Session 10, Part B:
Reasoning About Measurement (40 minutes)

In This Part: Exploring Standards | Analyzing a Case Study

The National Council of Teachers of Mathematics (NCTM, 2000) has identified measurement as a strand in its Principles and Standards for School Mathematics. In grades pre-K-12, instructional programs should enable all students to do the following:

 • Understand measurable attributes of objects and the units, systems, and processes of measurement • Apply appropriate techniques, tools, and formulas to determine measurements

In grades 6-8 classrooms, students are expected to do the following:

 • Understand both metric and customary systems of measurement • Understand relationships among units and convert from one unit to another within the same system • Understand, select, and use units of appropriate size and type to measure angles, perimeter, area, surface area, and volume • Use common benchmarks to select appropriate methods for estimating measurements • Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision • Develop and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles, and develop strategies to find the area of more complex shapes • Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders • Solve problems involving scale factors, using ratio and proportion • Solve simple problems involving rates and derived measurements for such attributes as velocity and density

The NCTM (2000) Measurement Standards suggest that "frequent experiences in measuring surface area and volume can also help students develop sound understandings of the relationships among attributes and of the units appropriate for measuring them. For example, some students may hold the misconception that if the volume of a three-dimensional shape is known, then its surface area can be determined. This misunderstanding appears to come from an incorrect over-generalization of the very special relationship that exists for a cube: If the volume of a cube is known, then its surface area can be uniquely determined. For example, if the volume of a cube is 64 cubic units, then its surface area is 96 square units. But this relationship is not true for rectangular prisms or for other three-dimensional objects in general. ... Students can reap an additional benefit by considering how the shapes of rectangular prisms with fixed volume are related to their surface area. By observing patterns in the tables they construct for different fixed volumes, students can note that prisms of a given volume that are cubelike (i.e., whose linear dimensions are nearly equal) tend to have less surface area than those that are less cubelike" (NCTM, 2000, pp. 242-243).

 Principles and Standards for School Mathematics © 2000 by the National Council of Teachers of Mathematics, Inc. www.nctm.org. All rights reserved. This material may not be copied or redistributed electronically or in other formats without written permission from NCTM. standards.nctm.org Standards are listed with the permission of the National Council of Teachers of Mathematics (NCTM). NCTM does not endorse the content or validity of these alignments.
 Session 10, Grades 6-8: Index | Notes | Solutions | Video

© Annenberg Foundation 2015. All rights reserved. Legal Policy