Perimeter — Various Polygons

Perimeter is the walk around. A rectangle: 2(l+w). A regular n-gon: n×s. Children often confuse with area — distinguish clearly. Indirect aim: geometric reasoning, formula derivation, preparation for optimization problems.

• Framework: Montessori
• Unit: Mathematics
• Learning area: Geometry
• Level: Ages 7-9

Objectives

• Compute perimeter by adding all side lengths
• Derive perimeter formulas for regular polygons (P = n × s)
• Measure perimeters of real objects
• Distinguish perimeter from area

Materials

• Rulers
• Polygon shapes (paper cutouts and real objects)
• String to measure curves
• Recording paper

Instructions

1. Measure all sides of a rectangle; sum. 2. Derive P = 2(l+w). 3. Measure a triangle: P = a+b+c. 4. Regular pentagon with side 4: P = 5×4 = 20. 5. For a circle: use string to measure circumference; relate to π. 6. Find perimeter of a classroom object. 7. Compare perimeter to area for different rectangles with same perimeter. 8. Record all.

Educator tip

Children sometimes think larger perimeter = larger area. Show a 1×10 and 3×3 rectangle (both P=22 for the former, P=12 for the latter? redo) — instead: 1×9 (P=20, A=9) vs 3×6 (P=18, A=18). Area can vary wildly at fixed perimeter.

Assessment

Observe accurate measurement, formula use, and distinction from area.

More from Mathematics

• Angles and Protractor Use
• Ratio and Proportion
• Integer Operations — Signed Number Arithmetic
• Word Problems — Distance, Rate, Time
• Geometry Chart 1 — Basic Figures
• Congruence and Similarity
• Geometric Symmetry — Reflection, Rotation, Translation
• Measurement — Length in Metric