Isabela G. student at the John D. O’Bryant School of Math and Science
Prompt: A classmate of yours only has a vague sense of how to graph systems of linear equations and is suddenly facing the prospect of graphing a system of linear inequalities! Lucky for them, they have you as an ally. Graph the following system to the best of your ability and then write a brief, but informative narrative which makes use of the vocabulary on the board. The goal is to explain to your classmate HOW you graphed the system as well as HOW to interpret the outcome.
“We first start by graphing our lines and determining which lines are going to be a solid line or a dashed line. Inequalities that are less or greater than are dashed and when they are less than, greater than or equal to is a solid line. It is easier to graph a line by plugging order pairs of the inequality first to plug a line. when we graph our lines we can determine the boundaries of each inequality and this is going to help up isolate the solutions that make each inequality happy. We are going to see the colors overlapping and this is overlapping region that represent the solution of the three inequalities.”
On Writing in Math
Writing in mathematics is as essential to making sense of content as anything else we do in the course. Too often, students have a tenuous grasp of material, almost a passing familiarity, if you will, that is rarely satisfying to them and certainly not sufficient to see them through their future math-related endeavors. Slowing things down and being asked to process the conceptual and marry it to the computational is vital if we hope to cultivate ownership and immediacy. Writing forces a quieting of the mind and offers an honest inventory of fluency that students may not appreciate at first (as it is often painfully sobering!), but will certainly value in retrospect when they recognize the metacognitive benefits.
-Nikan Hodjat, teacher at John D. O’Bryant School of Math and Science