Honors Algebra 1 Lesson

Balancing Act: Multi-Step Equations & Algebraic Fractions

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9th GradeBTC Style / Thinking ClassroomsCCSS.MATH.CONTENT.HSA.REI.A.1, CCSS.MATH.CONTENT.HSA.REI.B.350 min

Learning Objective

Students will solve multi-step linear equations including those with variables on both sides and algebraic fractions by applying properties of equality, identifying the LCD, and justifying why each step preserves the solution set.

Lesson Overview

Students progress from one-step equation intuition through multi-step equations with variables on both sides, then discover why multiplying by the LCD transforms fractional equations into integer equations without changing solutions. Honors depth is maintained through justification of each property of equality.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers and erasers
Random grouping cards
Four-Quadrant note sheets (printed)
Rulers (optional)

Scaffolded Task Progression

1Task 1

Solve each equation. For each step, write the name of the property of equality you used.
a)

x + 9 = 20

3 x = 21

x - 5 = - 2

\frac{x}{4} = 7

- 6 x = 42

2Task 2

Solve each equation. Justify every step by naming the property used.
a)

2 x + 5 = 17

3 x - 4 = 11

- 4 x + 7 = - 9

\frac{x}{2} - 3 = 5

5 - 2 x = 13

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