## Reflection: Discourse and Questioning Area Under a Curve - Day 1 of 2 - Section 2: Share

After I let the class know that we are going to stick with rectangles to estimate the area of the region, I ask them how we could get a more accurate estimate than just using the 6 rectangles we started with. Here are a few (really clever and insightful) ideas that my students came up with - I was really impressed with their thinking.

1) Find the area of the six rectangles below the curve and the area of the six rectangles above the curve. Then take the average of both of these to get a better estimate.

2) Instead of having the height of each rectangle on the left or the right of the interval, have the rectangle's height in the midpoint of each region. This way there is a shaded and unshaded portion of each rectangle (shown here) and these regions can almost cancel each other out.

3) Use the rectangles that are above the curve and then estimate the area of the overage by using triangles. Then we can subtract the values to get a better estimate.

Discourse and Questioning: How to Get a Better Estimate

# Area Under a Curve - Day 1 of 2

Unit 9: Sequences and Series
Lesson 13 of 18

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

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Standards:
Subject(s):
Math, Precalculus and Calculus, Sequences and Series, partial sum, area, limit
50 minutes