During my student teaching work sample unit, I will be teaching linear systems of equations.  It is difficult to argue against the importance of mathematics in the modern world.  Mathematics is used by everyone in performing simple tasks like balancing a checking account to more complex tasks like determining the likely growth percentage of the US economy.  More specifically, the ability to solve systems of linear equations is key in many technical fields and is used in the process of linearization of near-linear systems and in general in the fields of engineering, computer science, chemistry and et cetera.

In the process of teaching this unit, I will address a number of different standards across multiple levels of mathematics.  The first standard I will address is Oregon State Math standard 8.1.4, which states, “[Students will be able to] use linear functions and equations to represent, analyze and solve problems, and to make predictions and inferences.”  Students will demonstrate this ability through word problems.  Students will construct a linear system of equations to represent and solve word problems in many different situations.  The second standard I will be addressing is 8.1.5, which states “[Students will be able to] relate systems of two linear equations in two variables and their solutions to pairs of lines that are intersecting, parallel, or the same line.”  The 3^rd standard that will be addressed during this unit is 8.1.6, which states “[Students will be able to] use informal strategies (e.g., graphs or tables) to solve problems involving systems of linear equations in two variables.”  Students will demonstrate meeting these 2 standards through graphing and labeling the lines as parallel or through labeling the intersection (solution) point of the system.  Lastly, I will address standard H.2A.8, which states “[Students will be able to] solve systems of two linear equations graphically and algebraically, and solve systems of two linear inequalities graphically.”  Students will demonstrate meeting this last standard by solving a series of linear systems of equations problems including one inequality problem that they will solve using a graph on the post-test as well as during homework activities.

In order to address the varied learning styles of students, I will attempt to use assessments that assess across as many of the intelligences proposed by Gardner in his Theory of Multiple Intelligences as possible.  One such example of how I will attempt to appeal to the multiple intelligences of students is through including in this unit a performance assessment activity where the students describe in detail the process of using one of the algebraic methods to solving linear system of equations problems (graphing, substitution, or elimination) using a graphic organizer, flowchart, or some other visual medium while adding color and graphs.  This assignment will appeal to students who express themselves more successfully visually rather than through written expression.

Since there are no IEP students in the class of my student teaching, I will not have to make any changes to assignments given in class.  That being said, were there to be any students on an IEP, it would be necessary to change the assignment as per the instructions on the IEP.  Since there are many (identified and unidentified) TAG students in the class, it will be necessary to add optional content that forces the students to think more deeply and challenges them more than the base assignment would, aiding in improving their overall learning.

By the end of this unit, students should be able to answer the following essential questions:

1.           What is a linear system of equations?
2.           What does it mean to have a “solution” for a linear system of equations?
3.           What are the various methodologies one can employ to solve systems of linear equations?

A. Big Ideas

Analyze

Solve(graphically/algebraically)

Predict

Infer

B. Assumptions of student knowledge

1.           I’m assuming students know how to graph a line in y=mx+b form.

2.           I’m assuming students can algebraically manipulate equations to solve for a variable.

3.           I’m assuming students can recognize parallel lines and equivalent lines on a graph and as an algebraic representation.