Lesson Plan


Students will explore some classic optimization problems using The Geometers Sketchpad. This lesson has students begin by exploring a pattern, then has them extrapolate their findings into a generalization about inscribed shapes. Extension questions are included.


  • Mathematics > General
  • Mathematics > Applied Mathematics
  • Mathematics > Calculus
  • Mathematics > Equations
  • Mathematics > Graphing

Education Levels:

  • Grade 9
  • Grade 10
  • Grade 11
  • Grade 12


calculus rectangle inscribed inscription



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Creative Commons Attribution 3.0


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Curriki Rating
On a scale of 0 to 3
On a scale of 0 to 3

This resource was reviewed using the Curriki Review rubric and received an overall Curriki Review System rating of 3, as of 2009-07-24.

Component Ratings:

Technical Completeness: 3
Content Accuracy: 3
Appropriate Pedagogy: 3

Reviewer Comments:

This exercise uses trial-and-error (plus a computerized graphing tool) to estimate the solution to an optimization problem, namely finding the largest rectangle that can be inscribed under a parabola. This approach, though non-analytic, has a lot of intuitive appeal to it. The student who follows all the instructions will come to see why there should be a largest rectangle and what determines its size.

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