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Series

Professional Development > Learning Math: Measurement

Mathematics

K-2, 3-5, 6-8

Learning Math: Measurement

Examine some of the major ideas in measurement and their practical applications in this video- and web-based course for K-8 teachers.

A video- and web-based course for K-8 teachers; 12 half-hour video programs (10 per grade band), course guide, and website.

Learning Math: Measurement explores procedures for measuring and learn about standard units in the metric and customary systems, the relationships among units, and the approximate nature of measurement. You will also examine how measurement can illuminate mathematical concepts such as irrational numbers, properties of circles, and area and volume formulas, and discover how other mathematical concepts can inform measurement tasks such as indirect measurement. The 10th session explores ways to apply the concepts of measurement you’ve learned in K-8 classrooms.

Overview

Learning Math: Measurement, a video- and web-based course for elementary and middle school teachers, examines some of the major ideas in measurement. You will explore procedures for measuring and learn about standard units in the metric and customary systems, the relationships among units, and the approximate nature of measurement. You will also examine how measurement can illuminate mathematical concepts such as irrational numbers, properties of circles, and area and volume formulas, and discover how other mathematical concepts can inform measurement tasks such as indirect measurement.

The course consists of 10 approximately two-and-a-half-hour sessions, each with a half hour of video programming, problem-solving activities provided online and in a print guide, and interactive activities and demonstrations on the web. The 10th session (choose video program 10, 11, or 12, depending on your grade level) explores ways to apply the concepts of measurement you’ve learned in your own classroom.

Who's Who

Content Developer/Facilitator

Suzanne Chapin, Ed.D.

Dr. Chapin is a professor of mathematics education at Boston University, where she teaches graduate- and undergraduate-level courses in mathematics curriculum, mathematics content and methodology, mathematics for special-needs students (gifted and learning disabled), and educational reform. Dr. Chapin has been the principal investigator on a number of projects, including Project Challenge (Jacob K. Javits Gifted & Talented Students Education Program) and Partners in Change Project (U.S. DOE), and has worked with many colleagues as an investigator or consultant on grant-related research. Dr. Chapin is author or co-author of many mathematics textbooks and programs, including the Prentice Hall textbook series Middle Grade Mathematics: Tools for Success for students in grades 6-8; MEGA Projects: Math Explorations and Group Activities for students in grades 1-8; Algebra and Advanced Algebra for students in grades 8-12; and Classroom Discussions: Using Math Talk To Help Students Learn. She is also the senior author on Math Matters: Understanding the Math You Teach, Grades K-6. Dr. Chapin is a frequent speaker at national meetings of mathematicians, mathematics educators, researchers, and policy makers.

Video Index

Session 1: What Does It Mean To Measure?
Surface Area of a Rock
Nonstandard Units and Area
Nonstandard Units and Perimeter

Session 2: Fundamentals of Measurement
Partitioning Task
Constant Ratios in Triangles
Measurement as Approximation

Session 3: The Metric System
Referents for Measuring
Measuring Mass of Water
Metric Mutts

Session 4: Angle Measurement
Measuring Angles in Polygons
Sums of Angles in Polygons
Polygons in Geo-Logo

Session 5: Indirect Measurement and Trigonometry
Measuring Distance of a Tree
Measuring Height of a Tree
Using Trigonometric Ratios

Session 6: Area
Using the Rectangle Method
Triangles With Constant Area
Scaling Polygons

Session 7: Circles and π
Measuring Circumference and Diameter
Making Sense of the Formula
The Circle in Islamic Design

Session 8: Volume
Packaging Candy
Volume in Engineering

Session 9: Measurement Relationships
Maximizing Area
Volume and Surface Area
Maximizing Volume

Session 10: Classroom Case Studies

Grades K-2: Mary Guerino: 2nd Grade, Mabelle Burrell School
Grades 3-5: Jonathan Belber: 4th Grade, Milton Academy
Grades 6-8: David Cellucci: 8th Grade, Beachmont Middle School

Reading List

Duke, C. (May, 1998). Tangrams. Mathematics Teaching in the Middle School,485-487. (Session 1)

Download PDF File:
Tangrams


Taylor, P. Mark; Simms, Ken; Kim, Ok-Kyeong; and Reys, Robert E. (January, 2001). Do Your Students Measure Up Metrically? Teaching Children Mathematics, 282-287. (Session 3)


Reproduced with permission from Teaching Children Mathematics. © 2001 by the National Council of Teachers of Mathematics. All rights reserved.

Download PDF File:
Do Your Students Measure Up Metrically?

Fan, C. Kenneth (January, 1997). Areas and Brownies. Mathematics Teaching in the Middle School, 2 (3), 148-160. (Session 6)


Reproduced with permission from Mathematics Teaching in the Middle School.© 1997 by the National Council for Teachers of Mathematics. All rights reserved.

Download PDF File:
Areas and Brownies

 

Read the next passage from A History of the Circle by Ernest Zebrowski to consider further uncertainty in measurement: (Session 7)

Download PDF File:
A History of the Circle

 

Zebrowski, Ernest (1999). A History of the Circle (pp. 77-81). Piscataway, N.J.: Rutgers University Press. (Session 8)

Download PDF File:
A History of the Circle

 

Battista, Michael T. (March-April 1998). How Many Blocks? Mathematics Teaching in the Middle School, 3 (6), 404-11.

Reproduced with permission from Mathematics Teaching in the Middle School. © 1998 by the National Council of Teachers in Mathematics. All rights reserved.

Download PDF File:
How Many Blocks
How Many Blocks continued

 

Support Materials

The complete guide to the course is available here for download in PDF. You will need a copy of Adobe Acrobat Reader to read these files. You can download it for free from Adobe.

Introduction

Session 1: What Does It Mean to Measure

Session 2: Fundamentals of Measurement

Session 3: The Metric System

Session 4: Angle Measurement

Session 5: Indirect Measurement and Trigonometry

Session 6: Area

Session 7: Circles and

Session 8: Volume

Session 9: Measurement Relationships

Session 10, Grades K-2: Classroom Case Studies

Session 10, Grades 3-5: Classroom Case Studies

Session 10, Grades 6-8: Classroom Case Studies

Appendix, including Glossary

Progress Chart

Print out the progress chart to keep track of your progress through the Measurement online course. It is available in PDF format: Learning Math: Measurement Progress Chart

 

Credits

Website Production Credits

Learning Math: Measurement is a production of WGBH Interactive and WGBH Educational Productions for Annenberg Media.

© 2003 WGBH Educational Foundation. All rights reserved.

Senior Producer
Ted Sicker

Curriculum Director
Denise Blumenthal

Content Developer
Suzanne H. Chapin, Ed.D., Boston University, Massachusetts

Coordinating Producer
Sanda Zdjelar

Curriculum Developer
Anna Brooks

Core Advisors
Carol R. Findell, Boston University, Massachusetts
Bowen Kerins, Mathematics Consultant
Michelle Manes, Mathematics Teacher and Education Consultant

Designers
Plum Crane
Lisa Rosenthal
Christian Wise

Web Developers
Joe Brandt
Kit Buckley
Rishi K. Connelly

Online Video Segment Coordinator
Mary Susan Blout

Business Managers
Maria Constantinides
Adriana Sacchi

Special Assistance
Jennifer Davis-Kay
Regina Sloutsky
Julie Wolf

Video Series Production Credits

Learning Math: Measurement is a production of WGBH Educational Foundation for Annenberg Media.

Executive Producer
Michele Korf

Senior Project Director
Amy Tonkonogy

Producer/Director
Bob Roche

Content Developer/Facilitator
Suzanne H. Chapin, Ed.D., Boston University, Massachusetts

Advisors
Mary Eich, Newton Public Schools, Massachusetts
Susan Friel, University of North Carolina, Chapel Hill
Susan Lamon, Marquette University, Wisconsin
Miriam Leiva, University of North Carolina, Charlotte
Joan Lukas, University of Massachusetts, Boston
Myriam Steinback, TERC, Massachusetts

Content Editor
Srdjan Divac, Harvard University, Massachusetts

On Location Consultants
Kenton G. Findell
Bowen Kerins

Editor
Richard Katz

Additional Editing
Dickran H. Manoogian

Associate Producers
Irena Fayngold
Pamela Lipton

Project Manager
Sanda Zdjelar

Production Manager
Mary Ellen Gardiner

Post Production Associate Producer
Peter Villa

Location Coordinator
Mary Susan Blout

Teacher Liaison
Lisa Eure

Set Design
Irena Fayngold

Set Assistant
Elena Graceffa

Camera
Kevin Burke
Bill Charette
Lance Douglas
Larry LeCain
Steve McCarthy
Dillard Morrison
David Rabinovitz

Audio
Steve Bores
Chris Bresnahan
Charlie Collias
Jose Leon
Dennis McCarthy
Gilles Morin

Gaffers
Robert Cuddy

Interns
Timothy Barney
Ravi Blatt
Joe Gudema
Justin Hartery
Aimee Jones

Design
Gaye Korbet
Daryl Myers
Alisa Placas

Content Graphics
Richard Katz

On-line Editors
Mark Geffen
Richard Katz
John O’Brien

Sound Mix
John Jenkins
Dan Lesiw

Original Music
Tom Martin

Narrator
Jeff Loeb

Business Manager
Joe Karaman

Unit Manager
Maria Constantinides

Office Coordinators
Justin Brown
Laurie Wolf

Special Thanks

Session 2
Measure by Measure
Owen Young

Session 4
The Angle on Pool
Jillian’s — Boston, MA
Archival footage courtesy of Analog Devices Inc., High Speed Converter Lab and Wafer Fabrication Facilities

Session 5
GPS to the Rescue
Archival footage courtesy of NASA/JPL/Caltech

Session 9
The Giant Ocean Tank
The Staff at The New England Aquarium

Session 10
Classroom Case Studies
Mary Guerino, Mabelle Burrell School, Foxborough, MA
Jonathan Belber, Milton Academy, Milton, MA
David Cellucci, Beachmont Middle School, Revere, MA

Site Location
Ferryway School, Malden, MA

Series Directory

Learning Math: Measurement

Credits

Produced by WGBH Educational Foundation. 2002.
  • Closed Captioning
  • ISBN: 1-57680-728-2

Sessions

How to Use 0 About the Learning Math Courses

Session 1 What Does It Mean To Measure?

Explore what can be measured and what it means to measure. Identify measurable properties such as weight, surface area, and volume, and discuss which metric units are more appropriate for measuring these properties. Refine your use of precision instruments, and learn about alternate methods such as displacement. Explore approximation techniques, and reason about how to make better approximations.

Session 2 Fundamentals of Measurement

Investigate the difference between a count and a measure, and examine essential ideas such as unit iteration, partitioning, and the compensatory principle. Learn about the many uses of ratio in measurement and how scale models help us understand relative sizes. Investigate the constant of proportionality in isosceles right triangles, and learn about precision and accuracy in measurement.

Session 3 The Metric System

Learn about the relationships between units in the metric system and how to represent quantities using different units. Estimate and measure quantities of length, mass, and capacity, and solve measurement problems.

Session 4 Angle Measurement

Review appropriate notation for angle measurement, and describe angles in terms of the amount of turn. Use reasoning to determine the measures of angles in polygons based on the idea that there are 360 degrees in a complete turn. Learn about the relationships among angles within shapes, and generalize a formula for finding the sum of the angles in any n-gon. Use activities based on GeoLogo to explore the differences among interior, exterior, and central angles.

Session 5 Indirect Measurement and Trigonometry

Learn how to use the concept of similarity to measure distance indirectly, using methods involving similar triangles, shadows, and transits. Apply basic right-angle trigonometry to learn about the relationships among steepness, angle of elevation, and height-to-distance ratio. Use trigonometric ratios to solve problems involving right triangles.

Session 6 Area

Learn that area is a measure of how much surface is covered. Explore the relationship between the size of the unit used and the resulting measurement. Find the area of irregular shapes by counting squares or subdividing the figure into sections. Learn how to approximate the area more accurately by using smaller and smaller units. Relate this counting approach to the standard area formulas for triangles, trapezoids, and parallelograms.

Session 7 Circles and Pi (π)

Investigate the circumference and area of a circle. Examine what underlies the formulas for these measures, and learn how the features of the irrational number pi (π) affect both of these measures.

Session 8 Volume

Explore several methods for finding the volume of objects, using both standard cubic units and non-standard measures. Explore how volume formulas for solid objects such as spheres, cylinders, and cones are derived and related.

Session 9 Measurement Relationships

Examine the relationships between area and perimeter when one measure is fixed. Determine which shapes maximize area while minimizing perimeter, and vice versa. Explore the proportional relationship between surface area and volume. Construct open-box containers, and use graphs to approximate the dimensions of the resulting rectangular prism that holds the maximum volume.

Session 10 Classroom Case Studies, K-2

Watch this program in the 10th session for K-2 teachers. Explore how the concepts developed in this course can be applied through case studies of K-2 teachers (former course participants who have adapted their new knowledge to their classrooms), as well as a set of typical measurement problems for K-2 students.

Session 11 Classroom Case Studies, 3-5

Watch this program in the 10th session for grade 3-5 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 3-5 teachers (former course participants who have adapted their new knowledge to their classrooms), as well as a set of typical measurement problems for grade 3-5 students.

Session 12 Classroom Case Studies, 6-8

Watch this program in the 10th session for grade 6-8 teachers. Explore how the concepts developed in this course can be applied through case studies of grade 6-8 teachers (former course participants who have adapted their new knowledge to their classrooms), as well as a set of typical measurement problems for grade 6-8 students.