Algebra I Lesson

Unpacking the Radical: Geometric Area & Simplifying Square Roots

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8th or 9th GradeBuilding Thinking ClassroomsCCSS.MATH.CONTENT.8.EE.A.260 min

Learning Objective

Students will be able to simplify square root expressions by identifying and extracting the largest perfect square factor, write radicals in simplest radical form (including expressions with coefficients and variable radicands), and connect radical simplification to geometric side lengths of squares.

Lesson Overview

Students begin by connecting square roots to geometric side lengths of squares, then progressively simplify radicals by factoring out perfect squares, extend to coefficients and variable radicands, and culminate by combining like radicals and exploring cube roots.

Materials

Vertical whiteboards (VNPS) or large chart paper
Dry-erase markers (one per group)
Erasers or socks
Visibly random grouping cards
Desmos Classroom activity: Radical Equivalence Engine
Student notebooks for Four-Quadrant consolidation notes

Scaffolded Task Progression

1Task 1

Draw a square with an area of

50

units². Break the number

50

down into a product of a perfect square times another number (e.g.,

50 = 25 \cdot 2

). If a square has an area of

25

, its side length is

5

. What must the exact side length of a

50

-unit² square be in the form 'number

\cdot number

2Task 2

Simplify

72

by finding the largest perfect square from the list

(1, 4, 9, 16, 25, 36, 49, 64, 81, 100)

that divides evenly into

72

. Write your work as

perfect square \cdot remainder

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