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Have you tried to do the box problem without calculus? I usually give my students pieces of graph paper, have them cut out a predetermined rectangle and then assign different groups squares of different sizes to cut and make the box. First, it amazes me how many children have no idea how to make a box. We fill the boxes with popcorn. Each group is to keep their popcorn volume number secret. Then we collect them, and I ask the students to vote on which will have max volume? Special visualization is something we all need practice with! Anyway, then we record the volume from each group. Most of the time, kids vote for the wrong box! Popcorn units are much larger than the units the equation is based upon so that presents another problem. This method is fun; the kids can have the popcorn later. -Claudia, for the Teacher2Teacher service
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