Algebraic Reasoning Part 1

This is a partial pre-algebra course that will be continued in the spring for the students who desire to! These eight weeks will focus on the basics of algebraic reasoning. The big ideas covered are: 

1) Logical patterns exist and are a regular occurrence in mathematics that can be recognized, extended, and generalized with both words and symbols. 
2) You can use symbolism (variables) to express generalizations of patterns and relationships. 
3) Variables are symbols that take place of numbers or ranges of numbers. 
4) Equations and inequalities are used to express relationships between two quantities. 

During each class I will introduce the concept, provide examples and then time for students to work through examples. I always encourage students to share their thinking with the group as it's more fun to learn from one another! I have a very laid-back style and I have served students who feel uneasy about math well in my history. All of my classes are meant to encourage a playful relationship with numbers and hopefully instill more confidence in the learners that they can think logically and be good at math. 

What I plan to cover during each class (but please allow flexibility - I will modify to meet the group's needs once I meet the learners and see where they might need more or less support): 

Class one: Analyzing and extending patterns. We will examine patterns and use tables to figure out how to extend those patterns further. 
Class two: Moving from patterns to function and variable. We will use variables to write functions of patterns, as well as play several games involving functions, like "Guess my rule" and "Amazing Digits." 
Class Three: We will continue to explore variables as unknowns and play "Story Translations" where students write a story to go along with an equation and "Number Tricks" which they can use as a way to "magically" read someone's mind. 
Class Four: We will pause and review concepts covered around patterns and functions, and play any games that were class favorites. 
Class Five: Equations and inequalities. We will use the concept of a balanced scale to write equations that are equal, greater, or less than each other. 
Class Six: Solving equations. We will continue using the concept of a balanced scale to solve for a variable in an equation. 
Class Seven: Solving equations continued. We will add complexity to the equations being solved! 
Class Eight: Review of all the concepts covered. 

The spring term of this course will continue on by working with real numbers, integers, exponents and graphing.