###### Unit 1: Sequences and Linear Functions

**Day 1:**Recursive Sequences**Day 2:**Applications of Arithmetic Sequences**Day 3:**Sum of an Arithmetic Sequence**Day 4:**Applications of Geometric Sequences**Day 5:**Sequences Review**Day 6:**Quiz 1.1 to 1.4**Day 7:**Linear Relationships**Day 8:**Point-Slope Form of a Line**Day 9:**Standard Form of a Linear Equation**Day 10:**Quiz 1.5 to 1.7**Day 11:**Unit 1 Review**Day 12:**Unit 1 Test

###### Unit 2: Linear Systems

**Day 1:**Linear Systems**Day 2:**Number of Solutions**Day 3:**Elimination**Day 4:**Larger Systems of Equations**Day 5:**Quiz 2.1 to 2.4**Day 6:**Systems of Inequalities**Day 7:**Optimization Using Systems of Inequalities**Day 8:**Quiz 2.5 to 2.6**Day 9:**Unit 2 Review**Day 10:**Unit 2 Test

###### Unit 3: Function Families and Transformations

**Day 1:**Interpreting Graphs**Day 2:**What is a Function?**Day 3:**Translating Functions**Day 4:**Quiz 3.1 to 3.3**Day 5:**Quadratic Functions and Translations**Day 6:**Square Root Functions and Reflections**Day 7:**Absolute Value Functions and Dilations**Day 8:**Equations of Circles**Day 9:**Quiz 3.4 to 3.7**Day 10:**Unit 3 Review**Day 11:**Unit 3 Test

###### Unit 4: Working with Functions

**Day 1:**Using Multiple Strategies to Solve Equations**Day 2:**Solving Equations**Day 3:**Solving Nonlinear Systems**Day 4:**Quiz 4.1 to 4.3**Day 5:**Combining Functions**Day 6:**Composition of Functions**Day 7:**Inverse Relationships**Day 8:**Graphs of Inverses**Day 9:**Quiz 4.4 to 4.7**Day 10:**Unit 4 Review**Day 11:**Unit 4 Test

###### Unit 5: Exponential Functions and Logarithms

**Day 1:**Writing Exponential Functions**Day 2:**Graphs of Exponential Functions**Day 3:**Applications of Exponential Functions**Day 4:**Quiz 5.1 to 5.3**Day 5:**Building Exponential Models**Day 6:**Logarithms**Day 7:**Graphs of Logarithmic Functions**Day 8:**Quiz 5.4 to 5.6**Day 9:**Unit 5 Review**Day 10:**Unit 5 Test

###### Unit 6: Quadratics

**Day 1:**Forms of Quadratic Equations**Day 2:**Writing Equations for Quadratic Functions**Day 3:**Factoring Quadratics**Day 4:**Factoring Quadratics. Part 2.**Day 5:**Solving Using the Zero Product Property**Day 6:**Quiz 6.1 to 6.4**Day 7:**Completing the Square**Day 8:**Completing the Square for Circles**Day 9:**Quadratic Formula**Day 10:**Complex Numbers**Day 11:**The Discriminant and Types of Solutions**Day 12:**Quiz 6.5 to 6.9**Day 13:**Unit 6 Review**Day 14:**Unit 6 Test

###### Unit 7: Higher Degree Functions

**Day 1:**What is a Polynomial?**Day 2:**Forms of Polynomial Equations**Day 3:**Polynomial Function Behavior**Day 4:**Repeating Zeros**Day 5:**Quiz 7.1 to 7.4**Day 6:**Multiplying and Dividing Polynomials**Day 7:**Factoring Polynomials**Day 8:**Solving Polynomials**Day 9:**Quiz 7.5 to 7.7**Day 10:**Unit 7 Review**Day 11:**Unit 7 Test

###### Unit 8: Rational Functions

**Day 1:**Intro to Rational Functions**Day 2:**Graphs of Rational Functions**Day 3:**Key Features of Graphs of Rational Functions**Day 4:**Quiz 8.1 to 8.3**Day 5:**Adding and Subtracting Rational Functions**Day 6:**Multiplying and Dividing Rational Functions**Day 7:**Solving Rational Functions**Day 8:**Quiz 8.4 to 8.6**Day 9:**Unit 8 Review**Day 10:**Unit 8 Test

###### Unit 9: Trigonometry

**Day 1:**Right Triangle Trigonometry**Day 2:**Solving for Missing Sides Using Trig Ratios**Day 3:**Inverse Trig Functions for Missing Angles**Day 4:**Quiz 9.1 to 9.3**Day 5:**Special Right Triangles**Day 6:**Angles on the Coordinate Plane**Day 7:**The Unit Circle**Day 8:**Quiz 9.4 to 9.6**Day 9:**Radians**Day 10:**Radians and the Unit Circle**Day 11:**Arc Length and Area of a Sector**Day 12:**Quiz 9.7 to 9.9**Day 13:**Unit 9 Review**Day 14:**Unit 9 Test

#### Learning Targets

Solve linear, quadratic, square root and absolute value equations using algebraic manipulation.

Solve linear, quadratic, square root and absolute value equations by graphing.

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

Activity | 15 minutes |

Debrief Activity with Margin Notes | 10 minutes |

QuickNotes | 5 minutes |

Check Your Understanding | 15 minutes |

#### Activity: How Do You Solve?

#### Lesson Handouts

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#### Answer Key

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#### Homework

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#### Our Teaching Philosophy:

**Experience First,**

Formalize Later (EFFL)

Formalize Later

Learn More

#### Experience First

We're taking today to work on solving equations. Students *should* know how to solve all of the equations presented. However, we know as educators that students come in to our classes with different prior experiences. We don't want to assume they're fluent at something this foundational now when this is a skill they MUST have in order to get to more advanced content later on. This lesson will also help you to get an understanding of how comfortable your students are with solving nonlinear equations.

So let students get started working and try to observe them as much as possible. Ask them to explain their work. Don't tell them how to solve the equations or where they made errors. We are hoping they will be able to reason through the solving, not just blindly following an algorithm.

As you are checking in with groups, be on the lookout for multiple solution paths, both in the activity and in the Check Your Understanding problems. Point out how different approaches have advantages and disadvantages depending on the equation structure.

#### Formalize Later

When debriefing the activity, ask students to explain their work as much as possible. It's easy for solving equations to turn very algorithmic and formulaic. But a goal for today's lesson is to get students thinking flexibly about solving equations. We want students to recognize why they need to include +/- when they square root and why the square root of -4 does not have a solution. When debriefing problems #4-5, remind students about their work with linear systems in Unit 2. We want students to understand that they can take any equation and split it into two separate equations thus creating a system which can be graphed.

We've created the Check Your Understanding problems with this in mind. In problem 1a, students may notice that both sides of the equation have a term with (*x*-8). Instead of distributing, they can combine the terms with (*x*-8) to be more efficient. We call this "Using Structure". In problems 1b and 1c, students need to think about how to use +/-. In the last problem, 1d, students should see that there is no solution. Remind students about how this ties back to our work with linear systems.

All of the solutions to the Check Your Understanding are showing the algebraic work but students can also solve by graphing. Try to find groups solving with different methods to have them share out their process.