Algebra 1 Course: Exponential Functions and Sequences; Polynomial Equations

During this class we will complete 2 challenging chapters on exponential functions and sequences and polynomial equations and factoring. This class is part 1 of a 3 part of continuation sections. Students will also apply their prior mathematical knowledge to solve real world word problems. Students will complete an opener problem in the beginning of class that will be a previously learned concept. After the warm up students will be introduced to the week's math concept. The structure of class will be formatted in an I do, we do, you do. Students will have the opportunity to independently complete problems at the end and receive feedback from the teacher. 

The topics are as follows: 

Chapter 6- Exponential Functions and Sequences

Week 1: Properties of Exponents
This week students will begin evaluating expressions using zero and negative exponents. They will also learn 3 core concepts of the properties of exponents (Product of powers property, quotient of powers property, and power of a pwer property). Students should have prior knowledge on expanded form as this concept will help students evaluate expressions with exponents. 

Week 2: Radicals and Rational Exponents
This lesson introduces the language and notation of nth roots and how to evaluate expressions involving nth roots. Students will also be evaluating expressions with rational exponents and solving real-life word problems involving rational exponents. Calculator will be necessary to evaluate nth roots. 

Week 3: Exponential Functions
Students will learn what are exponential equations and distinguish between linear and exponential equations. Students will practice graphing exponential functions. A graphing calculator will be helpful to graph the exponential equations. 

Week 4: Exponential Growth and Decay
This challenging session students will be introduced to exponential growth and exponential decay. Students will identify and distinguish between exponential growth and decay from inspecting an equation, given a table of values, and by looking at a graph. Then, students will interpret and rewrite exponential growth and decay functions. 

Week 5: Solving Exponential Equations 
The first part of this lesson uses algebraic technique and looks at examples that already have the same base, as well as examples in which the exponential expressions must be rewritten to have a common base. 

Week 6: Geometric Sequences
In this lesson, students will make connections between geometric sequences and exponential equations. Students will write terms of a geometric sequence and extend a given sequence. 

Week 7: Recursively Sequences
Students will write terms of recursively defined sequences and translate between recursive rules and explicit rules. 

Week 8: Chapter 6 Review
Students will review the prior lessons as they will revisit this concept in Algebra 2. 

Chapter 7-Polynomial Equations and Factoring 

Week 9: Adding and Subtracting Polynomials
In this first lesson, the first part is on the language of polynomials is introduced. The second part of the lesson is on addition and subtraction of polynomials. Recognizing that only like terms can be combines by addition and subtraction. 

Week 10: Multiplying Polynomials
This lesson introduces multiplication of binomials and trinomial, using 3 different approaches (distributive property, a table, and FOIL). 

Week 11: Special Products of Polynomials
This lesson focuses on special products of binomials are computed by the square of a binomial pattern, and the sum/difference pattern. 

Week 12: Solving Polynomial Equations in Factored Form
In this lesson, students will solve polynomial equations by using the Zero-Product Property.

Week 13: Factoring x2 + bx + c
Students will factor trinomials of the form x2 +bx +c and the different case of c > 0 and c < 0. Although, factoring of trinomials is the focus of this lesson the ultimate goal is for students to solve polynomial equations and simplify expressions with common factors. 

Week 14: Factoring ax2 +bx +c and Chapter 7 Review
In this lesson, students will factor trinomials of the form ax2 +bx + c. Then, students will review prior math concepts.