Algebra 1 Lesson

Two Lines, One Answer: Discovering Systems of Linear Equations

Shared by A STEM Educator

8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.8.EE.C.8a, CCSS.MATH.CONTENT.8.EE.C.8b, CCSS.MATH.CONTENT.HSA.REI.C.660 min

Learning Objective

Students will define a system of linear equations, graph two lines on a single coordinate plane, identify the intersection point as the simultaneous solution, and interpret that solution in a real-world context.

Lesson Overview

Students move from comparing gym membership costs numerically to graphing pairs of linear equations, identifying intersection points as simultaneous solutions, and interpreting the three possible solution types. Tasks thin-slice from plotting a single line through standard-form systems and special cases.

Materials

Vertical non-permanent surfaces (whiteboards or chart paper)
Dry-erase markers (one per group)
Random grouping cards or app
Rulers or straightedges
Desmos Classroom activity (teacher-prepared)
Exit slip handouts

Scaffolded Task Progression

1Task 1

You are looking to join a gym. Fit-Nation charges a flat sign-up fee of $30 plus $10 per month. Power-Gym has no sign-up fee, but charges $15 per month. If you plan to join for 2 months, which gym is cheaper? What if you plan to stay for 10 months? Draw a single coordinate grid on your board, plot both gym paths together, and find the exact month where they cost the exact same amount.

2Task 2

Identify the coordinates of the crossing point on your graph. Write down what the

x

-value and the

y

-value of this point represent in terms of months and dollars. (Slice 1)

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