Cumberland, Lincoln, and
Woonsocket Public Schools
District Curriculum Framework
Mathematics K–12
2010–2011
Cumberland, Lincoln, and Woonsocket Public Schools
District Curriculum Framework
Mathematics K–12
Who can use these documents?
The processes and strategies through which these documents were developed and the overall structure and
organization of these documents are the exclusive copyrighted property of the Charles A. Dana Center at The
University of Texas at Austin (the University) and may not be used or distributed outside Cumberland, Lincoln, and
Woonsocket public schools without written permission from the Dana Center.
Unless otherwise indicated, the content of these District Curriculum Frameworks was developed through a
collaboration between Cumberland, Lincoln, and Woonsocket public schools and the Charles A. Dana Center at The
University of Texas at Austin. The University thus grants permission in perpetuity for this content to be used within
the Cumberland, Lincoln, and Woonsocket public schools in any way the districts see fit.
The content of these District Curriculum Framework documents is not intended for use or sale outside Cumberland,
Lincoln, and Woonsocket public schools without express written permission from the University, which shall not be
unreasonably withheld.
Please send questions or permission requests to:
Charles A. Dana Center
The University of Texas at Austin
1616 Guadalupe Street, Suite 3.206
Austin, TX 78701-1222
Fax: 512-232-1855
dana-txshop@utlists.utexas.edu
The Rhode Island mathematics Grade-Level Expectations and Grade Span Expectations constitute the foundation of
these curriculum documents. These state standards, as well as released items from the New England Common
Assessment Program (NECAP) and additional resources for implementing the standards, may be found at
www.ride.ri.gov/instruction/curriculum, a website of the Rhode Island Department of Elementary and Secondary
Education (also known as RIDE—the Rhode Island Department of Education).
About the development of this resource
These curriculum documents were created through a collaboration between Cumberland, Lincoln, and Woonsocket
public schools and the Charles A. Dana Center at The University of Texas at Austin. This work was part of a
broader statewide effort in Rhode Island, sponsored and strongly supported by the Rhode Island Department of
Education (RIDE).
This is the first edition of this resource. July 2010 release.
Note that the materials cited in the Resources sections of these documents have been purchased by Cumberland,
Lincoln, and/or Woonsocket public schools.
Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do
not necessarily reflect the views of The University of Texas at Austin. The Charles A. Dana Center and The
University of Texas at Austin, as well as the authors and editors, assume no liability for any loss or damage resulting
from the use of this resource. We have made extensive efforts to ensure the accuracy of the information in this
resource, to provide proper acknowledgement of original sources, and to otherwise comply with copyright law. If
you find an error or you believe we have failed to provide proper acknowledgment, please contact us at
dana-txshop@utlists.utexas.edu.
Frontmatter
District Curriculum Framework, Mathematics K–12
Acknowledgments
These curriculum documents were created collaboratively by professionals from the Cumberland, Lincoln, and
Woonsocket Public Schools and the Charles A. Dana Center at The University of Texas at Austin. The Rhode Island
Department of Education (RIDE) was a funder and strong supporter of this work.
Rhode Island Department of Education
Heather Johnson, assessment and instruction
Peter McLaren, assessment and instruction
Kate Nigh, assessment and instruction
Mary Ann Snider, commissioner support
Cumberland, Lincoln, and Woonsocket Public Schools
Central Office Staff, Cumberland Public Schools
Donna A. Morelle, superintendent of schools
Susan Carney, assistant superintendent of schools
Central Office Staff, Lincoln School Department
Georgia Fortunato, superintendent of schools
Melinda Smith, director of curriculum, instruction, assessment and professional development
Central Office Staff, Woonsocket Education Department
Robert Gerardi, superintendent of schools
Linda Filomeno, director of literacy and professional development
Grades K–2
Nancy Andrews, Lincoln School Department
Susan Aurelio, Cumberland Public Schools
Lori Beauregard, Cumberland Public Schools
Loretta Carnes, Woonsocket Education Department
Lori DeSimone, Lincoln School Department
Deborah Duquette, Woonsocket Education Department
Kelly Dwyer, Cumberland Public Schools
Jessica Francis, Cumberland Public Schools
Samantha Freyre, Woonsocket Education Department
Angela Holt, Woonsocket Education Department
Kasia Kidd, Lincoln School Department
Mary Ellen Kucharski, Woonsocket Education Department
Audra Laplante, Woonsocket Education Department
Kelly Marini, Lincoln School Department
Tanya Martins, Cumberland Public Schools
Renee McCutcheon, Woonsocket Education Department
Mary Lynne Miller, Cumberland Public Schools
Kathy Plante, Lincoln School Department
Don Poli, Woonsocket Education Department
Ann Richards, Woonsocket Education Department
Donna Rowland, Lincoln School Department
Barbara Santos, Woonsocket Education Department
Jim Zanfini, Lincoln School Department
Grades 3–5
Shelly A. Allard, Lincoln School Department
Shannon Bessette, Cumberland Public Schools
Dianne Boisvert, Cumberland Public Schools
Roxane Cary, Woonsocket Education Department
Karen Costa, Lincoln School Department
Jeanine Echevarria, Woonsocket Education Department
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Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
District Curriculum Framework, Mathematics K–12
Frontmatter
Lisa Ferrucci, Woonsocket Education Department
Angela Holt, Woonsocket Education Department
Barbara A. Holt, Lincoln School Department
Linda Iannetta, Cumberland Public Schools
Paula Johnson, Cumberland Public Schools
Gayle L’Esperance, Lincoln School Department
Charleen Lagace, Lincoln School Department
Eileen LaRiviere, Woonsocket Education Department
Elizabeth Locklin, Cumberland Public Schools
Paul Melaragno, Lincoln School Department
Christine Parker, Woonsocket Education Department
Julie Pirraglra, Woonsocket Education Department
Patricia Pora, Woonsocket Education Department
Christine Rivard, Woonsocket Education Department
Jan Rogan
Renay Sawyer, Woonsocket Education Department
Susan Schaffer, Cumberland Public Schools
Monique Swiszcz, Cumberland Public Schools
Ann Whitelaw, Lincoln School Department
Grades 6–8
Janessa Allen, Woonsocket Education Department
Karen Brodeur, Cumberland Public Schools
Joyce Burlingame, Lincoln School Department
Kerry Carlson, Cumberland Public Schools
Elizabeth Nault Costa, Cumberland Public Schools
Bethany Coughlin, Cumberland Public Schools
Anne Crocker, Cumberland Public Schools
Lisa DeSante, Woonsocket Education Department
Rebecca Ducharme, Woonsocket Education Department
Kayla Emery
Sue Gorrie, Woonsocket Education Department
Roberta Harnois, Cumberland Public Schools
Michael Manzi, Lincoln School Department
Wendy McPeak, Lincoln School Department
Thomas J. Mellen, Lincoln School Department
Christine Mellor, Lincoln School Department
Linda Murphy, Woonsocket Education Department
Emily Perron, Woonsocket Education Department
Peter Prendergast, Lincoln School Department
Denise Queenan, Cumberland Public Schools
Elizabeth R. Ramsbey, Lincoln School Department
Heather Rose, Woonsocket Education Department
Nicole Tetreault, Lincoln School Department
Doug Wall, Lincoln School Department
Kristen Lowe, Lincoln School Department
High school mathematics
Colleen Bibeault, Woonsocket Education Department
Paula Burke, Cumberland Public Schools
Jerred Dean, Cumberland Public Schools
Regina Ferreira, Lincoln School Department
Cheryl Gesualdi, Cumberland Public Schools
Robert Gruetzke, Woonsocket Education Department
Teresa Hopkins, Lincoln School Department
Lisa Jacques, Woonsocket Education Department
Kristen M. Jahnz, Cumberland Public Schools
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
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Frontmatter
District Curriculum Framework, Mathematics K–12
Nancy Koczera, Woonsocket Education Department
Betsy Lachapelle, Cumberland Public Schools
Michelle, Lapierre, Woonsocket Education Department
Amy Laven, Lincoln School Department
Michael Lemay, Woonsocket Education Department
Renee Lepre, Lincoln School Department
Justene Loiselle, Cumberland Public Schools
Yvette Mongeon, Lincoln School Department
Allison Morgan, Cumberland Public Schools
Andrew Rao, Woonsocket Education Department
Christopher Scott, Cumberland Public Schools
Ronald St. Pere, Woonsocket Education Department
Suzanne Ross Walker, Woonsocket Education Department
Kathryn Williamson, Lincoln School Department
Charles A. Dana Center
David Hill, senior advisor
Amy Dolejs, supervising editor
Cara Hopkins, lead editor and production manager
Joe Gallegos, senior program coordinator
Bill Hopkins, research associate
Carolyn Moore, mathematics consultant
Joyce Polanco, mathematics consultant
Karen Snow, mathematics consultant
Emma Treviño, supervisor of mathematics programs
Special thanks also to the following Dana Center staff writers, editors, and consultants: Steve Engler, Phillip Hebert,
Rachel Jenkins, Laura Maldonado, Tom McVey, Norma Salas, Sarah Searcy, and Phil Swann.
About the Building a Strong Foundation initiative
Building a Strong Foundation: Improving Student Achievement in Mathematics and Science is a collaboration of the
Rhode Island Department of Elementary and Secondary Education and the Charles A. Dana Center at The
University of Texas at Austin. Its purpose is to increase student achievement in mathematics and science in Rhode
Island public schools. The Cumberland Public Schools, Lincoln School Department, and Woonsocket Education
Department are among the state’s school districts that have elected to participate in this initiative. For more
information about the Building a Strong Foundation work, see the Rhode Island Department of Education website
page at www.ride.ri.gov/instruction/mathsci.aspx.
About Cumberland Public Schools
The Cumberland Public Schools, located in Cumberland, Rhode Island (population: 30,000), serves about 5,000
students in grades kindergarten through 12. The district includes 1 high school, 2 middle schools, 5 elementary
schools, and 1 preschool. For more information on Cumberland Public Schools, please visit
www.cumberlandschools.org.
About Lincoln Public Schools
The Lincoln Public Schools, located in Lincoln, Rhode Island (population: 20,000), serves about 4,000 students in
grades kindergarten through 12. The district includes 1 high school, 1 middle school, 4 elementary schools, and 2
early learning centers. For more information on the Lincoln Public Schools, please visit www.lincolnps.org.
About Woonsocket Public Schools
The Woonsocket Public Schools, located in Woonsocket, Rhode Island (population: 44,000) serves about 6,500
students in grades kindergarten through 12. The district includes 1 high school, 1 high school-level career and
technical center, 2 middle schools, and 9 elementary schools. For more information on the Woonsocket Public
Schools, please visit www.woonsocketschools.com.
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Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
District Curriculum Framework, Mathematics K–12
Frontmatter
About the Charles A. Dana Center at The University of Texas at Austin
The Dana Center works to raise student achievement in K–16 mathematics and science, especially for historically
underserved populations. It does so by providing direct service to school districts and institutions of higher
education; to local, state, and national education leaders; and to nonprofits, agencies, and professional organizations
concerned with strengthening American mathematics and science education. The Center is committed to ensuring
that the accident of where a child attends school does not limit the academic opportunities he or she can pursue. For
more information and to access Center resources (many of them free), please see www.utdanacenter.org.
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
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Frontmatter
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District Curriculum Framework, Mathematics K–12
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
District Curriculum Framework, Mathematics K–12
Frontmatter
Mathematics K–12
District Curriculum Framework
Table of Contents
Introduction .................................................................................................................................................. 1
Section A: Scope and Sequence ............................................................................................................... A-1
Section B: Year at a Glance: Units of Study by Quarter .......................................................................... B-1
Section C: Units of Study ........................................................................................................................ C-1
Section D: Rhode Island Mathematics K–12 GLEs and GSEs ............................................................... D-1
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
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Frontmatter
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District Curriculum Framework, Mathematics K–12
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
District Curriculum Framework, Mathematics K–12
Frontmatter
Cumberland, Lincoln, and Woonsocket
Public Schools
Building a Strong Foundation
School Year 2010–2011
Overview
Purpose: Increase student achievement in mathematics in
Cumberland, Lincoln, and Woonsocket Public School Districts by
aligning curriculum, instruction, and assessment to the state
standards.
Objectives:
Actions:
Roles and Responsibilities:
1.
Implement the guaranteed
and viable curriculum every
day, in every classroom, for
every student.
Teachers, leaders, and
Charles A. Dana Center staff
will:
2.
Provide regular
opportunities for teachers
and leaders to
collaboratively study and
implement the curriculum.
Central office staff will…
Provide monitoring and support of
curriculum development and implementation,
collaborate with teacher writing team
members and Dana Center staff, and ensure
that the work of the initiative is aligned to the
district’s overall plan for increasing student
achievement in mathematics.
3.
Implement routines and
structures for monitoring
implementation of the
curriculum and providing
feedback.
a. Collaboratively generate
district-level curriculum
documents that delineate
which GSEs (Grade Span
Expectations) and GLEs
(Grade-Level Expectations)
should be taught in each
grade level, in what order,
and for what duration.
b. Engage in system-wide
study of the state standards
and district-developed
curriculum documents.
c. Develop and implement
support structures and tools
for leaders to increase their
ability to support teachers in
implementing the district
curriculum.
d. Refine and implement
support structures and tools
for teachers as they work
collaboratively to plan and
implement instruction that is
aligned to the state standards
and district curriculum.
Building leaders will…
Ensure teacher participation in professional
development, provide regular opportunities
for teachers to collaboratively plan and
implement instruction aligned to the
standards and curriculum, monitor
implementation of the curriculum, and
provide teachers with ongoing meaningful
feedback.
Teachers will…
Attend and actively participate in
professional development, implement the
curriculum in every classroom for every child
on every day, and regularly collaborate with
grade level/department colleagues to plan and
implement instruction aligned to the
standards and curriculum documents.
The Charles A. Dana Center at the
University of Texas at Austin will…
Provide technical expertise and on-site
support for planning and implementing this
work, facilitate the initial alignment work,
and help Cumberland, Lincoln, and
Woonsocket Public School Districts build
capacity in their systems throughout this
project.
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
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District Curriculum Framework, Mathematics K–12
Developing the Guaranteed and Viable Curriculum
Research* concludes that implementation of a guaranteed and viable curriculum plays a critical role in
improving student achievement. Guaranteed means that every child in every school receives essential
instruction every day; viable means that the curriculum can be taught in the amount of time provided. The
District Curriculum Frameworks developed in this collaboration between Cumberland, Lincoln, and
Woonsocket public schools and the Dana Center outline the guaranteed and viable curriculum and define
the essential knowledge that all students must learn in mathematics at each grade level and in each course
of study. Careful attention was given to the amount of time necessary to teach these essential knowledge
and skills.
This guaranteed and viable curriculum for Cumberland, Lincoln, and Woonsocket public schools was
developed through careful study of—and alignment to—the state standards (the Rhode Island Grade Span
Expectations, or GSEs, and Grade-Level Expectations, or GLEs). This process of starting from state
standards to identify essential student learning is referred to as backloading. The backloading process
supported the development of the scope-and-sequence document for each grade level or course.
Teacher representatives from every grade level and course taught in the district worked in teams (K–4,
5–8, and 9–12) to determine which standards would be taught in each quarter for each grade level or
course from kindergarten through grade 12. In addition, the teacher teams clustered standards into “big
idea” groups called units of study. The teacher teams, working in collaboration with Dana Center staff,
made the decisions about which standards best clustered together for each unit and in what sequence the
units should be taught. For mathematics, they made these decisions based on the GLEs/GSEs and
research from Principles and Standards for School Mathematics, A Research Companion to Principles
and Standards for School Mathematics, and Numeracy in Mathematics.
Structure of the District Curriculum Framework
The purpose of these district curriculum documents is to support quality implementation of the Rhode
Island mathematics GSEs and GLEs every day, in every classroom, for every student—to ensure gradelevel and subject-area alignment and coherence across the district. In the District Curriculum Framework
documents for mathematics, we have tried to identify which standards are taught, when, and for how long.
We have also tried to clarify standards and describe the implications of the standards for each grade level
or course.
The District Curriculum Framework documents do not provide daily lesson plans, eliminate the need for
lesson planning, or recreate the teacher’s edition of classroom resources. Rather, the curriculum
framework provides a workplan that directs the instruction delivered in every classroom in every school
in the district. The curriculum framework consists of the following sections.
Section A: Scope and Sequence
This section includes the relevant content standards (GSEs/GLEs) taught in each unit of study, organized
by quarter.
*
See, for example, Chapter 3, A Guaranteed and Viable Curriculum, pages 22–34 in Robert J. Marzano’s What
works in schools: Translating research into action. Alexandria, VA: Association for Supervision and Curriculum
Development, 2003.
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Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
District Curriculum Framework, Mathematics K–12
Frontmatter
Section B: Year at a Glance: Units of Study by Quarter
This section lists the title of each unit of study for that grade or course along with the number of days
needed to conduct the unit.
Section C: Units of Study
Important Note: The units of study are currently being developed by teams of educators from
Cumberland, Lincoln, and Woonsocket public schools, with support from the Dana Center. This section
will be completed as the units are completed prior to the beginning of each quarter in the 2010–2011
school year.
These instructional units outline specific student outcomes aligned to the GSEs/GLEs. These units are the
heart of the District Curriculum Framework documents. Each unit of study provides detailed information
to support lesson planning and is structured in two main sections:
•
Overview: Each one-page unit overview lists the total number of days needed to teach the unit and
defines expectations for student learning by articulating the content to be learned and processes to be
used—that is, the standards-based expectations of which students will demonstrate understanding.
The overview ends with a list of the Essential Questions that students should be able to answer by the
end of the unit.
•
Written curriculum: This section lists the specific parts of the relevant mathematics GSEs/GLEs to be
taught during the unit. The Clarifying the Standards subsection provides an analysis of the ideas
taught in the grade level(s) before (Prior Learning) and after (Future Learning) the grade level or
course being taught. This subsection also clarifies what should be learned in the current grade level or
course and reports important findings from research and the standards that support teachers in
narrowing the idea in the standards to the content taught in the grade level.
Section D: Rhode Island Mathematics K–12 GSEs/GLEs
These are complete copies of the state standards for mathematics, to aid in effective collaboration around
the District Curriculum Framework documents.
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin
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District Curriculum Framework, Mathematics K–12
Cumberland, Lincoln, and Woonsocket Public Schools, in collaboration with the
Charles A. Dana Center at the University of Texas at Austin