Area of a Rectangle — Formula from Counting

Area is the count of unit squares. A rectangle 3×4 contains exactly 12 unit squares. The child fills, counts, and derives the formula — not the reverse. A wrong count reveals itself when measurement is checked.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Geometry
• Level: Ages 7-8

Objectives

• Derive the formula A = l × w by counting squares
• Measure and compute area of real rectangles
• Compare areas of different rectangles
• Prepare for triangle and circle area

Materials

• Square tiles (1 cm squares)
• Rectangles of known dimensions printed on paper
• Rulers
• Calculator

Instructions

1. Take a printed rectangle of unknown dimensions. 2. Fill it with unit squares. 3. Count: say 24 squares. 4. Measure the sides: 3 cm × 8 cm. 5. Note 3 × 8 = 24. 6. Derive: A = l × w. 7. Apply to a second rectangle: measure first, compute. 8. Verify by counting. 9. Compute area of a classroom table or floor tile.

Educator tip

Start with rectangles that have whole-number sides. Irregular dimensions can come later. Let children enjoy the 'aha' of pattern discovery.

Assessment

Note accurate counting, formula derivation, and application to real objects.

More from Mathematics

• Area of a Triangle — Half the Rectangle
• Circumference and Pi — Measuring the Circle
• Percent Cards — Hundredths as Percentages
• The Coordinate Plane — Plotting Points
• Checkerboard Multiplication — Multi-Digit Products
• Racks and Tubes — Long Division
• Large Bead Frame — Up to 1,000,000
• Stamp Game — Long Multiplication Extension