Approximate area under a curve using geometric and numerical methods
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
Quick Lesson Plan
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.
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.
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.
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.