대수학의 기초 2

Mastering the Foundations of Algebra 2 (ages 14 - 18) 
Mastering the Foundations of Algebra 2 is a class designed to support students interested in learning more about Algebra 2 topics taught at the high school level. This is a weekly class that meets to discuss the most important topics in Algebra 2. Each class meeting is independent and does not build upon the previous sessions. While each session has a guided topic and objective, students will have opportunities each week to ask questions and discuss their knowledge about Algebra 2 related topics with myself and other students. 

1. Week of September 8th: Introduction to Algebra 2 – A Review of Algebraic Concepts that are foundational to Algebra 2, such as exponent rules
2. Week of September  15th: Simplifying Radicals - We will discuss the rules for working with radical operations and simplification. 
3. Week of September  22nd: Imaginary/Complex Numbers - Students will discuss and build upon their knowledge of complex numbers and the operations commonly used around these values. 
4. Week of September 29th: Quadratics - We will discuss what is means to be quadratic, properties of their graphs
5. Week of October 6th: Solving Quadratics - How to solve their equations using the quadratic formula, and other important techniques.
6. Week of October 13th:  Factoring - Students will discuss different types of factoring methods and how factoring is connected to graphing polynomials.
7. Week of October 20th:  Directrix and Focus of a Parabola - Students will learn and discuss special characteristics of a parabola called the focus and the directrix, and how they are used in graphing parabolas. 
8. Week of October 27th:  Roots - Students will make connections between roots, factors, and their graphing implications.  
9. Week of November 27th: End Behavior of Polynomials - We will discuss the end behavior of polynomials, as well as the notation involved that prepares students for Calculus!   
10. Week of November 3rd: Polynomial Division - Students will discuss long division and synthetic division as a process of determining factor relationships.
11. Week of November 10th: Systems of Equations - Students will discuss methods of solving systems of equations up to 3 variables
12. Week of November 17th: Function Average Rate of Change - Students will make deeper connections about slope as a concept of average rate of change within a curve. 

No Classes for Thanksgiving Break the Week of November 24th

Week of December 1st: Function Inverses: Students will begin to talk about what it means to be an inverse function and methods of finding an inverse for any function. We will also make connections to the Vertical (and Horizontal) Line Test used with algebraic functions.  
14. Week of December 8th: Radical and Rational Equations - Students will make connections between radical and rational equations, and discuss methods for solving their equations for specific output values.  


No Classes for Christmas Break for the rest of 2022


15. Week of January 12th: Exponential Functions and Logarithms - Students will discuss Logarithms and how they are used to solve exponential functions. 	
16. Week of January 19th: Solving Equations using Logarithms - We will explore how to solve exponential equations using the properties of  Logarithms.
17. Week of January 26th: Sequences - Students will discuss the differences between Explicit and Recursive formulas for both arithmetic and geometric sequences	
17. Week of February 2nd: Series - Students will discuss the differences between an infinite and a finite series for both arithmetic and geometric relationships. 
18. Week of February 9th:Trigonometry - We will discuss Trigonometry concepts such as SOHCAHTOA taught in Geometry, and how these same concepts are connected to the graphs of sine, cosine, and tangent 
19. Week of February 16th: The Unit Circle – Students will talk about the unit circle and how it supports our knowledge of Trigonometry. 
20. Week of February 23rd - Pythagorean Identity - Students will learn about finding coordinates on the unit circle, Sine and Cosine Identities, along with other trig identities.
21. Week of March 2nd - Trig Graphs - We will spend the sessions mastering the graphs of trig functions through parent transformations. 
22. Week of March 9th - Normal Distribution - Students will discuss normal distribution and z-scores used in early chapters of Statistics Probability - Students will discuss probability of various events, how to read a Two-way table, and how simulations leads mathematicians to better understandings of probability 
23. Week of March 16th - Statistical Regressions - We will talk about the power of using data to find regressions equations on all types of parent functions (linear, quadratic, exponential, etc.)

No classes due to Spring Break the Week of March 23rd

24. Week of March 30th - Solving Any Equation - Students will discuss a mixed review of solving equations at the Algebra 2 level.
25. Week of April 6th - Expression Strategies - Students will discuss a mixed review of simplifying any expression, combining various algebraic approaches like factoring, long division, etc.
26. Week of April 13th -  Probability - Students will discuss probability models (and/or), two-way tables, and conditional probability
27. Week of April 20th - Permutation and Combination - We will will learn about permutation and combination,  as well as other common probability application topics.


In each of these lessons, I will …
1.	… utilize my accessibility to professional educational software and free websites available to all learners on the internet. 
2.	… provide the class with scaffold learning opportunities, where each student can be successful and grow at their pace.
3.	… give students opportunities to ask questions and interact with the lesson in ways that are purposeful and meaningful towards developing long-term, concrete understanding of the concepts presented. 
4.	… inspire students to understand the deeper meaning and purpose of mathematics and all its importance to the progress of humankind. 
5.	… show students free resources they can use to improve the skills presents.