The student will use a rectangle of fixed perimeter to find the dimensions of the rectangle of maximum area.
Before the Activity
Instruction that precedes this lesson must include discussion and practice with quadratics and regression from data. The skill of data capture may be previously introduced, or introduced at this time.
During the Activity
See student handout. Have each student begin by using the randInt command, and picking a number between 10 and 50 (or something reasonable) for their fixed perimeter. This will randomize the results, but students can still work together and help each other.
After the Activity
Assessment and evaluation:Students' documents provide either formative or summative assessment data for the teacher. A similar problem can be given later and students asked to solve on their own.
Use different shapes for the perimeter part of the problem, but continue to maximize volume
Have students build their shapes of maximum volume and create a nice diagram or 3-D display