Does it matter which discount is taken first? Can you prove it?

What a great way to talk about function compositions, right? My kids totally took the bait and started arguing…sigh…my heart is so happy when they argue about math.

Then I posed another question:

Target is offering 20% off on tax-free weekend. So, 20% off AND (about) 8% off. Which discount should you ask the cashier to apply first to most benefit your wallet?

Again, the kids took the bait….this time their intuition wasn’t as good, so we needed math. Hooray!

This is pretty little, but it really lifted my spirits. I’ve been struggling with the question of whether I’m getting any better at this math teacher gig. I don’t want just to do a good job. I want to see improvements each year. This is a topic I’ve taught every year for the past five years…but this is the first time I’ve thought to really teach it this way. So, YAY! There’s an improvement. 🙂

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