Algebra 1 Lesson

Side Hustle Math: Systems of Linear Inequalities & the Feasible Region

Shared by A STEM Educator

8th-9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.HSA.REI.D.1260 min

Learning Objective

Students will graph a system of two or more linear inequalities on the same coordinate plane, identify the feasible region as the set of all points satisfying every inequality simultaneously, and verify solutions by substituting test points into each inequality.

Lesson Overview

Students begin with a real-world t-shirt/hoodie business scenario to build intuition for single inequality constraints, then layer a second constraint to discover the feasible region as the overlapping shaded area. Progression moves from contextual graphing to pure algebraic systems with solid/dashed boundaries.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (2 colors per group)
Erasers or paper towels
Visibly random grouping cards
Desmos Classroom activity (teacher-prepared)
Printed exit slip (1 per student)

Scaffolded Task Progression

1Task 1

[TEACHER-ANCHORED — Low-Floor Launch] You are running a small weekend business making customized t-shirts and hoodies. It takes you 1 hour to make a t-shirt and 2 hours to make a hoodie. You have a maximum of 10 hours available to work this weekend. Draw a coordinate grid with t-shirts on the

x

-axis and hoodies on the

y

-axis, and shade in every possible combination of shirts and hoodies you could realistically make.

[ Interactive graph / diagram — available in the full lesson ]

2Task 2

[Slice 1] Write a single inequality that models your work-hours constraint from Task 1. Use

x

for t-shirts and

y

for hoodies.

Then test two points:
- Point A:

(2, 3)

— inside your shaded region?
- Point B:

(8, 4)

— inside your shaded region?

Substitute each into your inequality to prove your shading is correct.

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