Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 3, Session 1: Geometric Measurement: Area of Irregular Shapes andPolygons1. What are the important concepts?a) Area is a measurement of a two-dimensional surface and is expressed in squareunits.b) All two-dimensional surfaces (irregular figures, polygons, circles, and ellipses) canbe measured to estimate their area.c) Various methods and tools can be used to estimate area.d) All measurements (not just of area) are considered estimates and depend on thelevel of accuracy of the tools used.e) Measurement depends on determining a unit of measure and then repeating thatunit until an estimated measurement has been obtained.f) Formulas for finding the area of a rectangle can be used to determine the area ofother polygons such as triangles, parallelograms, and trapezoids.2. How do children think about these concepts?a) Children initially tend to confuse the concepts of area and perimeter. Once theyacquire these misconceptions it is extremely difficult for youngsters to "unlearn"them. Therefore they need extensive, hands-on activities in measuring area andperimeter so that they have a clear understanding of how area and perimeter aredifferent and what each of these measurements entails.b) If area is introduced in textbooks beginning with squares and rectangles with theirdimensions labeled, children tend to assume that area only applies to squares andrectangles.This is why it is important to begin with the generalized concept of area as themeasurement within any shape, and why this topic begins by measuring the areainside irregular shapes.c) Once children hear that area is expressed in "square units" they assume that only"square" (or at least rectangular) surfaces have area. This is another reason to beginwith the area of irregular shapes. Beginning with the area of irregular shapes alsoleads to the idea that circles (which are certainly not square) have an area measured insquare units.d) Textbooks often label rectangles and squares with their dimensions, allowingchildren to simply multiply the given side lengths in order to find area. However,even if youngsters are able to do this accurately, it does not guarantee that theyunderstand the fundamental concept of area.e) Elementary school textbooks usually present formulas for area: Length x Widthfor rectangles, Side x Side for squares, and 1/2 (Base x Height) for triangles. This isoften extended to polygons that are divided into simpler shapes where each "subshape's"area can be calculated, with the resulting measurements added to find thepolygon's total area.