LESSON PLAN FOR WEEK 1 Sections to be covered: 5.1, 5.2, 5.3 --------------------------------------------------------------- MONDAY: review activity from last week discuss what assumption is being made in the problem how did they solve it: dicussion of area under a curve as distance start new example: area under x^3 write down estimate using rectangles then introduce sigma notation now they want to know how to figure out what sigma(i^3) is so... activity: sigma detectives (use as is, 15 minutes) now use activity to write down sum formulas & properties of sums so they'll be handy for tomorrow tell students they need to read book, since we won't cover every detail in class hand out homework #1 --------------------------------------------------------------- TUESDAY: definition of a definite integral/Riemann sum in full notational glory set up several examples activity: Barehands Ingration (parts 1-8, 25 minutes?) --------------------------------------------------------------- WEDNESDAY: finish up activity and go over it review definition of definite integral/Rieman sums discuss generic sample points/midpoint rule discuss idea of signed area briefly mention basic properties of integration go over comparision of integrals lead into idea that this method is too difficult for most real problems, and we want a quicker method for finding areas (this foreshadows Evaluation Theorem) --------------------------------------------------------------- THURSDAY/FRIDAY: state Evaluation Theorem -- isn't it wonderful, we now have a much easier way to do integrals define concept of an indefinite integral interactively write down all the easy indefinite integrals that they should already know activity: Clearing the Hill (use as is, 25-30 min?)