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)(11-2x)(8.5-2x). 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.