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)
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.