(Not tech. specific. Sent from another CFF School) After introducing local extrema, assign each student a different size rectangular piece of cardboard and challenge them to build the box (no top, just a bottom and sides) of maximum volume by cutting squares out of the corners. They have to decide how much to cut out so the volume will be maximized. If they let the side of the square they cut out to be 'X', they can come up with an equation for the volume. They could then graph this equation and use the graph to find the maximum volume. (That's only one way students tend to solve this problem.) Then I have them actually build the box. Part of the score for the project is based on the accuracy of the final dimensions of the box they built. This problem is very appropro today because, as more people order from the web, a lot of stuff is getting shipped. The cardboard in the box has a cost that comes off the bottom line, hence greater volume for a given cardboard dimension has become important.

## Table of Contents

## Trig Project Idea:

(Not tech. specific. Sent from another CFF School) After introducing local extrema, assign each student a different size rectangular piece of cardboard and challenge them to build the box (no top, just a bottom and sides) of maximum volume by cutting squares out of the corners. They have to decide how much to cut out so the volume will be maximized. If they let the side of the square they cut out to be 'X', they can come up with an equation for the volume. They could then graph this equation and use the graph to find the maximum volume. (That's only one way students tend to solve this problem.) Then I have them actually build the box. Part of the score for the project is based on the accuracy of the final dimensions of the box they built. This problem is very appropro today because, as more people order from the web, a lot of stuff is getting shipped. The cardboard in the box has a cost that comes off the bottom line, hence greater volume for a given cardboard dimension has become important.## Geo Sketchpad Files

## Hippocampus Calculus/Advanced Calculus

## MathCasts

=== ===## Calc Applets - Organized by Limits, Derivatives, Integrals