Rapid City Area Schools
ELEMENTARY SCHOOL
Mathematics Curriculum
Approved by the Boards of Education, November 2002
Revision approved by the board of Education, June 2005
RAPID CITY AREA SCHOOLS
300 6TH Street
Rapid City, South Dakota 57701
BOARD OF EDUCATION
Mrs. Margie Rosario / PresidentMrs. Sheryl Kirkeby / 1st Vice President
Mrs. Leah Lutheran / 2nd Vice President
Mrs. Holly Lemay
Mr. David Janak
Mr. Douglas Kinneburgh
ADMINISTRATION
Dr. Peter M. Wharton, Superintendent of Schools
Dr. Patricia Smith Peel, Director of Student Achievement and Staff Development
Ms. Nancy Ward, Mathematics Coordinator
Mrs. Lisa Plumb, Facilitator of Mathematics Curriculum Committee
COMMUNITY ADVISORY COMMITTEE
Mrs. Micheline Hickenbotham
/Black Hills State University
Mrs. Vicki Kapust
/Center for Advancement of Math and Science Education
Mrs. Danielle Goodwin / Center for Advancement of Math and Science EducationMATHEMATICS CURRICULUM WRITING COMMITTEE
Name / School / GradeAnderson, Judy / Rapid Valley / Fifth Grade
Barker, Gaylene / Grandview / First Grade
Beaumont, Rosella / Corral Drive / First Grade
Boechler, Tara / Valley View / First Grade
Conrad, Dan / Central
Dahme, Linda / South Canyon / Fourth Grade
Darrow, Sharon / Central
Dormann, Carol / Southwest / Sixth Grade
Fincher, Shannon / 9th Gr. Academy
Gilliland, Deb / Grandview / Third Grade
Greenwalt, Donna / Southwest / Seventh Grade
Heberlein, Sally / South / Eighth Grade
Heck, Suzy / Black Hawk / Fifth Grade
Hunt, Peggy / Pinedale / Fourth Grade
Johns, Connie / Corral Drive / Fifth Grade
Johnson, Al / South / Eighth Grade
Johnson, Rosemary / West / Sixth Grade
Johnston, Mary / Horace Mann / Third Grade
Keck, Jeanette / Bergquist / First Grade
Keck, Tom / Stevens
Kertzman, Deann / Rapid Valley / First Grade
Kundel, Ken / North / Sixth Grade
Larsen, Pat / Wilson / Special Education
Liggett, Carol / Robbinsdale / First Grade
Loomer, Lynn / South Canyon / Third Grade
Miller, Glenda / Bergquist / Fourth Grade
Olson, Robin / South Canyon / First Grade
Olson, Shelly / WDTI / Preschool
Peterson, Leslie / South Park / Second Grade
Pratt, Peg / Horace Mann / Second Grade
Reiling, Ann / South Park / Fourth Grade
Renner, Misty / Valley View / Kindergarten
Richardson, Kim / Central
Schara, Kim / Dakota / Sixth Grade
Schaefer, Kim / West / Eighth Grade
Shelton, Debi / General Beadle / Third Grade
Steinberg, Craig / Wilson / Fifth Grade
Stephens, Danelle / Pinedale / First Grade
Tschetter, Stacie / Canyon Lake / Fifth Grade
Uecker, Judy / Meadowbrook / First Grade
Weaver, Bernetta / Central
Webber, Kim / Black Hawk / Second Grade
Zimiga, Cheryl / Meadowbrook / Fourth Grade
MATHEMATICS CURRICULUM REALIGNMENT COMMITTEE
Name / School / GradeAhrens, Connie / Knollwood / Math Teacher Leader
Gilliland, Deb / Grandview/Wilson / Math Teacher Leader
Heberlein, Sally / North / Math Teacher Leader
Goodell, Donna / Wilson / Math Recovery
Johnston, Mary / Valley View / Math Teacher Leader
Kramer, Linda / Black Hawk/Corral Drive / Math Teacher Leader
Manning, Jennifer / Knollwood / Math Teacher Leader
Pierce, Paula / Grandview / First Grade
Ritten, Marie / District / Secondary Math Coordinator
Stewart, Chris / Meadowbrook / Fifth Grade
Swanson, Jackie / General Beadle / Math Recovery
Tschetter, Stacie / Canyon Lake/Pinedale / Math Teacher Leader
Webber, Kim / Meadowbrook / Math Teacher Leader
ELEMENTARY SCHOOL TABLE OF CONTENTS
Introduction
Introduction
Philosophy
Essential Knowledge
Principles of National Council of Teachers of Mathematics
Nation Council of Teachers of Mathematics Content Standards
Nation Council of Teachers of Mathematics Process Standards
Elementary School Curriculum
South Dakota Mathematics Standards, Goals, and Indicators
Guide to Document Numbering
Pre-Kindergarten Standards
Kindergarten Standards
First Grade Standards
Second Grade Standards
Third Grade Standards
Fourth Grade Standards
Fifth Grade Standards
Vertical Alignment
Glossary
Introduction
This document was written by the members of the Mathematics Curriculum Writing Committee to reflect the National and South Dakota Standards for Mathematics Instruction. The committee was facilitated by Lisa Plumb, Administrator, and Nancy Ward, Math Coordinator, approved by the members of the Mathematics Curriculum Advisory Committee and the Instructional Council and authorized by the Board of Education for the Rapid City Area Schools.
The document was realigned by the Math Curriculum Realignment Committee to the South Dakota Math Content Standards approved on May 17, 2004. The 2004 South Dakota standards is simple a place to begin – it lays the foundation for measurable, consistent, high-level student learning; however, the curriculum of each district must provide students with rigor and topics beyond those of the standards in order to ensure mastery.
Vision Statement
Our vision is the development of a curriculum with common language and continuity that provides a strong and diverse foundation where the teaching and learning of mathematics are in harmony to meet individual needs that promote success, confidence and an insatiable thirst for learning.
Introduction
We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics continue to emerge and evolve. Quantitative information available to limited numbers of people a few years ago is now widely disseminated through popular media outlets.
The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures.
The Mathematics Curriculum committee was formed in 2000 and charged with the task of reviewing and revising the K-12 Mathematics curriculum to align with the South Dakota Mathematics Content Standards and the National Council of Teachers of Mathematics Principles and Standards 2000. The committee used relevant research from a variety of resources including the National Council of Teachers of Mathematics and the South Dakota State Mathematics Content Standards adopted in 1998.
Persons desiring in-depth information regarding this research are directed to the following publications:
- / South Dakota Mathematics Content Standards: South Dakota Department of Education and Cultural Affairs. Adopted May 17, 2005- / National Council of Teachers of Mathematics Principles and Standards 2000
Mathematics Curriculum Foundation – Grades Pre-K-12
Philosophy
The educational mission of the Rapid City Area Schools is to prepare students to lead fulfilling and responsible lives. Mathematics education should provide students with a useful base of mathematical knowledge, skills, and understanding that will enable them to think and reason mathematically. The mathematics curriculum is designed to develop mathematically powerful students who:
· Value mathematics
· Are confident and proficient in their ability to do mathematics
· Are mathematical problem solvers
· Can communicate mathematically
· Reason mathematically
Our students deserve and need the best mathematics education possible, one that enables them to fulfill personal ambitions and career goals in an ever-changing world. The NCTM Principles for School Mathematics 2000 describe particular features of high-quality mathematics education.
Essential Knowledge
The Rapid City Area Schools mathematics curriculum is based on the South Dakota Mathematics content standards. Standards articulate an essential core of knowledge and skills. They specify the understanding, knowledge, and skills that students are expected to achieve in their K-12 academic career.
Since education is often described as a “journey through learning,” that analogy helps clarify the components that make up a set of standards. The goals represent the final/ultimate destination--where all students should “arrive” after the required years of mathematics study. The indicators provide targets and guideposts throughout the journey. The performance descriptors serve as mile markers and weigh stations along the way and the grade level standards represent the turns, hills, traffic signs, and the white lines along the road.
o Goals: The six broad, conceptual goals (content area/discipline standards) are the K-12 strands that define the essence of the discipline of mathematics. Because the goals are the “end results” of what we would expect after thirteen years of mathematics study, they are worded the same at each grade level. This is done to provide consistency in K-12 curricular focus and alignment. It should also be noted that although algebra, geometry, and statistics have traditionally been thought of as “courses,” in this document, they refer to mathematical strands that should be addressed throughout a K-12 program.
o Indicators: The indicators further define the goals and set the framework for mathematics. The indicators remain the same at all instructional levels (K-2, 3-5, 6-8, 9-12), thereby providing an ongoing and constant focus for the standards. The indicators also provide the targets and anchors for broad district-level, program evaluation.
o Performance Descriptors: The performance descriptors are organized into proficiency levels. These proficiency levels describe how a student at that level would be expected to perform the grade-level standards.
§ Advanced: A student performing at the advanced level exceeds expectations for that grade level. The student is able to perform the content standards for the grade at a high level of difficulty, complexity, or fluency beyond that specified by the grade-level standards.
§ Proficient: A student performing at the proficient level meets expectations for that grade level. The student is able to perform the content standards for the grade at the level of difficulty, complexity, or fluency specified by the grade-level standards.
§ Basic: A student performing at the basic level performs below expectations for that grade level. The student is able to perform some of the content standards for the grade below the level of difficulty, complexity, or fluency specified by the grade-level standards.
A student performing below the basic level is unable to perform the content standards for the grade. Therefore, no description is provided below the basic level.
o Grade Level Standards: These statements represent the classroom learning objectives or activities that should be provided at each grade level to help students reach the expectations articulated in the performance descriptors, indicators, and goal.
Mathematics in the Rapid City Area Schools will be taught according to these six principles written by the National Council of Teachers of Mathematics.
* Equity: Excellence in mathematics education requires equity—high expectations and strong support for all students.
* Curriculum: A curriculum is more than a collection of activities; it must be coherent, focused on important mathematics and well articulated across the grades.
* Teaching: Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.
* Learning: Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.
* Assessment: Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.
* Technology: Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.
NCTM Content Standards
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
understand numbers, ways of representing numbers, relationships among numbers, and number systems. / understand patterns, relations, and functions. / analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships. / understand measurable attributes of objects and the units, systems, and processes of measurement. / formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.
understand meanings of operations and how they relate to one another. / represent and analyze mathematical situations and structures using algebraic symbols. / specify locations and describe spatial relationships using coordinate geometry and other representational systems. / apply appropriate techniques, tools, and formulas to determine measurements. / select and use appropriate statistical methods to analyze data.
compute fluently and make reasonable estimates. / use mathematical models to represent and understand quantitative relationships. / apply transformations and use symmetry to analyze mathematical situations. / develop and evaluate inferences and predictions that are based on data.
analyze change in various contexts. / use visualization, spatial reasoning, and geometric modeling to solve problems. / understand and apply basic concepts of probability.
These standards describe mathematical content goals. Inclusion of content and process standards is critical to the effective teaching of mathematics.
NCTM Process Standards
Instructional programs from pre-kindergarten through grade 12 should enable all students to:
Problem Solving Standard / Reasoning and Proof Standard / Communication Standard / Connections Standard / Representation Standardbuild new mathematical knowledge through problem solving. / recognize reasoning and proof as fundamental aspects of mathematics. / organize and consolidate their mathematical thinking through communication. / recognize and use connections among mathematical ideas. / create and use representations to organize, record, and communicate mathematical ideas.
solve problems that arise in mathematics and in other contexts. / make and investigate mathematical conjectures. / communicate their mathematical thinking coherently and clearly to peers, teachers, and others. / understand how mathematical ideas interconnect and build on one another to produce a coherent whole. / select, apply, and translate among mathematical representations to solve problems.
apply and adapt a variety of appropriate strategies to solve problems. / develop and evaluate mathematical arguments and proofs. / analyze and evaluate the mathematical thinking and strategies of others. / Recognize and apply mathematics in contexts outside of mathematics. / use representations to model and interpret physical, social, and mathematical phenomena.
monitor and reflect on the process of mathematical problem solving. / select and use various types of reasoning and methods of proof. / use the language of mathematics to express mathematical ideas precisely.
These standards describe mathematical process goals. Inclusion of content and process standards is critical to the effective teaching of mathematics.
K-12 – Mathematics Standards
Goals and Indicators