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Series
Learning Math: Geometry
Discover how geometric reasoning can be used as a method of problem solving 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, course guide, and website.
Learning Math: Geometry, a video- and Web-based course for elementary and middle school teachers, introduces geometric reasoning as a method for problem-solving. In this course, which is organized around the content standards of the National Council of Teachers of Mathematics (NCTM), you will explore the properties of geometric figures; make constructions using pencil and paper, and also using dynamic software; and practice using mathematical language to express ideas and justify your reasoning. Some important geometric ideas, such as symmetry, similarity, and trigonometry, will also be examined. You will begin to explore the basis of formal mathematical proofs and solid geometry. The course material progresses from more visual, intuitive ways of solving problems to more formal explorations of geometric ideas, properties, and proofs.
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 or 11 and 12, depending on your grade level) explores ways to apply the concepts of geometry you’ve learned in your own classroom.
Course Overview
Geometry introduces geometric reasoning as a method for problem solving. In this course, you will explore the properties of geometric figures such as triangles, quadrilaterals, and other polygons. You will make constructions using pencil and paper, and also dynamic software, and you will practice using mathematical language to express ideas and justify your reasoning. Some important geometric ideas such as symmetry, similarity, and trigonometry will also be examined. Lastly, you will begin to explore the basis of formal mathematical proofs and solid geometry. The course material progresses from more visual, intuitive ways of solving problems to more formal explorations of geometric ideas, properties, and, finally, proofs.
The course consists of 10 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. Although each session includes suggested times for how long it may take to complete all of the required activities, these times are approximate. Some activities may take longer. You should allow at least two and a half hours for each session. The 10th session explores ways to apply the concepts of geometry you’ve learned in K-8 classrooms. You should complete the sessions sequentially.
Who's Who
Content Developer/Facilitator
Michelle Manes
Michelle Manes earned a Bachelor’s degree in mathematics from UC Berkeley and a Master’s of Education from Boston University. She has taught mathematics at all levels, from third grade through college. She is a primary author on the Connected Geometry, Impact, and Mathematical Methods curricula. She has special interests in mathematics history, women and girls studying mathematics, and Deaf education. She is currently working towards a Ph.D. in mathematics at Brown University.
Onscreen Participants
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Laverne Agard Special Needs Teacher, Grades 2-5 |
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Lolita Mattos Math Teacher, Grades 7-8 |
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Brad Ankney Math Teacher, Grades 4-10 |
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Joy Roy Teacher, Grade 4 |
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Jean Beebe Teacher, Grade 6 |
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Catalina Saenz Math Teacher, Grade 6 |
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Javier Castillo Teacher, Grades 4-5 |
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Helen Sellers Teacher, Grade 5 |
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Kenton G. Findell Math Teacher, Grade 6 |
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Vicky Sutton Teacher, Grade 5 |
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Michelle Kurchian Math Teacher, Grade 5 |
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Constance Vanne Math Teacher, Grade 8 |
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Filberto Santiago-Lizardi Math Specialist, Grade 6 |
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Heidi Weber Math Teacher, Grade 8 |
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Ric Mosher Math Teacher, Grades 7-9 |
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Thomas Zaya Math Teacher, Grade 8 |
Video Index
Session 1: What Is Geometry?
Describing Geometric Designs
Constructing Triangles
Defining Basic Objects in Geometry
Session 2: Triangles and Quadrilaterals
Rules for making Triangles
Another Rule for Making Triangles
Building Toothpick Towers
Session 3: Polygons
Finding Hidden Polygons
Testing Definitions
Demonstrating Sum of Angles in a Triangle
Sum of Angles in a Polygon
Session 4: Parallel Lines and Circles
Inscirbed Angle in a Semicircle
Constructing with Circles
Session 5: Dissections and Proof
Transforming Shapes
Window Making and Proof
Session 6: Pythagorean Theorem
Calculating Area of Squares on a Triangle
Proving Angles and Areas of Squares
Session 7: Symmetry
Reflecting with Perpendicular Bisectors
Exploring Angles of Rotation
Session 8: Similarity
Comparing Copies
Estimating Height with Mirrors
Similar Triangles and Radiation Therapy
Session 9: Solids
Constructing Platonic Solids
Representing 3-D Figures in 2-D
Session 10: Classroom Case Studies
Grades K-2: Rose Christiansen: 2nd Grade, Lincoln School
Grades 3-5: Michelle Kurchian: 5th Grade, Alice M. Barrows Elementary School
Grades 6-8: Catalina Saenz: 6th Grade, Roxbury Prep Charter School
Heidi Weber: 8th Grade, F.A. Day Middle School
Reading List
Education Development Center, Inc. (2000). Perspective: What Is Geometry? In Connected Geometry: A Habits of Mind Approach to Geometry. Glencoe/McGraw-Hill. (Session 1)
Reproduced with permission from the publisher. Copyright © 2000 by Glencoe/McGraw-Hill. All rights reserved.
Download PDF File:
Perspective: What Is Geometry?
Steen, Lynn Arthur (1990). Pattern. In On the Shoulders of Giants: New Approaches to Numeracy. Edited by Lynn Arthur Steen (pp. 1-10). Washington, D.C.: National Academy Press. (Session 2)
Reproduced with permission from the publisher. Copyright © 1990 by National Academy Press. All rights reserved.
Download PDF File:
Pattern
Continued…
Senechal, Marjorie (1990). Shape. In On the Shoulders of Giants: New Approaches to Numeracy. Edited by Lynn Arthur Steen (pp. 139-148). Washington, D.C.: National Academy Press. (Session 3)
Reproduced with permission from the publisher. Copyright © 1990 by National Academy Press. All rights reserved.
Download PDF File:
Shape
Continued…
Cuoco, Al; Goldenberg, E. Paul; and Mark, June (December, 1996). Geometric Approaches to Things. In the paper “Habits of Mind: An Organizing Principle for Mathematics Curriculum.” The Journal of Mathematical Behavior, 5, (4), 375-402. (Session 4)
Reproduced with permission from the publisher. Copyright © 2002 by Elsevier Science, Inc. All rights reserved.
Download PDF File:
Geometric Approaches to Things
Senechal, Marjorie (1990). Shape. In On the Shoulders of Giants: New Approaches to Numeracy. Edited by Lynn Arthur Steen (pp. 148-160). Washington, D.C.: National Academy Press. (Session 5)
Reproduced with permission from the publisher. Copyright © 1990 by National Academy Press. All rights reserved.
Download PDF File:
Shape
Continued…
Continued…
Continued…
Crowe, D. and Thompson, Thomas M. (Reston, VA: National Council of Teachers of Mathematics, 1987). Transformation Geometry and Archaeology. Learning and Teaching Geometry, K-12, 1987 Yearbook. Edited by Mary Montgomery Lindquist. (Session 7)
Reproduced with permission from the publisher. Copyright © 1987 by the National Council of Teachers of Mathematics. All rights reserved.
Download PDF File:
Transformation Geometry and Archaeology
Schifter, Deborah (February, 1999). Learning Geometry: Some Insights Drawn from Teacher Writing. Teaching Children Mathematics, 5, (5), 360-366. (Session 8)
Reproduced with permission from Teaching Children Mathematics. Copyright © 1999 by the National Council of Teachers of Mathematics. All rights reserved.
Download PDF File:
Learning Geometry: Some Insights Drawn from Teacher Writing
Continued…
Van de Walle, John A. (2001). Geometric Thinking and Geometric Concepts. In Elementary and Middle School Mathematics: Teaching Developmentally, 4th ed. Boston: Allyn and Bacon. (Session 9)
Reproduced with permission from the publisher. Copyright © 2001 by Pearson Education. All rights reserved.
Download PDF File:
Geometric Thinking and Geometric Concepts
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 is Geometry?
Session 2: Triangles and Quadrilaterals
Session 3: Polygons
Session 4: Parallel Lines and Circles
Session 5: Dissections and Proof
Session 6: Pythagorean Theorem
Session 7: Symmetry
Session 8: Similarity
Session 9: Solids
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 chart below to keep track of your progress through the Geometry online course. It is available in PDF format.
Credits
Learning Math: Geometry is a production of WGBH Interactive and WGBH Educational Programming and Outreach for Annenberg Media.
Copyright © 2003 WGBH Educational Foundation. All rights reserved.
Senior Producer
Ted Sicker
Curriculum Director
Denise Blumenthal
Content Developer
Michelle Manes, Mathematics Teacher and Education Consultant
Curriculum Developer
Anna Brooks
Project Manager
Sanda Zdjelar
Special Projects Assistant
Nina Farouk
Core Advisors
Suzanne Chapin
Srdjan Divac
Carol Findell
Bowen Kerins
Designers
Plum Crane
Lisa Rosenthal
Christian Wise
Web Developers
Joe Brandt
Kirsten Connelly
Bob Donohue
Peter Pinch
Online Video Segment Coordinator
Mary Susan Blout
Business Managers
Walter Gadecki
Joe Karaman
Unit Managers
Maria Constantinides
Adriana Sacchi
With the assistance of
Geoffrey Dixon
Stephani Roberts Lincoln
Yasmin Madan
Kate Smyres
Julie Wolf
Video Series Production Credits
Learning Math: Geometry is a production of WGBH Educational Foundation for Annenberg Media.
Executive Producer
Michele Korf
Senior Project Director
Amy Tonkonogy
Producer
John Browne
Content Developer/Facilitator
Michelle Manes, Mathematics Teacher and Education Consultant
Advisors
Nicholas Branca, San Diego State University, CA
Miriam Leiva, University of North Carolina, Charlotte
Carol Malloy, University of North Carolina, Chapel Hill
Bill Masalski, University of Massachusetts, Amherst
Arthur Powell, Rutgers-Newark College of Arts and Sciences, NJ
Content Editor
Srdjan Divac, Harvard University, MA
On Location Consultants
Kenton G. Findell
Bowen Kerins
Editor
Miguel Picker
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
Production Manager
Mary Ellen Gardiner
Post Production Associate Producer
Peter Villa
Location Coordinator
Mary Susan Blout
Teacher Liaison
Lisa Eure
Set Assistant
Elena Graceffa
Camera
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
Interns
Timothy Barney
Ravi Blatt
Joe Gudema
Justin Hartery
Aimee Jones
Design
Gaye Korbet
Daryl Myers
Alisa Placas
Content Graphics
Mark Geffen
John O’Brien
On-line Editors
David Eells
John O’Brien
Sound Mix
John Jenkins
Dan Lesiw
Original Music
Tom Martin
Additional Music
Concerto in G Major, J.B. de Boismortier
Soloist
John Tyson
Recorder
Frances Conover Fitch
Harpsichord
Jane Starkman, Kathryn Shaw
Violins
Jann Cosart
Viola
Alice Robbins
Violincello
Tom Coleman
Double Bass
Narrator
Jeff Loeb
Business Manager
Joe Karaman
Unit Manager
Maria Constantinides
Office Coordinators
Justin Brown
Laurie Wolf
Special Thanks
Session 2: Triangles and Quadrilaterals: Boston’s New Bridge
Kirk Elwell
Lead Field Engineer
Bechtel/Parsons Brinkerhoff
Session 3: Polygons: Three-Dimensional Printing
David Russell
Director of Engineering
Z Corporation
Marina Hatsopoulos
CEO
Z Corporation
Tom Clay
President
Z Corporation
Session 4: Parallel Lines and Circles: Three-Dimensional Maps
Seth Teller
Associate Professor
Lab for Computer Science, MIT
Hilary Karls
Student, MIT
Priya Agrawal
Student, MIT
Session 5: Dissections and Proof: Window Making and Proof
Jim Ialeggio
Architectural Detail In Wood
Session 6: The Pythagorean Theorem: The Pythagorean Theorem and 18th-Century Cranes
Rick Brown
Massachusetts College of Art
Wyly Brown
Session 7: Symmetry: Wooden Boats and Line Symmetry
Nat Benjamin
Gannon and Benjamin Marine Railway
Session 8: Similarity: Similar Triangles and Radiation Therapy
Dr. Anita Mahajan
Radiation Oncologist
Tufts – New England Medical Center
Maxon J. Buscher
Chief Dosimetrist
Tufts – New England Medical Center
Jason K. Talkington
Medical Dosimetry Student
Tufts – New England Medical Center
Sandra John-Baptiste, R.T.T.
Medical Dosimetry Student
Tufts – New England Medical Center
Kevin O’Leary
Tufts – New England Medical Center
Sean O’Leary
Tufts – New England Medical Center
Session 9: Solids: Architecture and Solid Geometry
Ann Beha
Principal
Ann Beha Architects
Session 10: Classroom Case Studies
Michelle Kurchian, Alice M. Barrows Elementary School, Reading, MA
Catalina Saenz, Roxbury Preparatory Charter School, Roxbury, MA
Heidi Weber, F.A. Day Middle School, Newton, MA
Site Location
Ferryway School, Malden, MA
