Narrative of a Relationships between Variables activity in an Arizona ABE/ASE Classroom

Resource:  EMPower’s Seeking Patterns, Building Rules: Algebraic Thinking, Lesson 2—Banquet Tables

 

I began the work just after the last Institute, but found that students were totally confused. They did not know the basics of algebraic operations or equations and the EMPower lessons did not seem to cover this. So we spent several lessons going over the basic algebra unit in our Pre-GED book (McGraw Hill/Contemporary’s Pre-GED) which is very well laid out and explained. We covered unknown variables and basic algebraic operations. We practiced isolating the unknown variable so as to solve the equation. I felt that this information and practice helped students better understand the work in the EMPower book.

In the time period which has transpired I have had a huge change of students. Students who have enrolled, those who have stayed for a few classes and left, and others which have remained but are relatively new to the class. It has been extremely challenging trying to follow a consistent course of study in algebra. In addition, I try to find a time when all my students will be present, but many are absent or leave early. It has been a frustrating experience. Adjustments have been necessary at times which have included allowing students to catch-up on necessary graphs for the upcoming lesson by working a few minutes before the start of the lesson, giving some individual instructions, and having other students guide the absent and/or incoming students.

What was planned and why

I wanted students to understand patterns in a specific situation. I also wanted them to use the charting and equation writing practice we had done in chapter 1 and apply it in this situation. Additionally I wanted them to understand the phrase: Please Excuse My Dear Aunt Sally.

 

My students range from ABE I to ASE II+. These are the skills they got from this lesson:

• ABE I algebra sub-indicators state that students create and describe a variety of patterns and formulates generalizations to make predictions.
• ABE II algebra sub-indicators state that students use variables to understand and solve simple algebraic expressions.

These skills are pre-cursors to those needed for the next levels which are:

• ABE III algebra sub-indicators stating that students write and solve linear equations, inequalities and functions. They graph and interpret their results.
• Students write and solve word problems using algebraic expressions and equations.
• ASE I algebra sub-indicators stating that students set up and solve linear equations and inequalities with complex coefficients using algebraic and graphical methods. Set up and solve systems of equations and inequalities. Solve quadratic equations. Perform operations using polynomial expressions. Demonstrate a basic understanding of functions.
• ASE II algebra sub-indicators stating that students understand and compare the properties of classes of function. Interpret algebraic equations and inequalities geometrically and describe geometric relationships algebraically. Perform mathematical operations on matrices. Use the methods and operations of algebra to simplify expressions and to solve equations, inequalities, and systems of equations and inequalities.