Going forward, I plan to share various presentations, worksheets, or other resources I created for use with my students. Some will focus on AP Calculus, but most will focus on algebra 1, or its prerequisites. I know my students benefit greatly when I leverage existing material found on the World Wide Web and adapt it to their needs. Perhaps others may benefit from mine.
My first share consists of excerpts of a presentation I created to review the key characteristics of linear equations as well as how to graph linear equations that are in slope-intercept form.
I will post the entire presentation, or a link to it, when I figure out how best to do so without requiring too much storage space from my WordPress account.
Reviewing Linear Equations
The following slides were excerpted from a thirteen slide presentation. I purposely used different colors when representing slope (green), the y-intercept (red), the dependent variable y (blue), and the independent variable x (purple). Consistent use of the colors through the presentation helped some students zero in on specific parameters such as slope. At the same time, one student, who I expected to resonate with the colors, as he loves to doodle with various colored markers, commented that there were too many colors. Oh well, you win some, you lose some.
Note that I included many synonyms for each parameter above. I use these interchangeably with students and encourage them to do the same. As a former engineer, with a physics credential, and as an AP Calculus teacher, I want all of my algebra 1 students to understand the many ways we describe a linear equation.
Not to diminish the importance of the y-variable (output) or the x-variable (input), this slide directs students’ focus to the key parameters in the slope-intercept form of a line: slope (m) and y-intercept (b), as these provide the key information needed to graph the linear equation.
The following two slides provide step-by-step guidance on how to graph a line when it is in slope-intercept form. The first is generalized for any line, y = mx + b, while the second is a specific example.
The complete presentation includes similar examples as well as how to graph a linear equation using a t-table, how to write the linear equation for a line between two points using the point-slope form of a line, and how to interpret the slope of a line from a graph.
I hope this is helpful to one or two mathematics teachers out there somewhere!