Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 4, Session 1: Geometric Measurement: Circles, Circumference,Developing Pi1. What are the important concepts?a) Circles have a diameter, the widest width from edge to edge measured through thecircle's center.A radius is the measurement from the center to the edge. It is half the length of thediameter. (Conversely, the diameter is twice the length of the radius.)b) Circles have a perimeter, which is referred to as circumference.b) Circumference can be measured directly by using flexible tools such as a tapemeasure.c) There is a relationship between a circle's diameter and its circumference, which isknown as pi.d) In cases where circumference cannot be measured directly, it can be calculated byusing pi.2. How do children think about these concepts?a) Since the perimeter of polygons is typically taught first before that of circles,children may think circumference is a totally new topic. They need to understand thatcircumference is just a specialized term for a circle's perimeter.b) Textbooks usually treat circumference by giving an approximation of pi (3.14),then giving the formula pi(d) = C or pi(2r) =C, and then finally asking students tocalculate the circumference of several circles with different diameters.However, in order to understand pi and how it relates to any circle, regardless of size,youngsters need to measure circular and cylindrical objects, chart their findings, andanalyse their data in order to come to the conclusion that pi is a constant that has ameaningful relationship to the diameter of the circle.c) Children need to envision that when they measure around a 3-dimensional cylinderthey are actually measuring a 1-dimensional length.d) Children need to have a clear understanding of the difference between diameterand radius. This is because the circumference is usually expressed as a function of itsdiameter, while the same circle's area usually is calculated by using its radius.3. What is essential to know or do in class?a) Introduce the vocabulary of circles: diameter, radius, circumference. But do notintroduce pi.