Algebraic Peg Board — Equations and Signed Numbers

Algebra is made concrete on the peg board. A green peg is +1, a red peg is −1; together they cancel. An equation like 2x + 3 = 11 is laid out peg by peg, and the child physically rearranges to isolate x. The board enforces the rules — a misplaced peg breaks the equation's balance.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Algebra
• Level: Ages 9-10

Objectives

• Represent signed numbers (positive and negative) with colored pegs
• Solve simple linear equations with the peg board
• Understand 'moving a term to the other side changes its sign'
• Prepare for abstract algebra

Materials

• Algebraic Peg Board (grid with columns for positive/negative values and rows for operations)
• Colored pegs: green (positive), red (negative), blue (variables x, y)
• Equation cards

Instructions

1. Introduce positive pegs (green) and negative pegs (red). 2. Show that +1 and −1 cancel (green + red = 0). 3. Set up 2x + 3 = 11 with pegs. 4. To isolate x, subtract 3 from both sides: remove three green pegs from each side. 5. Now have 2x = 8. 6. Divide both sides by 2: group the pegs into 2 sets of 4. 7. Each x = 4. 8. Verify by substituting back. 9. Work through increasingly complex equations.

Educator tip

Physical cancellation of positive and negative pegs is the breakthrough. Don't rush past it — the intuition carries all later algebra.

Assessment

Note correct peg placement, systematic solving, and verification by substitution.

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• Word Problems with Materials
• Short Chains — Squaring Visualized
• Ratio and Proportion
• Volume — Measuring Three Dimensions
• Factor Trees and Prime Factorization
• Addition Snake Game
• Subtraction Snake Game
• Multiplication Snake Game