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- students will be able to demonstrate their knowledge of the different types of functions within the course

- students will solve a relevant real-world problem utilizing the different types of function families and technologies utilized within the course

- students will use critical thinking skills to persevere in the problem-solving process and solve real-world problems

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-students will understand the classroom expectations and policies
- students will understand how to access the available resources in the course including the instructor
- students will be able to identify the different characteristics of a quadratic function given the function and/or graph
- students will utilize the different forms of a quadratic function to determine different characteristics of the function
-students will use a variety of techniques such as factoring and the Quadratic Formula to determine solutions to quadratic functions

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- Padlet Activity: Create a Padlet containing all of the function types discussed in the course, discuss their basic characteristics, if they are similar or related to other function or integer families, how to find the characteristics of each, and provide an example and visual of each

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- students will be able to add, subtract, multiply, and divide rational functions
- students will use factoring techniques to simplify rational functions and identify domain and range restrictions
- students will identify horizontal and vertical asymptotes given a rational function
- students will graph rational functions by identifying asymptotes

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-students will identify the basic characteristics of a polynomial based on the given function and/or graph
-students will understand the similarities and differences between integer operations and polynomial operations
- students will add, subtract, and multiply polynomials
- students will divide polynomials using Synthetic Division and Long Division
- students will solve polynomials by factoring and/or Synthetic Division
- students will graph polynomials using the solutions and basic characteristics of the polynomial

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-students will be able to determine the inverse of a function algebraically and graphically
-students will solve radical equations and understand the restrictions on the domain and range of radical functions
-students will be able to identify asymptotes
- students will be able to graph radical functions given the parent function
-students will understand how transformations in the form g(x) = af(b(x-c))+ d effect the graph of the parent function

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- Syllabus
- Syllabus Quiz
-Flipgrid Introduce Yourself Activity
- Email Activity

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Week 2: Characteristics of Quadratic Functions 

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Week 2: Characteristics of Quadratic Functions 

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- describe characteristics of quadratic functions (max, min, vertex, axis of symmetry, etc.)
- Different forms of quadratics (Standard, Vertex, and Factored)
-Concept Map Activity: Describe each form of a quadratic; characteristics

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- Different Forms of Factoring
- Quadratic Formula
- Solving Quadratics Quiz

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- Characteristics based on the graphs of polynomials
- Desmos Activity with Polynomials
- Padlet Activity: Describe all characteristics of a polynomial, with example and how to determine them based on function and/or graph

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Week 5: Operations on Polynomials/ Synthetic Division

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Week 5: Operations on Polynomials/ Synthetic Division

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- Discussion: How are Integer Operations and Polynomial Operations similar? How are they different? Are each sets of numbers closed under each operation?
-DeltaMath with Operations on Polynomials
- Digital Escape Room: Long Divison and Synthetic Division of Polynomials

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Week 6: Solving and Graphing Polynomials

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Week 6: Solving and Graphing Polynomials

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- Desmos Activity, Solving Graphically
- Worksheet on Solving (submit through Kami)
- DeltaMath Assessment: Operations on Polynomials and Solving Polynomials

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- Capstone Project: students research college or trade school tuition and different loans, use their knowledge of functions to determine the cost of the tuition with loans, describe factors that may contribute or decrease the cost. Students then will determine how long it will take to pay off the loan given different circumstances. Determine which circumstance more closely resembles their situation. Students will then create a Google Doc and write the report with all the work and create a graph of the function on Desmos. Students will show all of their work through the Google Doc

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Week 7: Operations on Rational Functions

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Week 7: Operations on Rational Functions

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- Discussion Board: How are rational numbers and rational functions similar and how are they different?
- Padlet: Factoring Techniques
- DeltaMath assessment: Operations with Rational Functions

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- Discussion Board: What are inverse operations? How would you describe them in your own words? Examples?
- Desmos: Inverse Functions Activity
- Screencastify: Given a function, describe and show how to find the inverse function graphically and algebraically. Show how to prove the two functions are inverses of one another

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- Presentation on Identifying Asymptotes and Graphing Rational Functions

- Infographic: Similarities and Differences between Vertical and Horizontal Asymptotes

- Worked Example Assessment: Create a worked example given a specific rational function based on a real-world scenario. Students will use Google Slides, PowerPoint, or another presentation feature to display their work, must create a graph and show all work while also explaining each step

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- Presentation on Transformations and Radical Functions

- Desmos: Transformations on Radical Functions

- DeltaMath: Identifying Transformations and Graphing Radical Functions

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- Presentation on Solving using Inverse Operations and Extraneous Solutions

- DeltaMath assignment: Solving Radical Equations

- Screencastify: Describe the transformation on a given radical function and demonstrate how to graph the function. Students will explain the where the asymptotes occur and why they occur. Afterwards, students will demonstrate their knowledge of solving function by picking a specific y-value based on their graph and plugging it into their function to determine the x-value. Students should check for extraneous solutions and explain how they could have determined the x value based on the graph.

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- students will be able to solve exponential equations
- students will understand the structure of exponential functions
- students will use exponential functions to model real-world scenarios such as interest, exponential growth, and exponential decay
- students will be able to graph exponential functions and identify key features of the function based on the graph and the function

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Week 12: Modeling and Solving Exponential Functions

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Week 12: Modeling and Solving Exponential Functions

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- Presentation on Exponential Functions and Techniques to Solve
DeltaMath assignment: Solving Exponential Equations and Writing Exponential Equations (Given Context)
- Capstone Project Assignment: Loans and Interest Rates, research different types of loans and interest rates ( Find at least 3 different loan and interest options), determine the amount of interest paid on each loan depending on the type of loan (annual, semi-annual, continuous) and the length of the loan

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- Transformations Flipgrid Video: Students will do a Flipgrid video describing the different types of transformations in their own words. They will also discuss the main characteristics to look for in the graph of an exponential function
- Infographic: Students will create an infographic describing the differences between growth rate and decay rate
We will then hold a gallery walk and students will discuss and assess their peers work; students will assess their group members from the start of the course
- DeltaMath Assessment: Solving and Graphing Exponential Functions

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- students will be able to solve logarithmic equations
- students will be able to write logarithmic equations as exponential equations and understand the relationship between logarithms and exponentials
- students will use logarithms to model and solve real world problems
- students will be able to graph logarithmic functions and state possible asymptotes
- students will be able to condense and expand logarithms
- students will understand and utilize the laws of logarithms

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Week 14: Logarithm Laws and Operations on Logs

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Week 14: Logarithm Laws and Operations on Logs

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- Presentation on Logarithm Laws
- EdPuzzle: Logarithm Laws
- DeltaMath Assignment: Condense and Expand Logarithms
- Graphic Organizer: Describe each Logarithm Law in your own words and provide an example of each

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- Presentation: How to Solve Logarithmic Equations; Half Life and Double Time Problems
-Flipgrid Assignment: In a short video, explain in your own words how to convert a logarithm to an exponential and vice-versa. Explain what the output of logarithmic functions is.
- Capstone Project Assignment: For each exponential function created in previous Capstone Assignment, use Logarithms to solve each equation and determine the amount of time it will take to pay off the loan with interest
- DeltaMath assignment: Solving Logarithmic Equations
- Solving Logarithms Real World Applications Worksheet: Use Kami to show and upload the work. Provide feedback to students so they can understand where their mistakes are made

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-Presentation: Graphing Logarithmic Functions
- Discussion Board: How are exponential functions and logarithmic functions related? How can you use the relationship between both function families to make graphing logarithmic functions easier?
-Desmos Activity: Graphing Logarithmic Functions
- DeltaMath Assessment: Solving and Graphing Logarithmic Functions

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- students will persevere in the problem solving process
- students will identify each function family given the graph or function and the key characteristics of each function family
- students will be able to describe the similarities and differences between function types and the relationships between function families
- students will solve real-world problems using a variety of problem-solving techniques and critical thinking skills
- students will be able to model different function types by hand and using technology
- students will use technology to help in the problem solving process
- students will recognize the structure behind functions and how different representations of functions describe different characteristics of the function
- students will use mathematical and algebraic processes to rewrite functions in different forms to determine different characteristics of the function