## Series

# 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.

**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