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Algebra I Lesson

Unmasking the Phantoms: Solving Radical Equations & Extraneous Solutions

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8th or 9th GradeBuilding Thinking Classrooms (BTC)CCSS.MATH.CONTENT.HSA.REI.A.260 min
Learning Objective

Students will be able to solve radical equations by isolating the radical and squaring both sides, identify and reject extraneous solutions by substituting back into the original equation, and explain structurally why squaring both sides can introduce false solutions.

Lesson Overview

Students progress from isolating and solving basic radical equations to uncovering extraneous solutions through squaring both sides, culminating in graphical verification of why phantom solutions appear on principal square root functions.

Materials

  • Vertical non-permanent surfaces (whiteboards, windows, chart paper)
  • Dry-erase markers (one per group)
  • Erasers or paper towels
  • Visibly random grouping cards
  • Desmos graphing access (device or projected)
  • Four-quadrant note-taking template (half-sheet)

Scaffolded Task Progression

1Task 1
Low-Floor Launch — Solve . What inverse operation undoes a square root? Show your work and prove your value of makes the original equation true.
2Task 2
Slice 1 — Isolate First — Solve . What steps must you take to isolate the radical term BEFORE squaring both sides?

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