Unit 1, Lesson 2: Solving Equations with Variables on Both Sides — The Balance Scale Model
Shared by A STEM Educator
Students will solve linear equations with variables on both sides by applying the balance-scale principle — performing identical operations on both sides to maintain equality — and translate visual scale moves into formal algebraic notation.
Lesson Overview
Students use physical balance-scale reasoning to build intuition for algebraic equality, progressing from visual mystery-bag puzzles to symbolic multi-step equations with variables on both sides. The lesson moves from concrete manipulatives to abstract notation through deliberate thin-slicing.
Materials
- Vertical whiteboards (VNPS) or large chart paper
- Dry-erase markers (one per group)
- Erasers or socks
- Random grouping cards or app
- Printed 'Legal Moves Checklist' cards (optional)
- Desmos Classroom activity link (projected or on student devices)
Scaffolded Task Progression
A balance scale is perfectly level.
[ Interactive graph / diagram — available in the full lesson ]
Left side: mystery bags. Right side: mystery bag and pound-weights.
How many pounds does one mystery bag weigh? Show your reasoning on the whiteboard. You may NOT just guess-and-check — show what you *did* to both sides.
A balance scale is perfectly level.
Left side: mystery bags and pound-weights. Right side: mystery bags and pound-weights.
Write the equation this scale represents. Then find the weight of one bag. Show every 'move' you make to both sides.
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