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=sinx, y=cosx

*Students will understand the formulas for the derivative of y=e^x, y=sinx, y=cosx

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=sinx, y=cosx

*Students will understand how to apply the chain rule and product rule to find derivative formulas for functions involving y=e^x, y=sinx, y=cosx

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