Algebra 1 Lesson

The Zero-Out Strategy: Solving Systems by Elimination

Shared by A STEM Educator

8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.8.EE.C.8b, CCSS.MATH.CONTENT.HSA.REI.C.560 min

Learning Objective

Students will solve systems of two linear equations in two variables using the elimination method — including cases requiring multiplication of one or both equations by a scalar — and justify each step by connecting it to the real-world logic of 'zeroing out' a variable.

Lesson Overview

Students begin with a real-world farm stand scenario to discover elimination logic intuitively, then progressively formalize the algebraic procedure from ready-made opposites through single-multiplier and double-multiplier cases, culminating in a generalization of when elimination is the best tool.

Materials

Vertical whiteboards or large chart paper (one per group)
Dry-erase markers (one per group)
Erasers or paper towels
Visibly random grouping cards or tool
Printed exit slip (optional)
Desmos Classroom activity link (teacher-shared)

Scaffolded Task Progression

1Task 1

[Teacher-Anchored Problem — Verbatim] At a local farm stand, two friends buy fruit. Maya buys 2 apples and 1 banana for a total of 5 dollars. Sam buys 2 apples and 3 bananas for a total of 9 dollars. Look closely at their purchases. Without guessing or setting up a long guess-and-check table, how can you immediately determine the exact price of a single banana? How does that reveal the price of an apple? Show your logic visually on your board.

2Task 2

[Slice 1 — Translating to Algebra] Now translate Maya and Sam's shopping trip into two standard-form algebraic equations using

a

for apples and

b

for bananas. Write them stacked on your board, lining up like terms vertically. Then draw a horizontal line underneath and show how subtracting the two full equations from each other mirrors the exact real-world logic you used in Task 1. What single-variable equation do you get? Solve it.

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