Algebraic Peg Board — Solving Linear Equations

Algebra with pegs is algebra with hands. The child physically removes identical amounts from both sides to isolate x. The balance is the control — an unbalanced move produces the wrong answer. Indirect aim: symbolic algebra, linear equations, preparation for systems of equations.

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

Objectives

• Model linear equations using the Algebraic Peg Board
• Use green (positive) and red (negative) pegs to represent signed numbers
• Solve equations like 3x + 5 = 14 by balancing both sides
• Bridge to abstract symbolic manipulation

Materials

• Algebraic Peg Board
• Green pegs (positive units) and red pegs (negative units)
• Variable pegs (tall colored pegs for x)
• Recording paper
• Control chart of solved equations

Instructions

1. Set up: 3x + 5 = 14 as pegs on two sides of the board. 2. Left side: three x-pegs and five green unit pegs. 3. Right side: fourteen green unit pegs. 4. Remove five green pegs from each side: 3x = 9. 5. Divide both sides by 3: x = 3. 6. Verify: place 3 in each x-peg slot; left side 14 green, right side 14 green. 7. Record: 3x + 5 = 14 → 3x = 9 → x = 3. 8. Solve a second equation: 2x − 4 = 10.

Educator tip

The peg board rescues children who freeze at abstract equations. Once they physically take five from each side, the algebraic rule is obvious.

Assessment

Observe correct peg placement, balanced operations, accurate solutions, and transfer to paper-and-pencil equation solving.

More from Mathematics

• Fractions — Addition with Unlike Denominators
• Fractions — Multiplication
• Fractions — Division
• Decimal Multiplication
• Decimal Division
• Perimeter — Various Polygons
• Angles and Protractor Use
• Ratio and Proportion