Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 3, Session 3: Relationship between Area and Perimeter1. What are the important concepts?a) Area and perimeter are two different types of measurementb) Shapes with a constant perimeter can vary in their areac) Shapes with a constant area can vary in their perimeterd) The mathematical concepts of maximum and minimum can be visualized whenworking with area and perimeter and charting the resulting measurements2. How do children think about these concepts?a) Even when children understand the difference between area and perimeter, theymay assume that any rectangle with an area of, for example, 24 square units will havea fixed perimeter.This is why it is important to have them experiment with making all possiblerectangles with a fixed area and whole number sides. This will allow them to see thatdifferent shaped rectangles (with different perimeters) can be made from a givennumber of square units.b) Research has shown that it is more difficult for youngsters to hold perimeterconstant and area variable. This is why it is important to have pre-service teachers usea variety of techniques to explore their own understanding of rectangles with the sameperimeter but different areas3. What is essential to know or do in class?a) Students will explore the relationship of area and perimeter from two differentperspectives:• Area as a constant with varying perimeters• Perimeter as constant with varying areasb) Have students use various tools, strategies, and formulas to determine the area ofirregular shapes, various quadrilaterals, compound polygons, and triangles.4. Class Activitiesa) Trace one's hand on grid paper, first with the fingers closed, then with the fingersspread apart. (Constant area, different perimeter.)b) Use a given number of square tiles (constant area) and arrange them in differentconfigurations to design polygons with different perimeters.c) Use a 2-metre loop of string or yarn (constant perimeter) and have four studentshold it to create rectangles of different areas.