Integer Operations — Signed Number Arithmetic

Integers extend arithmetic below zero. Same signs multiplied = positive; different = negative. The peg board shows why: removing -3 from a board is same as adding +3. Indirect aim: algebraic manipulation, preparation for signed equations.

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

Objectives

• Add and subtract integers (positive and negative)
• Multiply and divide signed numbers
• Apply the sign rules
• Model with algebraic peg board

Materials

• Algebraic Peg Board with red/green pegs
• Number line
• Integer problem slips
• Control chart of sign rules

Instructions

1. On a number line, 3 + (-5) = -2. 2. Subtracting: 3 - (-5) = 3 + 5 = 8 (subtracting a negative = adding positive). 3. Multiplying: (+)(+) = +; (-)(-) = +; (+)(-) = -. 4. Why? (-3)×(-2): taking away three groups of two negatives leaves positives. 5. Practice: (-4) × (+3) = -12. 6. Practice: (-6) ÷ (-2) = +3. 7. Use the peg board for verification. 8. Apply to temperature and elevation problems.

Educator tip

Negative times negative = positive is conceptually tricky. The peg board and temperature change stories are the two best anchors.

Assessment

Observe correct sign application, reasoning about why, and application to real contexts.

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