# 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
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

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

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)

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)

Areas and Brownies

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

A History of the Circle

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

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.

How Many Blocks
How Many Blocks continued

### Support Materials

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.

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

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

Maria Constantinides

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

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

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

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