Lesson 2: Graphing Equations by Plotting Points
Duration of Days: 2
Lesson Objective
Students will be able to use an equation to find points that satisfy the equation and then graph the equation on the x-y coordinate plane.
How do we use an equation to find ordered pairs that satisfy the equation?
Ordered pair; Coordinates (x, y); Equation; Graph
NA
Lesson Description: This lesson focuses on the point-plotting method as a universal strategy for graphing any linear equation. Students will master the process of transforming an equation into a visual representation by: Solving for y: Rearranging equations into function form (y = expression) to make calculations easier. Generating a Table of Values: Selecting at least three input values (x) to determine three output values (y). (Using three points instead of two serves as a "check" for arithmetic errors).Graphing with Precision: Plotting the ordered pairs and drawing the line that connects them, ensuring the line extends across the entire grid with arrows to indicate infinity. Handling Special Cases: Identifying and graphing horizontal lines (y = b) and vertical lines (x = a).
Purpose: The purpose of Section 6.2 is to build reliability and self-correction. By requiring three points instead of the geometric minimum of two, students learn to identify "outliers" caused by simple calculation mistakes—if the three points don't form a perfectly straight line, the student knows immediately to re-check their work. This section also solidifies the understanding of horizontal and vertical lines, which are often counter-intuitive for students but essential for describing boundaries in later sections.
Depth of Knowledge (DOK) Level
DOK Level 2
Level 2 (Skill/Concept): Students must perform a multi-step process: manipulate an equation, choose logical inputs, calculate outputs, and translate that data to a graph. It requires "mathematical foresight"—selecting x-values that result in integer y-values to ensure the graph is easy to plot and read. Students must also categorize equations as horizontal, vertical, or slanted based on the variables present.
Class and online work
Use practice problems 5-15, pages 144-147 to assess students' understanding of the lesson concepts