Polygonal Numbers

I’m finishing up arithmetic series in my class. I wanted to give my kids a challenge problem. I let them choose their groups, and handed this out at the top of class.

I told each group that they could ask me for one big hint along the way to help them out.

Only one of the five groups asked for the hint. Even when time was running out. That meant — to me — that they were interested in solving the problem and felt like they had the means to do it. That was my one good thing. My kids have perseverance!

What I loved was that one of the five groups did solve it — and other groups I think both were dissuaded (awww, they actually figured it out) but also inspired (if they could do it, this isn’t impossible!). The other groups were getting somewhere. Because they were really engaged and talking through things, I decided to let them continue in class tomorrow — even though that throws everything I had planned off!

I am going to do this activity again in my second precalc class in 20 minutes. Fingers crossed it goes well!


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