The students will solve the problem of finding the maximum volume of a box cut from an 18 x 24 cm peice of paper in several ways. The student will actually cut out and form several different boxes. The student will fill the boxes with "starburst" candies and then use their TI-Nspires to analyze the data in several different groups.
Before the Activity
The activity takes some time to get through. The teacher might have the students make the boxes one day and find and record the actual dimensions and volumes. The second day the students could find the "starburst" volumes and then explore the different relationships between the data. Attached is a student worksheet and 18 x 24 cm grid paper.
During the Activity
Have the boxes made and allow students to work through the TNS file. The boxes may be physically graphed by taping the boxes to a white board. The display also models the curve of the cubic polynomial.
After the Activity
Different explorations and extensions are possible from the data and can be manipulated on a Data and Stats page.