Investigating Area Under a Curve

This Investigating Area Under a Curve lesson plan also includes:

Taking a instructional activity straight from the calculus classroom and making it algebra appropriate is the task of the day. Learners go step by step through calculating different area approximations underlines and curves, reviewing many key geometry and algebra skills through the process. Sophisticated concepts (like the trapezoid rule) become approachable through this advanced but manageable worksheet.

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CCSS: Designed
Instructional Ideas

  • Have advanced learners research concavity and what leads different rectangles to over- or under-estimate area
  • Divide the class into two groups with one calculating left-handed rectangles and one right speeds calculations
  • Have groups devise functions and answer keys for one another
Classroom Considerations

  • Drawing the graph and calculating the table of values for number 3 without a graphing calculator provides a more extensive practice of skills
Pros

  • High degree of math rigor without a lot of jargon or intimidating symbols
  • Long enough for real practice of skills, but not with repetitious rote drill problems
  • Logical progression in problem difficulty
Cons

  • None