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## Unit 6 - Day 3

##### All Units
###### ​Learning Objectives​
• Approximate area under a curve using geometric and numerical methods

###### ​Success Criteria
• I can use trapezoidal sums to approximate area under a curve
I can explain why trapezoidal sums are the average of LRAM and RRAM values
I can use non-uniform partitions to approximate area under a curve given tabular data

###### Overview

We revisit Jayda’s motorcycle trip again to summarize student work with rectangular approximation methods and introduce trapezoidal sums. Students use trapezoids to approximate the area between a rate of change curve and the x-axis, then discover the relationship between trapezoidal sums and LRAM and RRAM approximations.

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###### Teaching Tips

Encourage students to consider the width of each subinterval (and therefore the width of each rectangle) before beginning their work. We have included more examples of non-uniform subintervals so students become comfortable working with that situation. Continue to expect labels and context-rich interpretations.

###### Exam Insights

The AP Test often presents information about the rate of change curve in tabular form. And, often, the values reflect non-uniform subintervals. Presenting multiple opportunities to work with subintervals of varying width will prepare your students to handle these questions on the AP Test.

###### Student Misconceptions

One of the most common frustrations students experience with rectangular approximation methods is identifying the appropriate x-value to use when finding the height of a rectangle. Providing extra practice may be necessary. Day 2 of Topic 6.2 is designed for review: revisit this skill as you introduce trapezoidal techniques and strategies for working with data in tabular formats.

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