Acknowledgments

The development of the Minnesota K-12 Mathematics Framework is the result of the combined efforts of many persons. Many stakeholders have worked collaboratively toward improving mathematics and science education in Minnesota. We are grateful to the members of the Board of SciMathMN, under the direction of Cyndy Crist and Kristi Rollag Wangstad, for affirming the impor- tance of this work and approving financial support for this effort.

Special thanks goes to Sharon Stenglein, Mathematics Specialist at the Minnesota Department of Children, Families, and Learning. In her role at MDCFL, Sharon was responsible for facilitating the work to delineate state standards for mathematics when the process of establishing graduation standards began. She has worked continuously since then to guarantee that the teachers of mathematics in Minnesota have had input into those standards and the revision process. Her vision for the Framework and her commitment to its implementation have been a source of inspiration and “quality improvement” in its development.

The Framework’s Leadership Team met three years ago to outline the present state of mathematics and science education in Minnesota and set goals that could be met in this state document. They have worked collaboratively since then to forge a common outline for both the mathematics and science documents and have continued to provide valuable input, direction, and guidance to both the process and the product.

Over one hundred thoughtful, talented, and committed K-16 educators from around the state participated in the difficult task of developing Chapter 3. During intense writing conferences, they brainstormed, argued and worked together to reach consensus on what K-12 Minnesota students should know and be able to do in mathematics. They then identified sample lessons that exempli- fied that vision. Their energetic conversations will continue to form the basis of the professional development work we do in the statewide dissemination work that continues.

Sharon Hessney and Michele Gage interviewed Minnesota citizens and highlighted their stories in the Reality Checks: Mathematics in the Workplace sections. Along with John Marshall, they also contributed the classroom vignettes to clarify the vision of the standards.

Over four hundred state and national reviewers contributed valuable and specific advice on final content revisions in Chapter 3. These comments challenged us to be more clear, concise, and specific and often identified some mathematical errors or miscommunications. Special thanks to John Marshall for his insightful review comments on these pages and his commitment to children.

The Minnesota Mathematics Best Practice Network is a group of teacher leaders, formed to provide professional development and personal support to Minnesota teachers. Many thanks to those Best Practice Teachers who have been involved in the Framework’s development, have participated in our pilot training sessions, and/or have made presentations themselves to disseminate the Framework in draft form around the state.

SciMathMN Minnesota K-12 Mathematics Framework 1 ACKNOWLEDGMENTS

Thanks to Arnie Cutler, Executive Director of the Minnesota Council of Teachers of Mathematics, for providing personal oversight and support in the development process of both the Minnesota Gradu- ation Standards and this Framework. Thanks to the Board of Directors of MCTM who provided official support for this document, and to the many MCTM members who worked on this project— as writers, reviewers, editors, and cheerleaders.

This project received daily support from SciMathMN staff: • As project manager, Anne Bartel initiated the writing conference format to develop the content of Chapter 3. This format fostered the professional conversations that translated into this policy work. Her vision for this project focused the work of many K-16 educators and her creative editing emp- tied many red pens as she worked with several writers and the Leadership Team to develop the remaining chapters.

• Vicki De Voss worked tirelessly to type, layout, and edit the entire review draft of Chapter 3. She also contributed to the drafts of several other chapters. Her remarkable organizational skills and her attention to details have been crucial in maintaining the consistent quality of these pages.

• Nancy Nutting contributed renewed energy to the project when she joined SciMathMN in the final two years of the Framework’s development. She challenged us to incorporate SciMathMN’s commitment to equity throughout this framework, wrote drafts of Chapter 4, oversaw the revision work, and managed the final last-minute details. • Nancy Desmond’s careful and thorough work made Chapter 2: Best Practice research based yet readable and useful to busy classroom teachers. She also took on a major editing role in the last few, hectic months of this project, learning more than anyone would ever want to know about citing references. • Deb Rose served as fiscal manager of the project and our right-hand assistant. We relied on her to handle a variety of tasks, from making conference and meeting room reservations to printing draft copies—all this while answering Frameworks-related phone calls and keeping the paper work organized. We are especially thankful for Deb’s sense of humor and personal support.

• Katie Bratsch, SciMathMN’s Communications Specialist, provided valuable assistance with compli- cated computer graphics, creative informational brochures, lengthy mailing lists, and communications with Don Schwert, our SciMathMN webmaster.

• Ed Hessler was our “adopted mathematician” who played a special role as our objective editor. His support of the development process, his insight into teaching and learning, and his friendship were invaluable to us.

• Kathleen Lundgren was a helpful sounding board, supportive friend, and inspired editor. • Laurie Peterman was always one step ahead of us as she developed the parallel K-12 Minnesota Science Framework. She very willingly and generously offered us her insights as well as the rough drafts of the science document for our perusal. • Bill Linder-Scholer, Executive Director of SciMathMN, maintained the vision of systemic reform and continually emphasized the role of the Framework in that vision throughout our work. His collaboration with the Graduation Standards Executive Committee and his networking with other state personnel were important factors in the endorsement of the Framework by the Minnesota Depart- ment of Children, Families and Learning and the Minnesota State Board of Education. We appreci- ate his ability to communicate our message so effectively throughout the state.

2 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

We would also like to express our appreciation for the cooperation we received from the cartoon- ists whose work introduces the sections of Chapter 3, from publishers whose tasks are included in the Sample Tasks within Chapter 3, and from persons who shared their personal stories of how mathematics is central to their jobs for the Reality Checks: Mathematics in the Workplace vignettes.

Finally, the creative graphics and layout work of Michael Hall and Debra Kelley and their staff trans- formed pages of text into a colorfully inviting and user-friendly document that clearly and coherently communicates our message.

Publication of this document is the culmination of three years of professional discussions, writing conferences, individual and group reviews, and editing sessions. This work has affirmed our belief in the power of collaboration. Those who have participated in this process are listed on the pages that follow. We offer apologies to anyone whose name was inadvertently omitted. The long list of names and the variety of participants’ locations reflect that this policy document is truly a statewide effort. We thank all of the educators who gave generously of their time, their ideas, and their energy to create the Minnesota K-12 Mathematics Framework. We will continue to work together to turn this vision of mathematics education into a reality for all Minnesota children.

SciMathMN Minnesota K-12 Mathematics Framework 3 ACKNOWLEDGMENTS Minnesota K-12 Mathematics Framework

Project Manager MN Anne Bartel SCIMATH Mathematics Project Manager SciMathMN

Project Staff

Vicki De Voss Mathematics Project Specialist SciMathMN

Nancy Nutting Mathematics Project Specialist SciMathMN

Nancy Desmond Consultant SciMathMN

Additional SciMathMN Staff

Margo Berg Bill Linder-Scholer A2A Technology Co-Project Manager Executive Director

Katie Bratsch Geri Nelson Communications Coordinator Science Frameworks Specialist

Cyndy Crist Laurie Peterman Manager of Teacher Education Initiatives Science Project Manager

John Erickson Deb Rose Professional Development Coordinator SciMathMN Fiscal Analyst

Ed Hessler Patty Simpson Professional Development Manager Transforming Teacher Education

Vera Ladd-Johnson Tina Welle Clerical Intern

Frameworks Leadership Team

Wayne Buckley Don Pascoe La Porte Public Schools Osseo Public Schools

Jim Foley Dale Pearson Anoka-Hennepin Public Schools St. Paul Public Schools

Mark Gugisberg Craig Rypkema Anoka-Hennepin Public Schools Bemidji Public Schools

Bonnie Hagelberger Beth Stauber-Johnson Anoka-Hennepin Public Schools Duluth Public Schools

Ed Hessler Sharon Stenglein SciMathMN/MSTA/MESFI MN Dept. of Children, Families & Learning

Joyce Kloncz Martha Wallace Moundsview Public Schools St. Olaf College

Kathleen Lundgren Nancy Zwickey MN Dept. of Children, Families & Learning Lake Crystal-Wellcome Memorial Area Schools

4 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

Participants: Writing & Editing Conferences

Paul Agranoff James Foley St. Francis Intermediate School Champlin Park High School St. Francis, Minnesota Champlin Park, Minnesota

Denise Anderson Paula Freidson St. Francis Elementary Tanglen Elementary School St. Francis, Minnesota Minnetonka, Minnesota

Patti Bambenek Marsha Gabrielson Nettleton Math/Science Magnet Lakeview Elementary Duluth, Minnesota Cottonwood, Minnesota

Steve Benson Joan Garfield University of New Hampshire University of Minnesota Durham, New Hampshire Minneapolis, Minnesota

Larry Copes Lana Golembeski Augsburg College Minnetonka High School Minneapolis, Minnesota Minnetonka, Minnesota

Arnie Cutler Bernadette Green U of M-Geometry Center Loring Elementary Minneapolis, Minnesota Minneapolis, Minnesota

Peter DeMars Alice Mae Guckin Austin High School College of St. Scholastica Austin, Minnesota Duluth, Minnesota

Nancy Desmond Bonnie Hagelberger Consultant Monroe Elementary School Newport, Minnesota Anoka, Minnesota

Vicki De Voss Katy Hallberg Minneapolis Public Schools Prior Lake High School Minneapolis, Minnesota Prior Lake, Minnesota

Jan Dirlam Rollie Hanks Hopkins North Junior High School Retired Hopkins, Minnesota Minnetonka, Minnesota

Mike Donahue Jennifer Hanzak Cloquet High School Pillsbury Math/Science/Technolgy Cloquet, Minnesota Minneapolis, Minnesota

John Erickson Ed Hessler Hopkins Schools SciMathMN/MSTA/MESFI Hopkins, Minnesota St. Paul, Minnesota

Gene Fabes (deceased) Ilene Hokanson University of Minnesota Reede Gray Elementary School Minneapolis, Minnesota Redwood Falls, Minnesota

Gail Feneis Karen Holsten Buffalo Public Schools Cedar Elementary School Buffalo, Minnesota Cedar, Minnesota

Shawn Fish Dennis Holt Oxbow Creek Elementary Champlin Park High School Champlin, Minnesota Champlin Park, Minnesota

Giovanna Fjelstad Al Hoogheem Retired Hudson High School Northfield, Minnesota Hudson, Wisconsin

SciMathMN Minnesota K-12 Mathematics Framework 5 ACKNOWLEDGMENTS

Participants: Writing & Editing Conferences (cont.)

Garry Housker Jeanette McDonald Glen Lake Elementary School Nettleton Magnet Elementary Minnetonka, Minnesota Duluth, Minnesota

Tina Housker Heidi Mlynarczyk Glen Lake Elementary School Lowell Elementary School Minnetonka, Minnesota Duluth, Minnesota

Jim Huber Andrew Moen Faribault High School Blue Earth Elementary School Faribault, Minnesota Blue Earth, Minnesota

Jan Kieber Earl Molden Shakopee Senior High School Appleton Elementary School Shakopee, Minnesota Appleton, Minnesota

Tom Kilkelly Mary Moreira St. Thomas Academy Windom Open School St. Paul, Minnesota Minneapolis, Minnesota

Carolyn Kreibich Tom Muchlinski Turtle Lake Elementary School Wayzata High School Turtle Lake, Minnesota Plymouth, Minnesota

Don Kuusinen Jodi Nelson Grand Rapids High School Sheridan Hills Elementary Grand Rapids, Minnesota Richfield, Minnesota

Connye LaCombe Nancy Nutting Open School Minneapolis Public Schools St. Paul, Minnesota Minneapolis, Minnesota

Emily Larsen Marlys Otis Austin High School White Bear Lake High School Austin, Minnesota White Bear Lake, Minnesota

Loren Larson Dale Pearson St. Olaf College Highland Park High School Northfield, Minnesota St. Paul, Minnesota

Kathy Lawyer-Niebeling Helene Perry Galtier Magnet School Barton Open School St. Paul, Minnesota Minneapolis, Minnesota

Roger Leary Tim Peil Retired Moorhead State University Richfield, Minnesota Moorhead, Minnesota

JoAnn Luhtala Mary Quam Ordean School Taylors Falls Elementary Duluth, Minnesota Taylors Falls, Minnesota

Nancy Lundeen Becky Raimann Nettleton Magnet Elementary Inver Hills Community College Duluth, Minnesota Inver Grove Heights, Minnesota

Linda Lundquist-Lintgen Mary Kay Rheingans Cedar Elementary School Appleton Elementary School Cedar Minnesota Appleton, Minnesota

John Marshall Judy L. Rohde University of South Florida John Glenn Middle School St. Petersburg, Florida Maplewood, Minnesota

6 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

Participants: Writing & Editing Conferences (cont.)

Kristin Rood Barbara Swanson St. Olaf College Capitol Hill Magnet School Northfield, Minnesota St. Paul, Minnesota

Susan Roosenraad Anne Tank Northfield High School Minneapolis Public Schools Northfield, Minnesota Minneapolis, Minnesota

Craig Rypkema Jon Tellekson Bemidji Middle School Minnetonka High School Bemidji, Minnesota Minnetonka, Minnesota

Roger Sadlowsky Bobbie Tonkin Columbia Heights High School Breck School Columbia Heights, Minnesota Golden Valley, Minnesota

Kathy Salminen Kathy Trier Nettleton Magnet School Eagan High School Duluth, Minnesota Eagan, Minnesota

Kay Sanken Ted Vessey Hutchinson High School St. Olaf College Hutchinson, Minnesota Northfield, Minnesota

Ron Schulte Elaine Vezina Wayzata High School Sioux Trail Elementary School Plymouth, Minnesota Burnsville, Minnesota

Kay Shager Ken Vos North High School College of St. Catherine North St. Paul, Minnesota St. Paul, Minnesota

Patty Simpson Martha Wallace St. Cloud State University St. Olaf College St. Cloud, Minnesota Northfield, Minnesota

Jack Sorteberg Patty Wallace St. Paul Academy Lowell Elementary School St. Paul, Minnesota Brainerd, Minnesota

Beth Stauber-Johnson Linda Warfield Duluth Public Schools Pillsbury Math/Science/Technolgy Magnet School Duluth, Minnesota Minneapolis, Minnesota

Sally Sudo Steve Weflen Retired Jackson High School Minneapolis Public Schools Jackson, Minnesota

Eileen Sullivan Judy Zachariason Consultant Redwood Valley Middle School Minnetonka, Minnesota Redwood Falls, Minnesota

SciMathMN Minnesota K-12 Mathematics Framework 7 ACKNOWLEDGMENTS

Contributing Authors

Steve Benson Loren Larson University of New Hampshire St. Olaf College Durham, New Hampshire Northfield, Minnesota

Anne Bartel John Marshall SciMathMN University of South Florida St. Paul, Minnesota St. Petersburg, Florida

Arnie Cutler Nancy Nutting Geometry Center - U of M SciMathMN Minneapolis, Minnesota St. Paul, Minnesota

Mark Cutler Don Pascoe University of Washington Osseo Public Schools Seattle, Washington Osseo, MN

Nancy Desmond Laurie Peterman Consultant SciMathMN Newport, Minnesota St. Paul, Minnesota

Vicki De Voss Mary Quam SciMathMN Taylors Falls Elementary St. Paul, Minnesota Taylors Falls, Minnesota

Danna Elling Lynn Steen Consultant St. Olaf College Hastings, MN Northfield, Minnesota

Michele Satty Gage Sharon Stenglein New York City Technical College of CUNY MN Dept. of Children, Families & Learning Brooklyn, New York St. Paul, Minnesota

Alice Guckin Sally Sudo College of St. Scholastica Retired Duluth, MN Minneapolis Public Schools

Rose Gundacker Anne Tank Rosemount High School Minneapolis Public Schools Rosemount, Minnesota Minneapolis, Minnesota

Bonnie Hagelberger Ted Vessey Monroe Elementary St. Olaf College Anoka, MN Northfield, Minnesota

Eric Hart Ken Vos Western Michigan University College of St. Catherine Kalamazoo, Michigan St. Paul, Minnesota

Ed Hessler Martha Wallace SciMathMN/MSTA/MESFI St. Olaf College St. Paul, Minnesota Northfield, Minnesota

Sharon Hessney Fenway Middle College High School Boston Public Schools Boston, Massachusetts

8 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

Keynote Speakers: Chapter 3 Writing Conferences

Number Sense Randomness and Uncertainty Sharon A.C. Hessney Joan Garfield Fenway Middle College High School University of Minnesota Boston Public Schools Minneapolis, Minnesota Boston, Massachusetts Patterns, Relationships & Functions Shape, Space & Measurement Mary Jo Aiken Thomas Banchoff Retired-Benilde/St. Margaret’s Brown University Edina, Minnesota Providence, Rhode Island Discrete Mathematics Data Investigations Loren Larson John Marshall St. Olaf College Visiting Lecturer Northfield, Minnesota University of South Florida St. Petersburg, Florida

People Interviewed for “Reality Checks: Mathematics in the Workplace”

Number Sense Randomness & Uncertainty Rick Streff Sue Mulvihil St. Paul, Minnesota St. Paul, Minnesota

Shape, Space & Measurement Patterns, Relationships & Functions Joe Cohen Bruce Hill Plymouth, Minnesota Worthington, Minnesota

Data Investigations Discrete Mathematics Toni Hunstiger Warren Beck Edina, Minnesota Edina, Minnesota

National Expert Reviewers of Chapter 3

Betty Cheeley Joan Garfield Mathematics Consultant University of Minnesota Couer d’ Alene, Idaho Minneapolis, Minnesota

Arthur Coxford Eric Hart University of Michigan Western Michigan University East Lansing, Michigan Kalamazoo, Michigan

Roger Day Glenda Lappan Illinois State University Michigan State University Normal, Illinois East Lansing, Michigan

John Dossey Mary M. Lindquist Illinois State University Columbus State University Eureka, Illinois Columbus, Georgia

Susanna Epp Joseph Malkevitch DePaul University City University of New York (CUNY) Chicago, Illinois Garden City, New York

William Fitzgerald John Marshall Michigan State University University of South Florida East Lansing, Michigan St. Petersburg, Florida

Joseph Gallian Anthony Phillips University of Minnesota State University of New York (SUNY) Duluth, Minnesota Stony Brook, New York

SciMathMN Minnesota K-12 Mathematics Framework 9 ACKNOWLEDGMENTS

National Expert Reviewers of Chapter 3 (cont.)

Elizabeth Phillips Michael Shaugnessy Michigan State University Portland State University East Lansing, Michigan Portland, Oregon

Barbara Reys Lynn Steen University of Missouri St. Olaf College Columbia, Missouri Northfield, Minnesota

Thomas A. Romberg Ronald Stone University of Wisconsin Mathematics Consultant Madison, Wisconsin Hayden Lake, Idaho

Richard L. Scheaffer Ken Vos University of Florida College of St. Catherine Gainesville, Florida St. Paul, Minnesota

Marjorie Senechal Ann Watkins Smith College University of California Northampton, Massachusetts Northridge, California

Additional Reviewers

Mary Jo Aiken David Buhl Edina, Minnesota Superior, Wisconsin

Dorothy Anway Dave Buresh Duluth, Minnesota Litchfield, Minnesota

Bonnie Austin Joan M. Cady Northfield, Minnesota St. Paul, Minnesota

Al Barth Kathy Cahill St. Cloud, Minnesota Minneapolis, Minnesota

Pat Bergman Ford Campbell Robbinsdale, Minnesota Minneapolis, Minnesota

Bill Bjorum Kay Campbell North Branch, Minnesota Thief River Falls, Minnesota

Denise Black Janelle Daugaard Bemidji, Minnesota Duluth, Minnesota

Kathy Bochman Roy DeBoer White Bear Lake, Minnesota Benson, Minnesota

David Boone Annie Decker Winona, Minnesota Rochester, Minnesota

Kristi Borland Deborah Distad Hibbing, Minnesota St. Paul, Minnesota

David Bornfleth Mike Doro Kasson, Minnesota Remer, Minnesota

Carol Bracke Suraya Driscoll Minnetonka, Minnesota East Grand Forks, Minnesota

Bonnie Breza David Dye Winona, Minnesota St. Paul, Minnesota

Jim Brickwedde John Edmundson Golden Valley, Minnesota Stillwater, Minnesota

Deborah Brown Teri Edwards White Bear Lake, Minnesota Plymouth, Minnesota

10 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

Additional Reviewers (cont.)

Greg Ellsworth Dick Hanson Nicollet, Minnesota Burnsville, Minnesota

Amy Engen Jon Harley Savage, Minnesota Inver Grove Heights, Minnesota

William Eppright Danielle Hartman St. Paul, Minnesota Kasson, Minnesota

Darrell Erickson Sherry Hastings Austin, Minnesota Appleton, Minnesota

Julie Espe Sherry Hauck Austin, Minnesota Madison, Minnesota

Sharyn Fenwick Patty Hill Minnetonka, Minnesota Cedar, Minnesota

Kristy Flanaghan Janet Hoekman Rochester, Minnesota Minneapolis, Minnesota

Betty Funk Marcia Houtz Ham Lake, Minnesota St. Paul, Minnesota

Mary Jo Furtman Heidi Ifkewitsch Duluth, Minnesota Mounds View, Minnesota

Jeff Gallus Sandy Jernberg Savage, Minnesota Minneapolis, Minnesota

Chris Gathje Debbie Johnson Rochester, Minnesota Elk River, Minnesota

Dianne Gilbertson Kristin Johnson Golden Valley, Minnesota Coon Rapids, Minnesota

Shannah Gillespie Susan Johnson Edina, Minnesota St. Paul, Minnesota

Bryan Goraczkowski Terry Johnson Litchfield, Minnesota Shakopee, Minnesota

Martha Gretner Pam Katzman St. Paul, Minnesota River Falls, Wisconsin

Mike Greve Norb Kelly Rochester, Minnesota Elk River, Minnesota

Martha Gulner John Kemper Mendota Heights, Minnesota St. Paul, Minnesota

Rose Gundacker Peter King Rosemount, Minnesota Savage, Minnesota

Deb Guthrie Phylis Kisch Roseville, Minnesota Oakdale, Minnesota

Sue Haller Barbara Klaas St. Cloud, Minnesota Golden Valley, Minnesota

James M. Halvorson Elmer Koch Rosemount, Minnesota Bloomington, Minnesota

Judy Hansen T. Kurtte Pipestone, Minnesota Minneapolis, Minnesota

SciMathMN Minnesota K-12 Mathematics Framework 11 ACKNOWLEDGMENTS

Additional Reviewers (cont.)

Pamela Kyllingstad Lori Nord Atwater, Minnesota Laporte, Minnesota

Jean Laabs Theresa Reardon Offerman St. Cloud, Minnesota Edina, Minnesota

Pat Lamwers Linda Ostrom Stacy, Minnesota Clearbrook, Minnesota

Marcia Lang Lyle Pagnucco Two Harbors, Minnesota Duluth, Minnesota

Edna Langerock Judy Parizek Hills, Minnesota Minneapolis, Minnesota

Janice Loppnow Gary E. Parnes St. Charles, Minnesota Inver Grove Heights, Minnesota

Larry Luck David Pelzl Fridley, Minnesota New Ulm, Minnesota

Kelli Ludwig Steve Peterson Eden Prairie, Minnesota Owatonna, Minnesota

Michele M. Luke Mary Pfeifer Maple Grove, Minnesota St. Paul, Minnesota

Pam MacKinnon Christina Pierre Wayzata, Minnesota Woodbury, Minnesota

Betty Malesjewski Tom Plochev Winona, Minnesota Blue Earth, Minnesota

Joanne Martin Jeanette Polzine Rosemount, Minnesota Henning, Minnesota

Tom Martinson Bill Putnam Cloquet, Minnesota Rochester, Minnesota

Aida McCabe Nancy Raguse Roseau, Minnesota Wheaton, Minnesota

Julie McKenzie Shelley Randolph White Bear Lake, Minnesota Eyota, Minnesota

Jeff McLean Barbara Rath St. Paul, Minnesota Fargo, North Dakota

Kathy Meyer Karen Reuter Morris, Minnesota Moundsview, Minnesota

Jane Mianowski Ken Rood Grand Marais, Minnesota Shakopee, Minnesota

Chris Mills Joan Rustad-Huisman Benson, Minnesota Blue Earth, Minnesota

Evelyn Mustanski SciMath Team-Sauk Rapids/Rice Eden Prairie, Minnesota Sauk Rapids, Minnesota

D.B. Nelson John Sautner Coon Rapids, Minnesota Burnsville, Minnesota

RaNae Nelson Deanne Schmidt Wheaton, Minnesota St. Cloud, Minnesota

12 SciMathMN Minnesota K-12 Mathematics Framework ACKNOWLEDGMENTS

Additional Reviewers (cont.)

Harvey R. Schuldt Dale Taylor Faribault, Minnesota East Grand Forks, Minnesota

Melissa Shepard Susie Taylor St. Paul, Minnesota St. Paul, Minnesota

Joseph Shields Gail Thovson Winona, Minnesota Litchfield, Minnesota

Robert Shoemaker Joseph VanWie Henderson, Minnesota Marshall, Minnesota

Neal Skaar Sue Wacek Albert Lea, Minnesota Owatonna, Minnesota

Deirdre Smeitzer Gloria Warner St. Paul, Minnesota Prior Lake, Minnesota

Sally Smith Tracey Wensloft Eagan, Minnesota Roseau, Minnesota

Sr. Rose Mary Snaza Janet Westby Minneapolis, Minnesota Renville, Minnesota

Pam Solvie Cathy Wick Morris, Minnesota St. Cloud, Minnesota

Susan Sommerfeld Suzy Wiebold Minnetonka, Minnesota Mapleton, Minnesota

Joe Stangler Steve Wiltermuth Pelican Rapids, Minnesota Elk River, Minnesota

Cindy Taber Jane Wood Minneapolis, Minnesota Blaine, Minnesota

Kaye Tavernier Deb Zachman Grand Marais, Minnesota Minnetonka, Minnesota

B. Ross Taylor Carla Zevenbergen Minneapolis, Minnesota Edina, Minnesota

Photography

St. Paul Public Schools St. Paul, Minnesota

Graphic Design & Layout

Hall Kelley, Inc. Marine on St. Croix, Minnesota

SciMathMN Minnesota K-12 Mathematics Framework 13 14 SciMathMN Minnesota K-12 Mathematics Framework