## Approximating Area – Follow-Up

04 Nov

In an attempt to think more about setting goals and formative assessment, I posted my calculus lesson plan last night, and I am now reflecting on what actually happened.

I have learned deltax=((b-a)/(n)).

My question is why use rectangles and not trapezoid.

I have learned how geometry works in calculus.

My question is whats anosher way to do pump problem.

I have learned rieman sums.

My question is how to find the limit as the rectangles approach ∞.

I have learned more about approx area under curve.

My question is what mindbloxing thing are we learning next.

I have learned about Riemann rectangles and the difference in rectangle perspective.

My question is how to apply limits to this problem.

I have learned . trapizoids are extremely useful

My question is how to work an equation.

I have learned how to begin estimating area under curve.

My question is how to correctly find the area of curve.

I have learned that trapezoids are effective shapes to estimate area uner a curve.

My question is . how does the derivative relate

I have learned about riemann sums .

My question is i am confused on how to calculate midpoint rectangles.

I have learned that in order to obtain exact area, we must achieve infinite rectangles.

My question is how.

I have learned how to to estimate area .

My question is how to find exact area.

I have learned about how to not estimate area under a curve.

My question is why infinite rectangles doesn’t lead to infinite area.

I’ve sent an email to the student who is confused about midpoint rectangles to stop by during zero period on Thursday. She has already replied that she will come see me then.

The first I can statements for this unit are “I can approximate the area between two curves using left, right, and midpoint Riemann sums”, “I can approximate the area between two curves using the Trapezoidal Rule”, and “I can use an infinite number of rectangles to get the exact area between two curves”. I didn’t share these with students today, as I didn’t want to give what we were doing away too quickly. We definitely moved towards the first statement today. I’ll check where students think they are at the end of class next time as the journey continues …