Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 4, Session 3: Geometric Measurement: Surface Area of Cuboids andCylinders1. What are the important concepts?a) All 3-dimensional objects (not just geometric shapes such as cubes, cuboids, andcylinders) have surface area.b) Surface area is the sum of the all the areas covering any 3-dimensional object.c) A "net" is a 2-dimensional representation of a 3-dimensional object's surface area.d) Formulas for finding the surface area of cuboids may be expressed in variousways.2. How do children think about these concepts?a) Just as children tend to confuse the concepts of area and perimeter they alsoconfuse the concepts of surface area and volume.This may be attributed to a textbook's introducing these two models of measuring 3-dimensional objects in quick succession.b) Although surface area is a measurement of a 3-dimensional object, itsmeasurement is expressed in square, not cubic units.c) It is helpful for children to envision surface area not as a geometric abstraction butas the simple act of wrapping a box with paper.Omitting the overlap required for taping, how much paper is needed to cover thebox?For cylinders, what is the area of a can's paper label added to the area of its circulartop and bottom?d) For youngsters, the adjective "surface" in the term "surface area" can imply "onlyone surface." Thus, they may assume that they need find only one area of the surfacerather than the sum of all the object's surface areas.e) In most textbooks, the section on surface area includes diagrams of cuboids andcylinders labeled with their dimensions. This makes it relatively easy for youngstersto simply insert numbers into a surface area formula and perform the calculations.However, this is not how the surface area of boxes and cylinders is found in the realworld.3. What is essential to know or do in class?a) Introduce surface area as a generalized concept that applies to all 3-dimensionalobjects, not something unique to cuboids and cylinders.b) Introduce the idea of a "net" by cutting apart a box to demonstrate how a 3-dimensional object can be transformed into a 2-dimensional plane figure.