Fractions — Multiplication

1/2 × 1/3 = 1/6 — smaller, not larger. Shown on grid: take half of a third of a square. The grid is the control. Indirect aim: abstract fraction arithmetic, preparation for algebraic operations.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Fractions
• Level: Ages 8-10

Objectives

• Multiply fraction by fraction: (a/b) × (c/d) = (a×c)/(b×d)
• Interpret fraction × fraction geometrically
• Simplify products
• Apply to real problems

Materials

• Grid paper for area models
• Fraction Insets
• Problem slips
• Control chart

Instructions

1. Draw a rectangle; divide vertically into thirds — shade one (1/3). 2. Divide horizontally into halves — shade one (1/2). 3. Overlap region = 1/2 × 1/3 = 1/6. 4. Verify: 1/6 of the rectangle is double-shaded. 5. Rule: (a/b) × (c/d) = (a×c)/(b×d). 6. Compute 2/3 × 3/4 = 6/12 = 1/2. 7. Simplify by canceling before multiplying when possible. 8. Apply to recipe halving.

Educator tip

The grid area model is the sensorial foundation. Don't introduce 'multiply across' until the grid has been drawn many times.

Assessment

Observe correct multiplication, simplification, and grid-based reasoning.

More from Mathematics

• Fractions — Division
• Decimal Multiplication
• Decimal Division
• Perimeter — Various Polygons
• Angles and Protractor Use
• Ratio and Proportion
• Integer Operations — Signed Number Arithmetic
• Word Problems — Distance, Rate, Time