3 Acts: Volume of a Box

I’ve done this activity before, but I can’t seem to remember whether I’ve blogged on it. Here’s the gist of it (with pictures!).

1. Ask students if they can make a box out of 8.5 x 11 paper. Give them paper, scissors and stapler (or tape).
2. Once they’ve made the boxes, ask the students (or let them ask) “What’s the biggest possible box with an 8.5 x 11 paper?”
3. Let them make guesses first (way too high, way too low, just right).
4. Point out that we should get a bunch of trials and have students, as a class, decide which boxes to make (students select which box they’ll make which is different from other students. Have students make one box each to contribute to the table.
5. Plot these on Desmos. Then put the boxes on the board so we see what each of the points represents.
6. Talk with students about equation for volume. Have some students provide the equation.
7. Plot the equation and click on Desmos for the maximum (this is Precalculus, not Calculus). Acknowledge who was the closest and have students write down what they learned.