VIEWS: 9 PAGES: 2 POSTED ON: 11/6/2012 Public Domain
Lesson Plans Week-At-A-Glance Week: Aug 27th - 31th AP Calculus AB A. Blume / M. Bowman Monday Tuesday Wednesday Thursday Friday Essential Question: Essential Question: Essential Questions: Essential Questions: Essential Questions: How can we put all of the limit How can I find the limits of graphs What is a derivative? What is the What is the derivative of a How do you find the derivative as a concepts together? and algebraic functions? difference between average rate function at a point and how is it function and what does the function of change and instantaneous rate related to the tangent line? What tell us about the derivative? What is of change? are the units of f‘? How can we a second derivative? determine if a function is differentiable over an interval? Standard: Standard: Standard: Standard: Standard: M.Calc.1.13 Limits: Infinity. M.Calc.1.13 Limits: Infinity. M.Calc.1.2 Derivatives: Define M.Calc.1.2 Derivatives: Define M. Calc. 1.15 Differentiation: The learner will be able to describe The learner will be able to The learner will be able to apply The learner will be able to apply Function Over Interval: The asymptotic behavior in terms of limits describe asymptotic behavior in the derivative to determine the the derivative to determine the learner will be able to determine if a involving infinity. terms of limits involving infinity. slope of a tangent line at a point, slope of a tangent line at a point, function is differentiable over an M.Calc.1.1 Limits: Evaluate M.Calc.1.1 Limits: Evaluate the equation of the tangent line to the equation of the tangent line to interval. Find where the derivative of The learner will be able to evaluate The learner will be able to a curve at a point and the a curve at a point and the a function fails to exist. the limits of a function algebraically evaluate the limits of a function equation of the normal line to a equation of the normal line to a and apply the properties of limits, algebraically and apply the curve at a point. curve at a point. M. Calc.1.8 Differentiation: including one sided limits. properties of limits, including one The learner will be able to Apply/Relation M.Calc.1.14 Applying Calculus sided limits. approximate the rate of change at M. Calc. 1.15 Differentiation: The learner will be able to use the Concepts: Continuity. M.Calc.1.14 Applying Calculus a point, graph of a function or a Function Over Interval relationships between f(x), f’(x), and The learner will be able to apply the Concepts: Continuity. table of values and define the The learner will be able to f”(x) to determine the increasing and definition of continuity to a function at The learner will be able to apply derivative in various ways: The determine if a function is decreasing behavior of f(x). a point and determine if a function is the definition of continuity to a limit of the difference quotient. differentiable over an interval. Determine critical points of f(x). continuous over an interval. function at a point and determine The slope of the tangent line at a Determine points where the Determine the concavity of f(x) over M.Calc.4.1 Limits: if a function is continuous over an point. Instantaneous rate of derivative of a function fails to an interval, the points of inflection of Approximate/Graphs interval. change The limit of the average exist. f(x). Sketch the graphs of f’(x) and The learner will be able to estimate M.Calc.4.1 Limits: rate of change. f”(x) when given f(x) and the graph of limits from graphs or tables of data. Approximate/Graphs f(x) when given f’(x). Estimate graphs from limits. The learner will be able to estimate limits from graphs or tables of data. Estimate graphs from limits. Objectives: Objectives: Objectives: Objectives: Objectives: The learner will be able to evaluate The learner will be able to The learner will be able to The learner will determine if a The learner will determine: limits, apply properties of limits, evaluate limits, apply properties approximate the rate of change at function is differentiable. The increasing and decreasing behavior determine if a function is continuous, of limits, determine if a function is a point, graph of a function or a learner will determine where the of f(x); its’ critical points; concavity over an interval, describe asymptotic continuous, over an interval, table of values and define the derivative would fail to exist and and points of inflection. Sketch the behavior and estimate limits from describe asymptotic behavior and derivative in various ways. The find the derivative at a point using graphs of f’(x) and f”(x) when given graphs. estimate limits from graphs. limit of the difference quotient. the alternate definition. f(x) The slope of the tangent line at a point. Instantaneous rate of change The limit of the average rate of change. Activities: Activities: Activities: Activities: Activities: Classwork: Class Activity: -Return Limits Test/go over -Using Definition of a Derivative Partner Work Limits Review Sheet Administer Limits Unit Test -Class Activity: Discovering the --- -Day 2 prob.(on Unit Plan) -the Derivative Multiple Choice Limits Derivative at a Point -HWork: p.124 (See Unit plan) - Major Curve Pieces Collect Homework -Assign: p.66 (see Unit Plan) Plus selected problems on Unit - The Derivative Function Hwork: finish review work Plan - Intro into Curve Sketching - HWork: p. 140 (Unit Plan)