Course Guide - USAID Teacher Education Project

Unit 3 GeometryWeek 5 Session 1: Geometric Measurement: Volume of Cuboids and Cylinders1. What are the important concepts?a) Volume is the amount of space taken up by a 3-dimensional object.b) Volume can also refer to the capacity of an object (such as an empty box or cup)that can be filled.c) Volume is expressed in cubic units.d) The volume of a prism or cylinder is calculated by multiplying the area of its baseby its height.2. How do children think about these concepts?a) Youngsters often confuse surface area and volume, both attributes of 3-dimensional objects and usually taught in tandem.Children need to work with "nets" to understand surface area, and then fill boxes andcylinders to understand volume. In this way they can see that 1) an empty box can befilled to illustrate volume and 2) the same box, flattened into a net, shows surfacearea.b) Children tend to wonder why the volume of a cylinder can be expressed in cubicunits when the cylinder is "round," and cannot be tightly packed with unit cubes tocalculate volume.This is why it was important to stress (during the sessions on the area of irregularfigures and circles) that "square units" can be used as a form of measurement even ifthe shape under consideration is not "square."The same can be true for “cubic units.” A 3-dimensional figure does not have to be acuboid in order to discuss its volume in cubic units.c) Volume is something children experience every day without realizing it. Theirmothers may use measuring cups when cooking; bottles may have their volume notedon the label. These examples illustrate how an object's capacity can be expressed incubic units even if the item isn't a cuboid.3. What is essential to know or do in class?a) Introduce volume as a generalized concept that applies to both 3-dimensionalsolids as well as any 3-dimensional object that has a capacity that can be filled.b) Using what students know about area, have them calculate the volume of the boxesand cylinders that they brought to class.c) Have students develop generalized expressions that express how to calculate thevolume of boxes and cylinders.