Kansas Curricular Standards for Mathematics
Table of Contents
Kansas Curricular Standards for Mathematics Writing Committee
Kansas Curricular Standards for Mathematics Writing Committee – Special Education
Introduction to the Kansas Curricular Standards for Mathematics
Mission Statement
Vision Statement
Purpose of this Document
Prior History
The Revision Process
Format of the Kansas Curricular Standards
Standards, Benchmarks and Indicators
Grade Levels Where Benchmarks and Indicators Have Been Developed
Special Note Regarding Seventh and Tenth Grade Benchmarks and Indicators
Definitions Which Will Be Helpful In Understanding the Document
Uses of this Document
Development of Local Curriculum and Assessments
Development of the Kansas Mathematics Assessments
Grade Levels to be Assessed
Kansas Assessment Scores to be Reported
The Use of Calculators on Kansas Mathematics Assessments
Prioritization of Indicators to be Assessed
Supplemental Documents
One Page Summary of the Standards and Benchmarks
Curricular Standards by Standard and Benchmark
Number and Computation
Number Sense
Number Systems and Their Properties
Estimation
Computation
Algebra
Patterns
Variables, Equations, and Inequalities
Functions
Models
continued on next page
Curricular Standards by Standard and Benchmark (continued from previous page)
Geometry
Geometric Figures and Their Properties
Measurement and Estimation
Transformational Geometry
Geometry from an Algebraic Perspective
Data
Probability
Statistics
Assessment Framework
Appendix 1 - Information on Mathematical Communication,
Reasoning, and Problem Solving
Appendix 2 – Curricular Standards Grade by Grade
Appendix 3 – Glossary of Terms
Appendix 4 – National Standards in Personal Finance
Appendix 5 – Selected Bibliography
Appendix 6 – Helpful Resources
Appendix 7 – Template for Pattern Blocks
Appendix 8 – Scope and Sequence
Kansas Curricular Standards for Mathematics – July 2003
The Kansas Curricular Standards for Mathematics Writing Committee
The writing committee would like to thank the more than 1,600 individuals and/or groups who submitted written responses to the first and sixth working drafts of this document as well as the more than 100 persons who provided input at work sessions and at public meetings held throughout the state. The committee thoughtfully read and considered each of the responses received and felt this input was invaluable to the development of this document.
In addition, the committee would like to thank the teachers, school administrators, parents, and community members who have and will continue to work toward improving mathematics education in Kansas.
Co-Chair: Betsy Wiens, Auburn Washburn Public Schools (Topeka), USD 437
Co-Chair: George Abel, Emporia Public Schools, USD 253
Bill FaFlick, Wichita Public Schools, USD 259
Michelle Flaming, ESSDACK (Hutchinson)
Pat Foster, Oskaloosa Public Schools, USD 341
Ann Goodman, Garden City Public Schools, USD 457
Margie Hill, Blue Valley Public Schools (Overland Park), USD 229
Nancy McDonnell, Prairie View Public Schools (LaCygne), USD 362
Sarah Meadows, Topeka Public Schools, USD 501
Jo Musselwhite, Salina Public Schools, USD 306
Cheryl Murra, Leavenworth Public Schools, USD 453
Joan Purkey, Newman University (Wichita)
Judy Roitman, University of Kansas (Lawrence)
Teresa San Martin, Maize Public Schools, USD 266
Allen Sylvester, Geary County Public Schools (Junction City), USD 475
Ethel Edwards, KSDE – School Improvement and Accreditation
Canda Mueller Engheta, KSDE – Planning and Research
Lynnett Wright, KSDE – Student Support Services
Kansas Curricular Standards for Mathematics – July 2003
The Kansas Curricular Standards for Mathematics Writing Committee – Special Education
Chris Butler, Victoria Public Schools, USD 432
Melissa Donaldson, Columbus Public Schools, USD 493
Debra Esau, SCKSEC (Pratt)
Larry Finn, Kansas State School for the Deaf (Olathe)
Linda Hickey, Blue Valley Public Schools (Overland Park), USD 229
Marjorie Hill, Blue Valley Public Schools (Overland Park), USD 229
Sharon Laverentz, Perry Public Schools, USD 343
Charlene Lueck, Geary County Public Schools (Junction City), USD 475
Sheila R. Nigh, Wichita Public Schools, USD 259
Sally Richardson, Wichita Public Schools, USD 259
Cecilia Rijfkogel, Garden City Public Schools, USD 475
Deb Stephenson, Blue Valley Public Schools (Overland Park), USD 229
K. Nadine Voth, Hesston Public Schools, USD 460
Mary Kay Woods, Three Lakes Educational Cooperative (Quenemo)
Ethel Edwards, KSDE – School Improvement and Accreditation
Scott Smith, KSDE – School Improvement and Accreditation
Lynnett Wright, KSDE – Student Support Services
Introduction to the Kansas Curricular Standards for Mathematics
Mission Statement
The mission of Kansas mathematics education is for all Kansas students to learn mathematical content and skills that are used to solve a variety of problems.
Vision Statement
The vision of mathematics education in Kansas is to work toward the following:
· Kansas mathematics education will be recognized as one of the premier programs in the United States.
· Kansas mathematics education will be equally effective for all students, irrespective of gender, race, or socioeconomic background.
· Kansas families will broadly recognize the importance of and be encouraged to participate actively in their child(ren)’s mathematics learning.
· Technology will be a fundamental part of mathematics teaching and learning.
The Purpose of this Document
The standards, benchmarks, and indicators in this document have been created to assist Kansas educators in developing local curricula and assessments, as well as to serve as the basis for the development of the state assessments in mathematics. The committee strove to recommend high, yet reasonable expectations for all students. High, yet reasonable expectations for all students are components of fairness in education. All students includes: those who choose to attend college, those who choose technical preparation, those who will enter the workforce, those from various socio-economic backgrounds, those who have been identified as gifted in the area of mathematics, those who have been identified with learning disabilities, those who have previously been successful with mathematics, and those who have struggled with mathematics sometime in the past.
Students may need additional support both within and outside the regular classroom to meet those expectations. Teachers should be given the professional development and resources necessary to enable them to help all students strive to meet or exceed these expectations. This may seem a daunting task, but the alternative is not acceptable.
Prior History
The Kansas State Board of Education developed and adopted the Kansas Mathematics Improvement Program in 1989. As part of that plan, Kansas Mathematics Curriculum Standards were developed by Kansas educators in 1990. A new Kansas mathematics assessment program began as a statewide pilot in 1991. In 1992, the Kansas legislature directed that further work be done in the development of the mathematics curriculum standards, so that benchmarks would be established at a minimum of three grade levels. In 1993, the State Board adopted revised standards for mathematics. The 1993 Mathematics Curriculum Standards then served as the basis for the Kansas Mathematics Assessment program through the end of the 1998-99 school year. In August 1997, the State Board directed that additional work be done in each of the curriculum areas. The mathematics writing committee convened in October 1997 and worked through February 1999. At the March 1999 meeting of the Kansas State Board of Education, the Kansas Curricular Standards for Mathematics were approved. These standards served as the basis for the Kansas Mathematics Assessments that were administered for the first time during the spring of 2000. The Standards approved in March 1999 serve(d) as the basis for the Kansas Mathematics Assessments through the spring of 2005.
The Revision Process
At the May 2002 meeting of the Kansas State Board of Education, the State Board directed that academic standards committees composed of stakeholders from throughout Kansas were to be convened for the curriculum areas defined by state law, and, at this time, only reading, writing, and mathematics. The mathematics committee was charged to:
1) review the current standards document.
2) review modified and extended standards for inclusion in the document.
3) review the format to ensure usability.
4) determine the level of specificity of skills assessed.
5) recommend essential indicators to be assessed.
6) review previous assessment results and review past KSDE studies as they related to student achievement.
The mathematics writing committee began its work in June 2002. Members worked more than thirty days on revising the standards. Members of the committee reviewed various research articles, examples of mathematics curriculum standards from other states, and reviews of the current Kansas Mathematics Curriculum Standards by various individuals and organizations. Because earlier editions of the Kansas Mathematics Curriculum Standards had been used to guide curriculum, instruction, and assessment throughout the state since 1993, the committee felt it was very important to build upon existing efforts to improve mathematics education. The committee unanimously elected to use the 1999 Standards document as the basis of their work.
At their initial meeting, the writing committee reached consensus on the following revisions for the first draft of the revised Kansas Curricular Standards for Mathematics:
1) definitions of curriculum standards remain the same.
2) greater clarity and specificity to the benchmarks and indicators by grade level so teachers know what they should teach and what students should learn (grades K-8 and high school).
3) format and language revisions that make the standards and the benchmarks easier for non-mathematics educators to understand, as well as aligning the formatting of the mathematics standards document with standards documents from the other curriculum areas.
4) expectations for students were to be high, yet reasonable to achieve.
5) prioritize the state curriculum indicators to be assessed by the state assessments and provide advice regarding the assessment of the state curricular standards.
During meetings throughout the summer of 2002, members of the mathematics revision committee and subcommittees worked to bring specificity and clarity to the benchmarks in the current document by revising the benchmarks and indicators outlined in the 1999 Kansas Mathematics Curriculum Standards. In August 2002, the first working draft was mailed to schools throughout the state to obtain feedback on the draft. The committee continued to work during the fall and winter months reviewing and discussing the feedback from schools, revising grade level expectations, learning about and discussing various assessment issues, and brainstorming possible assessment priorities. By February of 2003, a sixth working draft was mailed to educators, community members, and professional organizations. Public meetings were held in March throughout the state to receive public input on the sixth draft. Summaries of the public meetings and written feedback were compiled for the committee. At the same time, the sixth draft was submitted to the State Board’s designated outside reviewer, Mid-Continent Regional Educational Laboratory, for review. In March and April, the writing committee met to make revisions based on recommendations from McREL’s review and to further prioritize indicators that would be used as the basis for assessment items on the revised Kansas Mathematics Assessments. In May, the committee met to refine the document. Grade level expectations were revised and further prioritization of benchmarks and indicators to be used in developing the Kansas Mathematics Assessments were evaluated. The tenth working draft was prepared for submission to the State Board and discussed at their June meeting.
After the June 2003 meeting of the State Board, subcommittees met to refine their work including additional examples, completing the Financial Literacy connection, and designing a glossary. In addition, during June and July, committee members were facilitating Summer Mathematics Standards Academies across the state; nine such academies were held. The committee's recommendations, as presented in the eleventh draft, were acted upon and approved at the July 2003 meeting of the Kansas State Board of Education. Kansas Mathematics Assessments, based on these standards, are to be administered for the first time during the spring of 2006.
To be completed for standards document:
Format of the Kansas Curricular Standards for Mathematics
Uses of this Document
Supplemental Documents
One Page Summary of the Standards and Benchmarks
Curricular Standards by Standard and Benchmark
Assessment Framework
Kansas Curricular Standards for Mathematics – July 2003
Standard 1: Number and Computation KINDERGARTEN
Standard 1: Number and Computation – The student uses numerical and computational concepts and procedures in a variety of situations.
Benchmark 1: Number Sense – The student demonstrates number sense for whole numbers, fractions, and money using concrete objects in a variety of situations.
Kindergarten Knowledge Base Indicators
/ Kindergarten Application IndicatorsThe student...
1. establishes a one-to-one correspondence with whole numbers from 0 through 20 using concrete objects and identifies, states, and writes the appropriate cardinal number (2.4.K1a) ($).
2. compares and orders whole numbers from 0 through 20 using concrete objects (2.4.K1a) ($).
3. recognizes a whole, a half, and parts of a whole using concrete objects (2.4.K1a,c) ($), e.g., half a pizza, part of a cookie, or the whole school.
4. identifies positions as first and last (2.4.K1a).
5. identifies pennies and dimes and states the value of the coins using money models (2.4.K1d) ($). / The student...
1. solves real-world problems using equivalent representations and concrete objects to compare and order whole numbers from 0 through 10 (2.4.A1a) ($).
Teacher Notes: Number sense refers to one’s ability to reason with numbers and to work with numbers in a flexible way. The ability to compute mentally, to estimate based on understanding of number relationships and magnitudes, and to judge reasonableness of answers are all involved in number sense.
When we say that someone has good number sense, we mean that he or she possesses a variety of abilities and understandings that include an awareness of the relationships between numbers, an ability to represent numbers in a variety of ways, a knowledge of the effects of operations, and an ability to interpret and use numbers in real-world counting and measurement situations. Such a person predicts with some accuracy the result of an operation and consistently chooses appropriate measurement units. This “friendliness with numbers” goes far beyond mere memorization of computational algorithms and number facts; it implies an ability to use numbers flexibly, to choose the most appropriate representation of a number for a given circumstance, and to recognize when operations have been correctly performed. (Number Sense and Operations: Addenda Series, Grades K-6, NCTM, 1993)
Mathematical models such as concrete objects, pictures, number lines, or unifix cubes are necessary for conceptual understanding and should be used to explain computational procedures. If a mathematical model can be used to represent the concept, the indicator in the Models benchmark is identified in the parentheses. For example, (2.4.K1a) refers to Standard 2 (Algebra), Benchmark 4 (Models), and Knowledge Indicator 1a (process models). Then, the indicator in the Models benchmark lists some of the mathematical models that could be used to teach the concept. In addition, each indicator in the Models benchmark is linked back to the other indicators. Those indicators are identified in the parentheses. For example, process models are linked to 1.1.K3, 1.2.K6, 1.3.K1, … with 1.1.K3 referring to Standard 1 (Number and Computation), Benchmark 1 (Number Sense), and Knowledge Indicator 3.
The National Standards in Personal Finance identify what K-12 students should know and be able to do in personal finance; benchmarks are provided at three grade levels (grades 4, 8, and 12) and are grouped into four major categories: Income, Spending and Credit, Saving and Investing, and Money Management. Although the National Standards in Personal Finance are benchmarked at three grade levels, the indicators in the Kansas Curricular Standards for Mathematics that correlate with the National Standards in Personal Finance are indicated at each grade level with a ($). The National Standards in Personal Finance are included in the Appendix.
Standard 1: Number and Computation KINDERGARTEN