Hands-on investigation of Riemann sums becomes possible without intensive arithmetic gymnastics with this interactive lesson plan. Learners manipulate online graphing tools to develop and test theories about right, left, and midpoint sums and limits of integration. An emphasis on interpretation of results keeps the young mathematician engaged in the material and not just the fun applet manipulations. A great way to integrate technology into your integration curriculum.

Concepts

area under a curve, integrals, limits, definite integrals, riemann sums

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Additional Tags

area under a curve, approximate area under a curve, limits of sums, curve summation, integral, math

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Instructional Ideas

• As the class investigates left/right/midpoint sums, extend by introducing concavity and over/underestimation predictions
• Divide the class into four parts and assign a function for integration approximation through left, right, midpoint, and trapezoid methods. Have the groups compare notes for which method converges most quickly and which methods converge from above and which from below
• Work with a physics class to perform velocity and distance experiments, then graph the results. Discuss the physical interpretation of integration in these situations

Classroom Considerations

• Playing with the InteGreat and Graphit applets yourself before class will speed up instruction and troubleshooting in class
• Applets require updated Java player and Internet access
• High-level language in the student worksheet might require additional supports for ESL learners

• This resource is only available on an unencrypted HTTP website.It should be fine for general use, but don’t use it to share any personally identifiable information

Pros

• Lesson provides teaching notes and instructional methods
• Technology adds deeper understanding and streamlines messy calculations without reducing the purpose of the lesson
• Problems progress naturally from linear to curved, exact to approximate results, finite to infinite limits
• Worksheet focuses on meaning and interpretation of results

Cons

• No answer keys provided
• No discussion of midpoint sums vs. left/right sums

Common Core

HSG-GPE.B.7 MP3 MP4 MP6 MP8