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Complete Example: 2(3x-5)-4(2x-3)

See how our three-stage approach transforms complex algebraic problems into manageable learning.

Stage 1: Definition Mastery

Students first learn what each multiplication means in plain language.

2(3x-5)

= "Add (3x-5) itself twice"

4(2x-3)

= "Add (2x-3) four times"

Stage 2: Logical Development

Using their definition knowledge, students work through the logical steps systematically.

2(3x-5) = (3x-5)+(3x-5) = 3x+3x-5-5 = 6x-10

4(2x-3) = (2x-3)+(2x-3)+(2x-3)+(2x-3) = 8x-12

2(3x-5)-4(2x-3) = (6x-10)-(8x-12)

= 6x-10-8x+12

= 6x-8x-10+12

= -2x+2

Stage 3: Fluency Training

After mastering stages 1 and 2, students practice until they can solve complex problems mentally in one step.

2(3x-5)-4(2x-3)

↓

-2x+2

Goal: One-step mental calculation of complex expressions

Build deep mathematical understanding step-by-step.

Our three-stage approach: master definitions, develop logical reasoning, then build computational fluency.

AlphaSnap

Interactive platform where teachers guide students through conceptual understanding and logical development of mathematical concepts.

Worknote

Structured practice platform for building computational fluency after conceptual mastery is achieved.