Student: Hey, Goldner, check this out! I started with multiples of 6:
18 + 24 + 30 + 36 + 42 = 150
Then I subtracted 2 from each one and it went down to the next 10!
14 + 22 + 28 + 34 + 40 = 140
And it keeps going!
12 + 20 + 26 + 32 + 38 = 130
10 + 18 + 24 + 30 + 36 = 120 … 

Me: That’s cool! Do you think it will keep working?
Student: Yeah! It’s a solid pattern!
Me: Why do you think it works? What’s going on?
Student, smiling: I don’t know!
Me: That’s awesome – see if you can figure out how it works.
Student, 15 minutes later: I don’t want this class to end!

Me neither. But you can always tell whether I’ve had enough sleep and a good breakfast on days like this. When I have, I’m thrilled to see someone get hooked by structure. When I haven’t, I despair because this marvelous encounter with distribution is happening to a senior who has been passed through Algebra II and is currently taking a course from me labeled “pre-calculus”.

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