# Review 5.6-5.9 (Lessons 5.6-5.9)

###### Unit 0: Prerequisites

**Day 1:**The Cartesian Plane**Day 2:**Equations of Circles**Day 3:**Solving Equations in Multiple Representations**Day 4:**Reasoning with Formulas**Day 5:**Quiz 0.1 to 0.4**Day 6:**Linear Relationships**Day 7:**Reasoning with Slope**Day 8:**Set Notation**Day 9:**Quiz 0.5 to 0.7**Day 10:**Unit 0 Review**Day 11:**Unit 0 Test

###### Unit 1: Functions

**Day 1:**Functions and Function Notation**Day 2:**Domain and Range**Day 3:**Rates of Change and Graph Behavior**Day 4:**Library of Parent Functions**Day 5:**Transformations of Functions**Day 6:**Transformations of Functions**Day 7:**Even and Odd Functions**Day 8:**Quiz 1.1 to 1.6**Day 9:**Building Functions**Day 10:**Compositions of Functions**Day 11:**Inverse Functions**Day 12:**Graphs of Inverse Functions**Day 13:**Piecewise Functions**Day 14:**Quiz 1.7 to 1.11**Day 15:**Unit 1 Review**Day 16:**Unit 1 Test

###### Unit 2: Polynomial and Rational Functions

**Day 1:**Connecting Quadratics**Day 2:**Completing the Square**Day 3:**Polynomials in the Short Run**Day 4:**Polynomials in the Long Run**Day 5:**Review 2.1-2.4**Day 6:**Quiz 2.1 to 2.4**Day 7:**Factor and Remainder Theorem**Day 8:**Factor and Remainder Theorem**Day 9:**Complex Zeros**Day 10:**Connecting Zeros Across Multiple Representations**Day 11:**Intro to Rational Functions**Day 12:**Graphing Rational Functions**Day 13:**Quiz 2.5 to 2.9**Day 14:**Unit 2 Review**Day 15:**Unit 2 Test

###### Unit 3: Exponential and Logarithmic Functions

**Day 1:**Exponential Functions**Day 2:**Graphs of Exponential Functions**Day 3:**Compound Interest and an Introduction to "e"**Day 4:**Review 3.1-3.3**Day 5:**Quiz 3.1 to 3.3**Day 6:**Logarithmic Functions**Day 7:**Graphs of Logarithmic Functions**Day 8:**Logarithm Properties**Day 9:**Solving Exponential and Logarithmic Equations**Day 10:**Quiz 3.4 to 3.7**Day 11:**Exponential and Logarithmic Modeling**Day 12:**Unit 3 Review**Day 13:**Unit 3 Test

###### Unit 4: Trigonometric Functions

**Day 1:**Right Triangle Trig**Day 2:**Inverse Trig Ratios**Day 3:**Radians and Degrees**Day 4:**Unit Circle**Day 5:**Unit Circle**Day 6:**Other Trig Functions**Day 7:**Review 4.1-4.6**Day 8:**Quiz 4.1 to 4.6**Day 9:**Graphing Sine and Cosine**Day 10:**Transformations of Sine and Cosine Graphs**Day 11:**Graphing Secant and Cosecant**Day 12:**Graphing Tangent and Cotangent**Day 13:**Quiz 4.7 to 4.10**Day 14:**Inverse Trig Functions**Day 15:**Trigonometric Modeling**Day 16:**Trigonometric Identities**Day 17:**Unit 4 Review**Day 18:**Unit 4 Review**Day 19:**Unit 4 Test

###### Unit 5: Applications of Trigonometry

**Day 1:**Law of Sines**Day 2:**The Ambiguous Case (SSA)**Day 3:**Law of Cosines**Day 4:**Area and Applications of Laws**Day 5:**Vectors**Day 6:**Review 5.1-5.5**Day 7:**Quiz 5.1 to 5.5**Day 8:**Polar Coordinates**Day 9:**Equations in Polar and Cartesian Form**Day 10:**Polar Graphs Part 1**Day 11:**Polar Graphs Part 2**Day 12:**Review 5.6-5.9**Day 13:**Quiz 5.6 to 5.9**Day 14:**Parametric Equations**Day 15:**Parametric Equations (With Trig)**Day 16:**Unit 5 Review**Day 17:**Unit 5 Test

###### Unit 6: Systems of Equations

**Day 1:**What is a Solution?**Day 2:**Solving Systems with Substitution**Day 3:**Solving Systems with Elimination**Day 4:**Review 6.1-6.3**Day 5:**Quiz 6.1 to 6.3**Day 6:**Solving Systems in 3 Variables**Day 7:**Solving Systems in 3 Variables**Day 8:**Partial Fractions**Day 9:**Unit 6 Review**Day 10:**Unit 6 Test

###### Unit 7: Sequences and Series

**Day 1:**Introducing Sequences**Day 2:**Using Sequences and Series to Describe Patterns**Day 3:**Arithmetic Sequences and Series**Day 4:**Review 7.1-7.2**Day 5:**Quiz 7.1 to 7.2**Day 6:**Geometric Sequences and Finite Series**Day 7:**Infinite Geometric Sequences and Series**Day 8:**Proof by Induction**Day 9:**Proof by Induction**Day 10:**Quiz 7.3 to 7.5**Day 11:**Unit 7 Review**Day 12:**Unit 7 Test

###### Unit 8: Limits

**Day 1:**What is a Limit?**Day 2:**Evaluating Limits Graphically**Day 3:**Evaluating Limits with Direct Substitution**Day 4:**Evaluating Limits Analytically**Day 5:**Evaluating Limits Analytically**Day 6:**Review 8.1-8.4**Day 7:**Quiz 8.1 to 8.4**Day 8:**Continuity**Day 9:**Continuity**Day 10:**Intermediate Value Theorem**Day 11:**Intermediate Value Theorem**Day 12:**Review 8.5-8.6**Day 13:**Quiz 8.5 to 8.6**Day 14:**Limits at Infinity**Day 15:**Unit 8 Review**Day 16:**Unit 8 Test

###### Unit 9: Derivatives

**Day 1:**Introduction to Derivatives**Day 2:**Average versus Instantaneous Rates of Change**Day 3:**Calculating Instantaneous Rate of Change**Day 4:**Calculating Instantaneous Rate of Change**Day 5:**The Derivative Function**Day 6:**The Derivative Function**Day 7:**Review 9.1-9.3**Day 8:**Quiz 9.1 to 9.3**Day 9:**Derivative Shortcuts**Day 10:**Differentiability**Day 11:**Connecting f and f’**Day 12:**Connecting f and f’**Day 13:**Review 9.4-9.6**Day 14:**Quiz 9.4 to 9.6**Day 15:**Derivatives of Sine and Cosine**Day 16:**Product Rule**Day 17:**Quotient Rule**Day 18:**Review 9.7-9.9**Day 19:**Quiz 9.7 to 9.9**Day 20:**Unit 9 Review**Day 21:**Unit 9 Test

###### Unit 10: (Optional) Conic Sections

**Day 1:**Intro to Conic Sections**Day 2:**Defining Parabolas**Day 3:**Working with Parabolas**Day 4:**Quiz 10.1 to 10.3**Day 5:**Defining Ellipses**Day 6:**Working with Elllipses**Day 7:**Defining Hyperbolas**Day 8:**Working with Hyperbolas**Day 9:**Quiz 10.4 to 10.7**Day 10:**Unit 10 Review**Day 11:**Unit 10 Test

#### Learning Targets

Tasks/Activity | Time |
---|---|

Explain Activity | 5 minutes |

Speed Dating | 35 minutes |

Debrief Activity | 10 minutes |

#### Activity: Speed Dating

#### Lesson Handouts

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#### Answer Key

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#### Additional Media

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#### Experience First

Arrange the desks into concentric circles or 2 straight rows, where two desks are always facing each other. Print the problems and cut them up, placing one problem on each pair of desks. Students can work in notebooks or on mini whiteboards. You will need a timer as well.

In this speed dating activity students will work with a variety of partners on some review questions. We recommend giving about 1-2 minutes for each “date” before having students switch desks to work on a new problem with a new partner. If your desks are arranged in circles, let the outer circle move clockwise and the inner circle move counterclockwise. If you have rows of desks, have one side move toward the front and the other move toward the back.

#### Formalize Later

Since students are reviewing for tomorrow’s checkpoint, there is no new information presented in today’s activity. Nevertheless, the activity does pose some challenges for students so a debrief of the hardest questions would round out the lesson well. The hardest questions for our students were A and D. Students still confused the meaning of a negative radius versus a negative angle, thinking that both represented a reflection, instead of an angle measured clockwise.

In question D, students had to write the equation of the line given by θ=5π/6. Many students were still not able to recognize this as a line passing through the pole with slope given by tan(5pi/6).