Algebra — Solving Multi-Step Equations

Solving equations is algebra's core skill. Isolate x by inverse operations. Both sides balanced. Indirect aim: formal algebra, preparation for quadratics and systems.

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

Objectives

• Solve 2-step equations: 3x + 5 = 14
• Solve 3+ step equations: 2(x+3) - 4 = 10
• Variables on both sides: 3x + 5 = x + 11
• Check solutions

Materials

• Algebraic Peg Board
• Problem slips
• Recording paper
• Check chart

Instructions

1. Solve 3x + 5 = 14: subtract 5, divide 3 → x=3. 2. Solve 2(x+3) - 4 = 10: distribute, combine, isolate → x=4. 3. Variables both sides: 3x + 5 = x + 11. Subtract x: 2x + 5 = 11. Subtract 5: 2x = 6. x = 3. 4. Check: 3(3)+5 = 14? Yes. 5. Repeat with varied problems. 6. Use peg board to verify. 7. Solve word problems. 8. File.

Educator tip

The check step catches most errors. Require it every time.

Assessment

Observe systematic solving, verification, and transfer to word problems.

More from Mathematics

• 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
• Exponents — Laws and Applications