MMSI APSI Day 5

Each person completing this for credit gave a brief explanation of a lesson.

(1)  FTC redesign of Definite Integral Unit

(2)  Graphs of f, f’, f”:  given a function find first, second derivative, review some precalc polynomial sketching.  Complete table after check-in for where graphs are concave up, increasing, positive, concave down, decreasing, negative.  Helps them find intervals where things are true.  Like f concave up with f” positive.  Use vertically aligned graphs and highlight same color, connected concepts.

(3) a.  FTC, working on getting kids to chain rule the upper limit using example we did this week.  b.  inverse functions working on getting kids to not memorize, but instead derive it each time–easy and not too bad to remember.  c.  volumes in cross-sections, how do we get kids to keep the pi out?

(4)  Passed out playdough and forks.  Graph a pair of functions on paper, use playdough to create a solid with semicircular, or triangular cross-sections.

(5) Exploration activity for starting integrals.  Find the area based on a graph.  Counting boxes and slicing up things using rectangular or trapezoidal approximation.

(6)  Overestimates and Underestimates based on concavity.  Using calculus in motion.  How do we know if a tangent line gives an over/under estimate based on curve.

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