Algebra — Simplifying Expressions

Before solving equations, algebra must be simplified. Like terms combine; distributive expands; order matters. Indirect aim: algebraic fluency, preparation for equations and polynomials.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 9-11

Objectives

• Combine like terms: 3x + 2x = 5x
• Apply distributive property: 2(x+3) = 2x+6
• Simplify multi-variable expressions
• Handle negative signs correctly

Materials

• Algebraic Peg Board
• Problem slips
• Recording paper
• Worked examples

Instructions

1. Simplify 3x + 4x = 7x. 2. Simplify 3x + 2y + 4x - y = 7x + y. 3. Distribute: 2(x+3) = 2x + 6. 4. 3(2x - 5) = 6x - 15. 5. Negatives: -(x+4) = -x - 4. 6. Multi-step: 2(x+1) - (x-3) = 2x+2-x+3 = x+5. 7. Verify by substituting x=2. 8. File.

Educator tip

Distributive is algebra's workhorse. Drill it.

Assessment

Observe accurate simplification, sign handling, and verification.

More from Mathematics

• Algebra — Solving Multi-Step Equations
• Order of Operations — PEMDAS
• Probability — Coin, Dice, Cards
• Statistics — Mean, Median, Mode
• Negative Numbers — Full Operations
• Linear Graphs — Slope and y-Intercept
• Mental Math — Shortcuts and Tricks
• Geometric Proofs — Simple Theorems