Linear Lesson Plan for 9th grade Algebra 1 Class
This is a good follow-up or extension after students have been taught system of equations.
Objectives: 1. Understand what linear algebra is; 2. Understand the importance (and controversy) of linearity in mathematics
Introduction to new material
Teacher asks the students what linear algebra means and compiles a list on the board.
Teacher then discusses definition from Wikipedia: Linear algebra is a branch of mathematics concerned with the study of vectors, with families of vectors called vector spaces or linear spaces, and with functions that input one vector and output another, according to certain rules. These functions are called linear maps or linear transformations and are often represented by matrices. Linear algebra is central to modern mathematics and its applications. An elementary application of linear algebra is to the solution of a systems of linear equations in several unknowns.
Of course many students many not know vectors and matrices, but it is a nice teaser for what is to come later in their math lives.
Teacher can then discuss linearity from a less mathematical perspective. Linearity can also mean doing things in a certain order. Progressing from one task to another in an orderly fashion. Implied is that you cannot go on to the next task without completing and understanding the previous task.
At this point, teacher can ask if that is important in mathematics?
If so, can you provide examples?
Teach can show examples of linearity.
To solve multistep equation, you need to know about variables and balancing equations through the inverse properties.
In school, there is linearity of math courses you will take:
Algebra 1 in 9th, Geometry in 10th, Algebra 2 in 11th, Precalculus in 12th.
We have learned how to solve systems of equations by graphing their lines and finding the intersecting point. What math principles did you need to know beforehand in order to do this activity?
What do you think you will learn in Algebra 2 as a junior? Do you think it is important to do well in Algebra 1 in order to do well in Algebra 2? Why? There are schools of thought that think sometimes math is taught in a way that is too linear. For example, do you think it might make sense to take Algebra 2 as a sophomore? Why?
Solve y=3x+1 and y=-x+5. Do you think there are other ways to solve a system of equations in addition to graphing?