Lesson 1: Systems Investigation
Duration of Days: 2
Lesson Objective
Students will understand that a system of two linear equations in two variables corresponds to the point of intersection of their graphs, as this point satisfies both equations simultaneously.
Students will use visual and table-based investigations to identify solutions and explore different types of linear relationships.
What does it mean for a point to be a "solution" to a system of equations?
How can we use graphs and tables to find where two lines meet?
Why might a system of equations have no solution or infinitely many solutions?
System of Equations, Point of Intersection, Solution, Ordered Pair, Linear Equation, y-intercept, Slope, Coefficient, and Constant
8.EE.C.8: Analyze and solve pairs of simultaneous linear equations.
8.EE.C.8a: Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs.
Purpose: To transition students from individual linear equations to analyzing how two lines interact. This lesson uses a "concrete-to-abstract" approach, starting with visual investigations before moving to formal graphing.
DOK Level: 2 (Basic Application of Skills/Concepts) and 3 (Strategic Thinking/Reasoning).
Students may believe a solution is just any point on a line, rather than the specific ordered pair (x,y) that satisfies both equations simultaneously.
Students often struggle to recognize that parallel lines have no solution or that overlapping lines have infinitely many solutions
Provide Math Concepts templates and visuals for students to record their understandings.
Use collaborative grouping for "Systems Investigations" parts 1-3, allowing students to compare tables and graphs.
Provide guided notes for students who need additional structure in identifying y-intercepts and slopes.
Student work
Observations
IAB (Interim Assessment Blocks): * Analyze & Solve Linear Equations.
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Expressions & Equations II