Today I issued a challenge to my 8th period class: Which group can construct an open box with the largest volume?

I explained that the box was to be constructed out of an ordinary sheet of paper – 8.5×11 inches and that they would need to cut out a square to fold up the corners.

Those were the only instructions I gave. I then handed out paper, rulers, and scissors. The only question they had was if the winning group would get candy. I suggested bragging rights. They wanted candy.

Then I walked around and observed.

Some groups immediately began cutting out squares.

A few groups argued about how they should approach the problem.

Some groups started making tables — length, width, height and volume.

They worked for about 15 minutes on this (much longer than I thought it would take my honors students). One group who had been making tables came up with the formula *y*=(*x*)(11-2*x*)(8.5-2*x*). I asked them what *x* and *y* represented. They told me. I said “So you have an equation that represents volume and you’re trying to find the maximum volume. Huh.” and walked away.

Two minutes later I asked for each groups’s volume. One group reported 72 cubic inches. The group with the formula told them it was impossible. Then they explained why.

They got their candy and I handed out the homework. Max/min modeling problems. As students were reading it I overheard “Oh, I get it. We just did this with scissors.”

I’m hopefull that they will have less difficulty than classes have had in the past with modeling. We’ll see tomorrow.

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Nice setup! I like it.

Do you get many kids get super mad when you “won’t tell them the answer”? I do.

“So you have an equation that represents volume and you’re trying to find the maximum volume. Huh.”

We really do need to teach a common prep. I love your approach there.

I’ll take a stab at answering Kate’s question. Kids who have never had you before get frustrated with your “non-answers” but by the time 4th quarter rolls around, they come to expect it. Kids who have been in your class before would be shocked for you to give a straight answer.

Do I get candy?

Bragging rights aren’t enough for you either David? I’ll provide the candy when we meet. (I’m hoping that is a when and not an if).

Kate – as David said by this time in the year, they aren’t mad. Heck, these guys were happy to get a hint. I’ve found that freshmen get used to it quicker. Upperclassmen… it depends on who their prior teachers were. They have more habits to unlearn.

Update: They did well with the modeling. A bit of cloudiness with the domain in the context of the problem – but this GeoGebra file really helped. (Thanks David)

I’m sure it’ll be a

when. I’m wishing I was going to SD for the NCTM conference since it’s right down the road (about 3.5 hours) but time with the family is just way too precious right now–and $ is tight in the district.Glad the GGB file helped.

And I like Peanut M&M’s. 😉

Your posts make me really miss teaching math. That’s a good thing.

If you keep writing, I’ll keep reading.

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