Cookies and Pi

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Objective

SWBAT to apply the Fundamental Theorem of Calculus (FTC) to model and solve problems using integration.

Big Idea

Everyone loves cookies, even calculus students. Students apply their knowledge of integration to divide a special cookie fairly.

Video Narrative - Lesson Overview

Setting the Stage

40 minutes
Lesson Plan - Cookies and Pi, Setting the Stage.pdf page 1
Lesson Plan - Cookies and Pi, Setting the Stage.pdf page 2

Investigation

45 minutes
Lesson Plan - Cookies and Pi, Investigation.pdf page 1
Lesson Plan - Cookies and Pi, Investigation.pdf page 2

Closure + Homework

5 minutes

Closure Activity: Explain to your neighbor how we used the Fundamental Theorem of Calculus today in class.  Be specific about each use of the two parts of the FTC.

I want my students to understand the two parts of the FTC informally:

1) Derivatives and integrals “undo” each other

2) Definite integrals can be evaluated by computing the difference between the integrated function evaluated at the upper and lower limits of integration. 

Our work with variable limits of integration, including on the warm-up, graphically with the Trace Area Under Curve v1 applet, and with the Cookies and Pi applet, rely heavily on part 2 of the FTC but obviously we cannot exclude the relevance of part #1 either.

 

Tonight’s Homework:

F -  1988 #40,  1993 #34,   

I -   By Hand, evaluate RRAM4 for  on the interval .   

V - TEXTBOOK – read examples, solve problems evaluating definite integrals with variable upper limits of integration given graphs.   

E -  Set 6:  1969 #41, 1973 #42,  1985 #42,  1988 #39,  1993 #12,41,  2003 #77