Reflection: Complex Tasks Area Under a Curve - Day 1 of 2 - Section 1: Launch and Explore


I am always interested in how students will estimate the area of the shaded region. Here are the different options that some students came up with. Student #1 used a triangle to estimate the region. Student #2 used rectangles (similar to how we will use more and more rectangles to get a better estimate). These rectangles are below the curve but we will use the rectangle above the curve. Student #3 used trapezoids since they more closely resembled the curve of the parabola. Finally, student #4 used rectangles but then deducted the unshaded areas of the triangle-like regions.

  Complex Tasks: Student Ideas
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Area Under a Curve - Day 1 of 2

Unit 9: Sequences and Series
Lesson 13 of 18

Objective: SWBAT use a sequence to estimate the area under a curve.

Big Idea: How can we find the area of highly irregular regions?

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Math, Precalculus and Calculus, Sequences and Series, partial sum, area, limit
  50 minutes
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