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# Calculus

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## Rick Hollenbeck

on 17 May 2016

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#### Transcript of Calculus

August 26th, 27th
Objective:
*Students will exhibit math practices #1, 3, 5, 6, 7, & 8 in interpreting key features of a function.
* Students will understand how to use function notation and describe key features of a function (i.e., increasing/decreasing; concave up/down)
*Students will understand how to measure the change of function (i.e., absolute, percentage, average)
Sketch a graph showing the relationship between temperature and time.
http://www.geogebratube.com/student/m46631

Measuring Change:
1. Determine the change in temperature between 4 A.M. and 5 P.M.
2. Determine the percentage change in temperature between 4 A.M. and 5 P.M.
3. Determine the average rate of change in temperature between 4 A.M. and 5 P.M.
http://www.geogebratube.com/student/m47093
August 28th, 29th
Objective:
*Students will exhibit math practices #1, 3, 5, 6, 7, & 8 in interpreting key features of a function.
*Students will understand how to measure the change of function (i.e., absolute, percentage, average)
*Students will graphically understand average rate of change
c) Calculate the average rate of change in the fish population (in fish per month) from 2002 to 2009
August 30th, September 3rd
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 5, 6 in creating position-time graphs
*Students will understand how to create and interpret position-time graphs

; over the interval [1,5]

September 4th, 6th
Objective:
*Students will exhibit math practices #1, 3, 5, 6, 7, & 8 in interpreting position-time graphs
*Students will understand how to determine total distance, displacement, and average-velocities given a position-time graph

http://www.geogebratube.com/student/m48000
a) Determine the object’s average rate of change in position over the interval 2≤t≤2.5 seconds?
b) Find an interval over which the average rate of change is as high as possible.
c) Determine the object's rate of change in position at t = 2 seconds.
September 9th, 10th
http://www.geogebratube.com/student/m48132
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 5, 6 in interpreting position-time graphs
*Students will understand how to compute instantaneous velocity
*Students will understand how to graphically compare average velocity with instantaneous velocity

Determine the object's velocity at t =12.
Sketch a graph of the object's velocity
September 11th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 5, 6 in interpreting position-time graphs
*Students will understand how to compute instantaneous velocity
*Students will understand how to graphically compare average velocity with instantaneous velocity

September 16th, 17th
Objective:
*Students will exhibit math practices #6, 7, 8, 1, 3, 5, to interpret derivatives.
*Students will understand derivative notation.
*Students will understand how to interpret derivatives in contexts other than position-time.

How much should the company spend on advertising? Explain.
September 18th, 19th, 20th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 5, 6 to interpret derivatives of functions expressed in multiple representations
*Students will understand derivative notation.
*Students will understand how to interpret derivatives in contexts other than position-time.

September 23rd, 24th
Objective:
*Students will exhibit math practices #6, 7, 8, 1, 3 to sketch derivative graphs
*Students will understand how to graph f' (x) given a graph of f(x).

September 25th, 30th, October 2nd, 3rd
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to determine a derivative algebraically
*Students will understand how to use the difference quotient and limits to evaluate a derivative
*Students will review the concept of a limit and understand how to evaluate a limit numerically, geometrically, and analytically

http://www.geogebratube.com/student/m50396
October 4th, 7th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to determine conditions for continuity; and to establish derivative rules for polynomial and power functions
*Students will understand how to use the concept of a limit to define continuity
*Students will understand how to find derivative equations for polynomial and power functions

October 8th, 9th
Objective:
*Students will exhibit math practices #1, 4, 3, 6, 7, 8 to solve a problem involving functions and its derivatives
*Review Power Rule
*Students will solve a problem involving cost and profit

October 14th, 15th
Objective:
*Students will exhibit math practices #2, 7, 8 to calculate rates of change for composite functions
*Students will apply prior knowledge to solve a contextual problem involving rates of change
*Students will understand how to calculate the rate of change of composite functions

October 17th, 21st
Objective:
*Students will exhibit math practices #2, 7, 8 to calculate rates of change for composite functions
*Students will apply prior knowledge to solve a contextual problem involving rates of change
*Students will understand how to calculate the rate of change of composite functions

October 22nd, 23rd
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to understand how to use the chain rule to determine derivatives of composite functions.
*Students will understand how to use the chain rule to determine derivatives of composite functions

October 28th, 29th
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to understand how to use the chain rule to determine derivatives of composite functions.
*Students will understand how to use the chain rule to determine derivatives of composite functions
October 30th, 31st
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to understand how to use the chain rule to determine derivatives of composite functions.
*Students will understand how to use the chain rule to determine derivatives of composite functions

November 4th, 5th
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to understand how find derivative involving the chain rule and product rule
*Students will understand how to find derivatives of functions involving the chain rule and product rule.

November 6th, 7th
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to understand formulas for the derivative of y=e^x, y=sin⁡x, y=cos⁡x
*Students will understand the formulas for the derivative of y=e^x, y=sin⁡x, y=cos⁡x

November 8th, 11th
Objective:
*Students will exhibit math practices #7, 8, 1, & 3 to use the chain rule and product rule with functions involving y=e^x, y=sin⁡x, y=cos⁡x
*Students will understand how to apply the chain rule and product rule to find derivative formulas for functions involving y=e^x, y=sin⁡x, y=cos⁡x

November 14th, 15th
Objective:
⁡*Students will exhibit math practices #7, 8, 1, 3, 6 to determine functions that are smooth (i.e. differentiable)
*Students will review how determine whether a function is continuous
*Students will understand how to determine whether a function is differentiable at a point
November 18th, 19th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to determine whether a function is differentiable and where a function has relative extrema
*Students will understand when a function is differentiable and when a function has relative extrema

Maxima, Minima, & Critical Points
First Derivative Test:
December 2nd, 3rd
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to understand the connection between an inflection point on f(x) and a relative extremum on f' (x)
*Review critical points, relative extrema. Understand absolute extrema.
*Students will understand the connection between an inflection point on f(x) and a relative extremum on f' (x).
December 4th, 5th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to understand the connections between f, f', and f''
*Students will understand the connections between f, f', and f''
Match a function graph with its derivative graph
December 6th, 11th
December 12th, 13th
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to understand the connections between f, f', and f''
*Students will understand the connections between f, f', and f''
Objective:
*Students will exhibit math practices #7, 8, 1, 3, 6 to understand the connections between f, f', and f''
*Students will understand the connections between f, f', and f''
December 18th, 19th
Objective:
*Students will exhibit math practices #1, 2, 3, 4, 5, and 6 to solve optimization problems.
*Students will solve optimization problems from economics (ch 4.5) and geometry and non-geometry constructed problems (ch 4.6)
January 2nd, 3rd
Objective:
*Students will exhibit math practices #1, 2, 3, 4, 5, and 6 to solve optimization problems.
*Students will solve optimization problems from economics (ch 4.5) and geometry and non-geometry constructed problems (ch 4.6)
January 6th, 7th
Objective:
*Students will exhibit math practices #1, 2, 3, 4, 5, and 6 to solve optimization problems.
*Students will solve optimization problems from economics (ch 4.5) and geometry and non-geometry constructed problems (ch 4.6)
January 13th, 14th
Objective:
*Students will exhibit math practices #1, 2, 3, 4, 5, 6, 7 and 8 to review for midterm
*Midterm Review
January 22nd, 23rd
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in determining displacement of an object given its velocity
*Students will understand how to use Riemann Rectangles to approximate the change in an object's position
*Students will understand the definition of an integral and how to use the calculator to determine the value of a definite integral
http://www.geogebratube.com/student/m78716
January 27th, 28th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in determining displacement of an object given its velocity
*Students will understand how to use Riemann Rectangles to approximate the change in an object's position
*Students will understand the definition of an integral and how to use the calculator to determine the value of a definite integral
Estimate the distance traveled by the object whose velocity is represented below:
January 29th, 30th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in applying the integral to solve problems
*Students will solve problems involving the use of a definite integral
Jan 31st, Feb 3rd
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in applying the integral to solve problems
*Students will solve problems involving the use of a definite integral
Feb 4th, 7th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in applying the integral to solve problems
*Students will solve problems involving the use of a definite integral
Feb 10th, 11th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in applying the integral
*Students will solve problems between f' and f without context
*Students will interpret the integral of f' when f' is positive and negative
Feb 18th - 21st
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in applying the integral
*Students will interpret the integral of f' in contexts when f' is positive and negative
Feb 24th, 25th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in solving problems involving the accumulation function (Section 5.3)
*Students will understand the accumulation function and solve problems involving it.
Feb 26th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in solving problems involving the accumulation function (Section 5.3)
*Students will understand the accumulation function and solve problems involving it.
March 5th, 6th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in solving problems involving the accumulation function (Section 5.3)
*Students will understand the accumulation function (starting at 0 and a) and solve problems involving it.
March 7th, 10th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in solving problems involving the accumulation function (Section 5.3)
*Students will understand the accumulation function (starting at 0 and a) and solve problems involving it.
*Students will understand the fundamental theorem of calculus (Section 5.4)
March 11th, 12th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in solving problems involving the fundamental theorem of calculus
*Students will solve problems relating to the fundamental theorem of calculus (Section 5.4)
March 13th, 14th
Objective:
*Students will exhibit math practices #7, 8 in understanding the connection between the integral function of f and the anti-derivative of f
*Students will review derivative rules for power functions & exponentials (base e)
*Students will calculate antiderivatives for power functions & exponentials (base e)
March 18th, 19th
Objective:
*Students will exhibit math practices #1, 3 in reviewing accumulating change (Sections 5.1 - 5.5)
*Solve problems involving accumulation of changes (5.1 - 5.5)
March 24th, 25th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding the Fundamental Theorem of Calculus (Part II)
*Students will understand the Fundamental Theorem of Calculus (Part II) [Section 5.6]
*Students will understand properties of definite integral
March 26th, 27th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding the Fundamental Theorem of Calculus (Part II) & Finding Areas Between Curves
*Students will use the FTC to determine area (Section 5.6) and understand how to find areas between curves (Section 5.7)
Determine the Area of the Shaded Region:
March 31st - April 3rd
Objective:
*Students will exhibit math practices #1, 3, 7, 8 to solve problems involving areas between curves
*Students will solve problems involving areas between curves (Section 5.7)
April 4th, 7th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 to understand the difference between average rate of change and average value of a function
*Students will solve problems involving average rate of change and average value (Section 5.8)
April 22nd, 23rd
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding demand curve and consumer surplus
*Final Exam Review #1
*Students will understand how to construct and interpret a demand curve.
*Students will understand how to calculate consumer expenditure and consumer surplus
April 25th, 28th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding demand curve and consumer surplus
*Final Exam Review #2
*Students will understand how to construct and interpret a demand curve.
*Students will understand how to calculate consumer expenditure and consumer surplus
April 29th,30th
May 6th, 7th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding demand curve and consumer surplus
*Final Exam Review #3
*Students will understand how to construct and interpret a demand curve.
*Students will understand how to calculate consumer expenditure and consumer surplus
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in reviewing for final
*Final Exam Review #4
May 8th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in understanding (informally) elasticity of demand
*Students will understand (informally) the concept of elasticity of demand
A demand curve is defined as follows:
For every \$1 increase in price, the quantity demanded decreases by 200.

Create scenarios for price and quantity where raising the price will create a greater revenue and scenarios for price and quantity where lowering the price will create a greater revenue.
May 9th, 12th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in reviewing for final
*Final Exam Review #5
May 13th, 14th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in reviewing for final
*Final Exam Review #6
May 15th, 19th
Objective:
*Students will exhibit math practices #1, 3, 7, 8 in reviewing for final
*Final Exam Review #7
SY 2013/2014
August 25th/26th
Objective: Students will understand the connection between the values of a function and the change of a function.
Students will understand how to calculate a function's average rate of change
http://www.geogebratube.org/student/m146164
The spread of a virus over a 30-day interval is modeled by the simulation shown below:
Big Idea
August 27th/28th
Objective: Students will understand how to represent average rate of change graphically
Students will understand characteristics of functions with positive, negative, zero, and constant rate of change
http://www.geogebratube.org/student/m146216
http://www.geogebratube.org/student/m146235
August 29th, September 2nd

Objective: Students will understand how to graphically represent the relationship between time and position of an object on a horizontal number line
Students will understand the meaning of the average change in position
Average vs. Instantaneous Velocity
Observations:
1. The farther the object travels in one second, the steeper the graph (Madi)
2. When the object stays in one place, the graph is constant (Leisha)
3. When the object is moving to the right, the graph is increasing;
when the object is moving to the left, the graph is decreasing (Madi)
September 4th, 5th
Objective: Students will use the context of a position-time graph to determine when a function's rate of change is positive or negative
Students will use the context of a position-time graph to determine when a function's rate of change is increasing or decreasing
For each of the graphs in Column B, create a table of values for [0, 6] that represents the function.
For each of the graphs in Column B, use your table of values to determine the average rate of change in position over [0,3] and [3,6].
Big Idea:
If the rate of change of f(x) is positive, then f(x) is increasing.
If the rate of change of f(x) is negative, then f(x) is decreasing.
If the rate of change of f(x) is increasing, then f(x) is concave up.
If the rate of change of f(x) is decreasing, then f(x) is concave down.

September 8th, 9th
Objective: Students will use the context of a position-time graph to understand how to determine a function's instantaneous change
Students will understand that an instantaneous rate of change involves finding a limit of an average rate of change
Big Idea
September 15th,16th
Objective: Students will understand the concept of a limit at a real number (and one-sided limits)
Students will understand how to evaluate a limit numerically and graphically
Definition of a Limit
One-Sided Limits
Understanding Limits
September 17th,18th
Objective: Students will understand the concept of a limit at a real number (and one-sided limits)
Students will understand how to evaluate a limit numerically, graphically, and analytically
Practice Problems
Practice Problems
September 19th,22nd
Objective: Students will understand the concept of continuity
Students will understand how to use limits to define continuity
Students will be able to evaluate a function to determine whether it is continuous
Big Idea
September 23rd, 29th
Objective: Students will understand how to determine the an instantaneous rate of change of a function numerically and analytically.
Students will understand how the definition of a derivative and understand derivative notation
Students will understand how to estimate rates of change from a graph
The Derivative and the Slope of a Graph
Big Idea
September 30th, October 1st,2nd
Objective: Students will understand the connection between derivative and slope
Students will understand slope written as a difference quotient
Students will understand the difference quotient definition of a derivative
(Another) Definition of a Derivative
October 3rd, 6th
Objective: Solve a problem involving the concept of slope and derivative
Students will understand how to evaluate a derivative using the TI-84 Calculator
Students will understand how to find the derivative function for polynomials and power functions.
Power Rule
SY 2014/2015
Finding a Derivative using TI-84
Derivative of Polynomials
Big Idea
October 7th, 8th
Objective: Apply the power rule to solve slope and rate of change problems
Understand how to interpret the derivative given a context
Interpreting Derivatives:
October 13th - 20th
Objective: Understand how to interpret the derivative given a context
Solve problems involving derivatives (economics context & position context)
October 21st, 22nd
Objective: Solve a problem from economics (Cost, Average Total Cost, Profit) involving the meaning of derivatives
Average Total Cost
Average Total Cost Example
October 27th, 28th
Objective: Solve a problem involving the rate of change of a composite function
October 29th, 30th
Objective: (Finish) Solve a problem involving the rate of change of a composite function
Understand the chain rule for finding derivatives of composite (polynomial) functions
Big Idea
Chain Rule:
October 31st, November 1st
Objective: Solve a problem involving the rate of change of a composite function
Understand the chain rule for finding derivatives of composite (polynomial) functions
November 5th, 6th
Objective: Understand and practice using the chain rule for finding derivatives of composite (polynomial) functions
Chain Rule
Big Idea
(Version 2)
November 7th, 10th
Objective: Practice applying the power rule and chain rule
Solve related rate problems
The radius of a circle is increasing at a rate of 0.5 cm/sec. At what rate is the area of the circle increasing (in square cm/sec) when the radius of the circle is 3 cm?
A circle starts off with a radius of 2 cm (at time t=0) and begins growing. The area of the circle is increasing at a rate of 2 square centimeters per second. Find the rate of change of the radius of the circle (in cm per sec) when the radius is 5 cm.
November 11th, 12th
Objective: Understand how to apply the chain rule to solve related rates problems.
Example 1
Example 2
November 17th, 18th
Objective: Understand the structure of the chain rule (be able to generalize the chain rule)
November 19th, 20th
Objective: Understand how to find the derivative of the product of two functions (the product rule)
Big Idea
The Product Rule
Quotient Rule
November 21st, 24th
Objective: Practice applying the power, chain, and product rule
Understand how to find the derivative of a quotient of two polynomials by using the quotient rule or using the product and chain rule
Nov. 25th, Dec. 1st, 2nd
Big Idea
Objective: Practice applying the derivative rules
Understand how to apply the derivative rules to find the slope of a curve using implicit differentiation
What is Implicit Differentiation
December 3rd, 4th
Objective: Review Algebra skills needed to solve implicit differentiation problems
Understand how to apply the derivative rules to find the slope of a curve using implicit differentiation
Homework:
December 5th - 10th
Objective: Practice differentiation techniques
December 15th, 16th
Graphing f'(x)

Objective: Algebra Review: Understanding features of f(x) -- increasing/decreasing, concave up/down, relative maximum/minimum
Students will understand how to sketch a graph of f'(x) from a graph of f(x)
December 17th, 18th
Objective: Midterm Review of: (1) Functions and Change; (2) Limits of Functions; (3) The Derivative Concept; and (4) Differentiation Techniques
January 9th,12th
Objective: Understand connections between f, f', and f''
Understand differentiable vs. non-differentiable functions
Match a function graph with its derivative graph
January 5th, 7th, 8th
December 19th, 22nd
Objective: Algebra Review: Understanding features of f(x) -- increasing/decreasing, concave up/down, relative maximum/minimum
Students will understand how to sketch a graph of f'(x) from a graph of f(x)
Big Idea
Objective: Understand connections between f, f', and f''
January 13th,14th
Objective: Understand connections between f, f', and f''
Understand differentiable vs. non-differentiable functions
January 20th
Objective: Midterm Review
Semester 1
Semester 2
January 28th, 29th
Objective: Develop problem solving and strategic competence skills for analyzing calculus multiple choice questions
Midterm examination rewind
Jan. 30th, Feb. 2nd
Objective: Understand the definition of critical points
Understand the first and second derivative tests for relative extrema
Maxima, Minima, & Critical Points
First Derivative Test
Second Derivative Test
February 3rd, 4th
Objective: Practice Solving Problems Re: interpreting f(x) given f'(x)
February 5th, 9th
Extreme Value Theorem
Examples of Sketching f'(x)
Objective: Understand strategies for sketching graphs of f(x) from f'(x)
February 12th, 13th
Objective: Understand that absolute extrema for a continuous function on [a, b] will occur either at relative extrema or an endpoint
(Extreme Value Theorem)
February 18th, 19th
Objective: (Review) Understand how to interpret position-time graphs.
Understand how to compute Riemann rectangles of a velocity graph to approximate a change in position
February 20th, 23rd

Objective: Understand how to compute Riemann rectangles of a velocity graph to approximate a change in position
Understand the definite integral is the limit of an infinite number Riemann rectangles
Use the integral function on the calculator to solve problems involving accumulation of change
Riemann Sum and the Definite Integral
Big Idea: The Definite Integral
Examples:
February 24th, 25th
Objective: Understand that area under a derivative curve of f(x) is the accumulation of change in f(x)
Area Under Velocity Curve
Feb 27th(B), March 4th(A)
Objective: Understand that area under a derivative curve of f(x) is the accumulation of change in f(x)
Solve a problem involving accumulation of change and rates of change
March 3rd(B), 10th(A)
Objective: Solve problems involving accumulation of change and rates of change
March 11th(B),16th(A)
Objective: Understand how areas accumulate when f' is positive and negative
Solve problems involving positive and negative change
Riemann Sums for Negative f(x)
March 17th(B), 20th(A)
March 23rd(B), 26th(A)
Objective: Understand how areas accumulate when f' is positive and negative
Solve problems involving positive and negative change
Antiderivatives
Objective: Understand how to find equations for f(x) (called antiderivatives) given f'(x)
Understand notation for antiderivatives (i.e. F(x) and indefinite integral)
Anti-Power Rule
Big Idea: Antiderivative
Big Idea: Antipower Rule
Mar 25th(B), Apr 7th (A)
Big Idea: Fundamental Thm. of Calculus
Objective: Use antiderivatives to solve problems (i.e. Apply the Fundamental Thm. of Calculus)

Fundamental Thm. of Calculus
April 8th (B), 9th (A)
Objective: Use antiderivatives to solve problems (i.e. Apply the Fundamental Thm. of Calculus)

April 10th(B), 13th(A)
Objective: Understand the accumulation function and a second form of the Fundamental Theorem of Calculus
Accumulation Function
Big Idea: (Another Version)
Fundamental Theorem of Calculus
April 14th(B), 15th(A)
Objective: Solve a problem involving the integral as a function (called the Accumulation Function)
Understand how to distinguish and compute average rates of change vs. average value
Big Idea:
Average value of f(x)
April 24th(B), 27th(A)
Objective: Final Exam Review #1
Practice solving questions involving 2 rates of change
April 16th(B), 21st(A)
Objective: Solve problems involving the integral as a function (called the Accumulation Function)
April 22nd(B), 23rd(A)
Objective: Understand how to distinguish and calculate average rates of change and average value
Solve problems involving 2 rates of change
April 28th(B), 29th(A)
Objective: Final Exam Review #2
Practice solving questions involving 2 rates of change
April 30th(B), May 4th(A)
Objective: Final Exam Review #3
Practice solving questions involving 2 rates of change
May 7th(B), 8th(A)
Objective: Final Exam Review #4
Practice solving questions involving non-time rates of change
May 11th(B), 12th(A)
Objective: Final Exam Review #5
SY 2015/2016
August/September
August 24th,25th
Objective: Students will understand how to interpret key features (i.e., positive/negative, increasing/decreasing, concave up/concave down) of functions represented multiple ways (i.e., graph, table, equation)
Positive/Negative Intervals
Increasing/Decreasing Intervals
Concave up/down Intervals
(Stop at 10:15 mark)
Big Idea
August 26th, 27th
Objective: Students will understand how to examine a table of function values to determine concavity
Determining Concavity from Tables
Big Idea
Understanding Linear Functions
August 31st
Objective: Students will understand the definition of concavity by comparing average rates of change.
Students will understand how to compute and interpret average rates of change.
Average Rate of Change
Big Idea
Big Idea
September 1st
Objective:
*Use a problem context to review functions and function notation.
*Use a problem to interpret average rate of change.
Sketch a graph showing the relationship between temperature and time.
http://tube.geogebra.org/material/simple/id/46631

September 2nd, 3rd
Objective: (Canvas Training First 1/2 both days)
*Use a problem to interpret average rate of change.

September 8th
Objective:
*(Again) Create a table of function values that are consistent with criteria of a function (i.e., positive/negative, increasing/decreasing, concave up/down

September 9th
Objective:
*Solve a problem in context involving average rate of change
September 10th
Objective:
*(More) Understand positive, zero, and negative rate of change
September 11th
Objective:
*Understand how to construct and interpret a position-time graph
September 15th
Objective:
*Understand the connection between average rate of change vs. instantaneous change
Average vs. Instantaneous Change
Big Idea

September 16th, 17th
Objective:
*Introduce the concept and definition of a limit (including one-sided limits)

Introducing the Limit Concept
Definition of a Limit
One-Sided Limits
August 28th
Objective: Students will understand constant rate of change and linear functions
September 21st,22nd
Objective:
*Understand representations of piecewise defined functions and use piecewise defined functions to answer limit questions

Understanding Limits of Piecewise Defined Functions
September 24th
Objective:
*Understand how to evaluate limits of piecewise defined graphs

September 24th, 28th
Objective:
*Understand how to evaluate limits of piecewise defined equations

Limits of Piecewise Defined Equations
September 29th
Objective:
*Understand how to evaluate limits of piecewise defined equations

September 30th
Objective:
*Understand how to evaluate limits analytically

Solution to #1 & #2
Solution to #3 & #4
October
October 5th, 6th
Objective: Students will understand the concept of continuity
Students will understand how to use limits to define continuity
Students will be able to evaluate a function to determine whether it is continuous
Big Idea
October 7th
Objective: Students will understand the concept of continuity and determine when a function is continuous
Review Instantaneous Change
October 8th
Objective: Introduce the definition of a derivative and derivative notation
Solve questions involving the derivate concept and notation
Introducing the Derivative
Derivatives and Slope
October 9th
Objective: Solve quetions involving rates of change and slope
October 12th, 13th
Objective: Evaluate derivatives with TI-84 nderiv command and analtyically using limits
Finding Derivatives with TI-84
October 20th, 21st
Objective: Understand how to use the power rule to calculate derivatives

Power Rule
Derivative of Polynomials
Difference Quotient
Difference Quotient
October 22nd
Objective: Apply the power rule to determine the concavity of a function
October 23rd, 26th
Objective: Apply the power rule to solve a problem in context
October 27th
Objective: Understand how to interpret meanings of derivatives in context
Introduce marginal analysis
October 28th,29th
Objective: Understand marginal cost and revenue and their interpretations
Marginal Cost
October 30th
Objective: Understand composite functions and change or composite functions
November
November 2nd
Objective: (Continue the problem from last class) Understand Composite functions and change of composite functions
November 3rd
Objective: Introduce the chain rule and apply the chain rule to solve a problem
Big Idea
Chain Rule:
November 4th, 5th
Objective: (Substitute - SAT Presentation) Review/practice quiz questions
November 9th
Objective: Review important concepts/misconceptions from quiz
November 10th
Objective: Practice applying the chain rule
November 11th
Objective: Understand the structure of the chain rule
November 12th
Objective: Solve a problem involving the change of products
November 13th
Objective: Understand and practice using the product rule.
Big Idea
The Product Rule
Quotient Rule
Big Idea
November 16th, 17th
Objective: Introduction to Related Rates Problems
#4 is solved at 5:15
November 18th, 19th
Objective: Practice solving related rates problems
Related Rates Example #1
Related Rates Example #2
November 24th
Objective: Understand the importance of problem solving
Ted Talk: A Passion for Math
December
Nov 30th, Dec 1st
Objective: Solve related rates problem explicitly and implicitly
December 2nd
Objective: Introduce the quotient rule; practice derivative rules
December 3rd
Objective: Introduce implicit differentiation; finding slopes of curves
Implicit Defined Functions
December 4th, 7th
Objective: Introduce implicit differentiation; finding slopes of curves
What is Implicit Differentiation
December 8th
Objective: Practice finding slopes of implicitly defined curves
December 9th, 10th
Objective: Revisit Related Rate Questions
Intensity of Light
Another Example
December 14th
Objective: Understand how to sketch f'(x) given a graph of f(x)
December 15th
Objective: Understand how to sketch f'(x) given a graph of f(x)
How to Sketch f'(x)
December 16th
Objective: Understand how to sketch f'(x) given a graph of f(x)
December 17th
Objective: Understand the concept of differentiability
December 18th
Objective: Understand the connections between f(x) and f'(x)
December 21st
Objective: Substitute -- Midterm Review
December 22nd
Objective: Understand connections between f(x) and f'(x)
December 23rd
Objective: Understand the graph of f(x) given f'(x)
January
January 4th
Objective: Understand the graph of f(x) given f'(x)
Example #1: f(x) from f'(x)
Example #2: f(x) from f'(x)
January 5th
Objective: Understand the graph of f(x) given f'(x)
January 6th
Objective: Understand the graph of f(x) given f'(x)
Match a function graph with its derivative graph
January 7th
Objective: Understand the graph of f(x) given f'(x) (in problem context)
January 8th
Objective: Introduce terminology (i.e., inflection points, critical points, second derivative)
January 11th
Objective: Review graphing f' to f and f to f'
January 13th, 14th
Objective: Midterm Review
January 15th
Objective: Midterm Review
February 11th
February
February 2nd, 3rd
Objective: (Again) Introduce terminology (i.e., inflection points, critical points, second derivative)
Big Idea: First Derivative Test
Big Idea: Critical Points
Objective: Understand how to determine the relative extrema for a function
Big Idea: Second Derivative Test
February 4th, 10th
Objective: Understand connections between f(x), f'(x), and f''(x)
February 12th
Objective: Understand how to classify critical points (1st & 2nd derivative test); Introduce how to evaluate f from f'
February 17th
Objective: Questions/Review connections between f, f', and f''
February 18th
Objective: Make conjectures regarding how to approximate values of f from f'
February 22nd, 23rd
Objective: Introduce Riemann sums and definite integral
Riemann Sum and the Definite Integral
Big Idea: The Definite Integral
February 24th
Objective: Understand how to compute areas to estimate f(x) from f'(x)
February 25th
Objective: Understand how to compute areas to estimate f(x) from f'(x)
February 26th
Objective: Understand how to compute areas to estimate f(x) from f'(x)
March
February 29th
Objective: Understand how to compute areas (positive & negative) to estimate f(x) from f'(x)
March 1st
Objective: Understand how to compute areas (positive & negative) to estimate f(x) from f'(x)
Riemann Sums for Negative f(x)
Big Idea
March 2nd
Objective: Understand how to compute areas (positive & negative) to estimate f(x) from f'(x); solve a problem involving f' to f
March 3rd
Objective: Understand how to compute areas (positive & negative) to estimate f(x) from f'(x); solve a problem involving f' to f
March 7th
Objective: Understand the integral as a function; (Part I) Fundamental Theorem of Calculus
Accumulation Function
Big Idea: Fundamental Theorem of Calculus
March 8th
Objective: Understand the integral as a function; (Part I) Fundamental Theorem of Calculus
March 9th
Objective: Understand how to compute average value vs. average rate of change
March 10th, 11th
Objective: Questions/review re: accumulation of change

March 14th, 15th
Objective: Understand how to compute average value vs. average rate of change
Big Idea
Average Value
March 16th
Objective: Understand the connection between average rate of change of f and average value of f'
March 17th
Objective: Solve sample quiz problems re: fundamental theorem of calculus and average change and value
March 21st
Objective: Understand when to use f(x), f'(x), int(f(x))
March 22nd
Objective: Understand when to use f(x), f'(x), int(f(x))
March 23rd
Objective: Understand how to find an anti-derivative
Antiderivatives
Anti-Power Rule
Big Idea: Antiderivative
Big Idea: Antipower Rule
April
March 24th
Objective: Review the companion (hw) problem from March 21st
April 4th
Objective: Understand how to use the anti-power rule to compute anti-derivatives
April 5th
Objective: Apply the anti-power rule to solve a problem (rectilinear motion)
April 6th
Objective: Understand the Fundamental Theorem of Calculus (Part II)
Big Idea: Fundamental Thm. of Calculus
Fundamental Thm. of Calculus
April 7th
Objective: Understand the Fundamental Theorem of Calculus (Part II)
April 8th
Objective: Solve problem contexts involving two rates of change
April 11th
Objective: Solve problem contexts involving two rates of change
April 12th
Objective: Solve problem contexts involving two rates of change
April 13th
Objective: Solve problem contexts involving two rates of change; Solve for areas between curves
April 14th
Objective: Determine areas and areas between curves
Big Idea
Area Between Curves

April 15th, 18th
Objective: Determine areas and areas between curves
April 20th
Objective: Redo quiz question #1
April 21st
Objective: Areas between curves -- Economics example
April 22nd
Objective: Final Review #1; Understand demand curve, expenditure, & consumer surplus
April 25th
Objective: Final Review #2; Understand demand curve, expenditure, & consumer surplus
April 27th
Objective: Understand demand curve, expenditure, & consumer surplus
April 28th
Objective: Understand demand curve, expenditure, & consumer surplus
May
May 2nd
Objective: (Substitute) Review for Quiz (Final Exam #3)
May 4th, 5th
Objective: Understand how to maximize revenue (introduction to elasticity of demand)
Elasticity of Demand
May 6th
Objective: Final Exam review #4
May 9th, 10th
Objective: Final Exam review #5
May 11th
Objective: Experience a sample Calculus lecture
Sample Calculus Lecture
(Fundamental Theorem of Calculus)
May 12th
Objective: Final Exam Review #6
Full transcript