Optimization is a tricky topic in calculus. This one-day activity allows students to discover how calculus can help them.
Each student (or small group) starts with an index card, which will be cut and folded up to form a box. First they calculate what would happen if the box is made various ways, and see that the volume changes depending on the size of the cuts.
Next students develop an equation and apply calculus to determine how to create a box with maximum volume - so that they can fill it up with the most candy!
You will need index cards, scissors, rulers (inches), tape and candy.
Includes full answer key, with work shown.