Lesson 1: System Investigation
Duration of Days: 2
Lesson Objective
Students will be able to define a system of linear equations and understand that the solution to a system corresponds to the point of intersection of their graphs. Students will investigate these relationships through both algebraic and graphical representations.
What is a system of linear equations, and what does it mean to "solve" one?
Why does the point of intersection satisfy both equations in a system simultaneously?
How can we use coordinates of points to determine if two lines will intersect?
System of Equations: A set of two or more equations with the same variables.
Intersection: The point (x, y) where two or more lines cross.
Solution: An ordered pair that makes all equations in the system true.
Ordered Pair: A pair of numbers (x, y) used to locate a point on a coordinate plane.
Linear Equation: An equation between two variables that gives a straight line when plotted on a graph.
8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.
8.EE.C.8.A: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs.
Target D.3: The student estimates solutions by graphing systems of two linear equations in two variables.
Description: This lesson serves as an investigation into systems. Students will explore how two lines behave on the same coordinate plane.
Purpose: To build the conceptual foundation that a solution must satisfy multiple constraints at once. This shifts students from analyzing single lines to comparing multiple linear models, a prerequisite for the Solving by Graphing lesson.
DOK Level: Level 2 (Basic Application) – Identifying solutions and graphing; Level 3 (Strategic Thinking) – Investigating and explaining why intersections represent simultaneous solutions.
Only One Line: Students may try to solve the equations independently rather than looking for a shared solution.
Non-Interacting Lines: Thinking that if they don't see an intersection on the provided graph window, a solution doesn't exist.
Intersection Logic: Difficulty understanding why a point on only one of the lines is not a solution to the system.
Support: Use color-coded graphs to distinguish between the two equations in a system.
Scaffolding: Provide a worksheet that breaks down the investigation into manageable steps.
Exit Tickets
Student Work