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!).

- Ask students if they can make a box out of 8.5 x 11 paper. Give them paper, scissors and stapler (or tape).
- 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?”
- Let them make guesses first (
*way*too high,*way*too low,*just right*). - 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.
- Plot these on Desmos. Then put the boxes on the board so we see what each of the points represents.
- Talk with students about equation for volume. Have some students provide the equation.
- 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.

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Awesomeness! Just where we are at! Making it real!

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