Picture Frames & Quadratics

Fawn Nguyen shared an awesome practical lesson on solving quadratics. Since we’re reviewing that in Precalculus, and I love doing fun lessons, I thought I’d do it as well. Note: I haven’t gotten my students to beg (yet).  I decided to use another teacher for the picture–he’s our Spanish teacher and he & I often make fun of each other to our students since we’re such good friends. Some of our students think we hate each other. It’s great.


So I wrote the following instructions on the board–this is an activity I wanted them to start after their quiz, so I had to explain it just by the writing on the board. I added the “tip” afterwards.



One student came up with the idea of cutting every slice of paper in half repeatedly until all the sides were full.  Pretty clever of him. So I made the unspecific rule “make as few cuts as possible”.




We’re not done: we’re going to finish this on Friday. And I’m always disheartened by how unmotivated many of the students are. They had 3 sheets of paper for trial & error, yet they were reluctant to cut anything. Some of them “gave up”, even though they did the very thing I told them not to, and they easily could have made each side longer.


One student got pretty close and claimed to have done “all the math necessary”, yet his sides & top/bottom were off from each other by a whole cm. It’ll be good to look more closely at his math with the class.


It was disheartening for them to give up and not beg. Perhaps that’s a difference between middle schoolers and high schoolers? I need to work on their curiosity and perseverance. Any suggestions?



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