# Mid-America Transportation Center

## Teacher Resource Center

Lesson Overview
 Lesson Title: Reimann Sums Teachers: Mrs. Sara Bonn (Primary) Brief Description: Students will explore finding the area under a curve using Left Rectangular, Right Rectangular, and Midpoint Rectangular Approximation Methods. Topics Introduced: Reimann Sums Suggested Grade Levels: 12th Grade Subjects: Mathematics

Lesson Information
Learning Expectations:

By the end of the lesson, students should be able to approximate the area under various curves using the rectangular approximation methods. They should understand when these approximations are over-estimates versus under-estimates. Finally, they should be left with the idea that ideally, we want to use as many rectangles as possible to give the most accurate approximation.

Plan Of Action:

Typically the first lesson taught when introducing integrals is this one. Students can use their knowledge of geometry to expand the concept of area to approximate the area when speed varies.

Data Set Used:

Students use the area formula for rectangles to approximate the area under a curve.

Materials Needed:

All students should have paper and a pencil to compute their estimates. Besides projecting this lesson, a separate dry erase board or flip chart is helpful, especially when drawing the difference between a left, right and midpoint rectangular approximation.

Preparation Period:

No preparation time is required for this lesson.

Implementation Period:

Students should be able to satisfactorily explore this lesson within 45 minutes.

Unexpected Results:

Several students identified not just the LRAM, RRAM and MRAM options, but also the Trapezoidal approximation. Typically, this method isn't discussed until later.

Lesson Files
Estimating with Finite Sums
Students will explore finding the area under a curve using LRAM, RRAM and MRAM.
[size: 870912] [date uploaded: Mar 24, 2012, 9:02 pm ]

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