New York State Mathematics Core Curriculum 2005

1. New York State MathematicsCore Curriculum2005

2. Curriculum, Instruction and Instructional Technology Anne Schiano Assistant Director aschiano@mail.nysed.gov (518) 474-5922

3. Board of Regents Approves • NYS Learning Standard in • Mathematics • and • NYS Mathematics • Core Curriculum • 2005

4. Mathematics, Science, and Technology Learning Standard 3: Mathematics • Students will: • •understand the concepts of and become proficient with the skills of mathematics; • •communicate and reason mathematically; • •become problem solvers by using appropriate tools and strategies; • through the integrated study of number sense and operations, algebra, geometry, measurement, and statistics and probability.

5. Standard 3 • The Three Components • Conceptual Understanding consists of those relationships constructed internally and connected to already existing ideas. • Procedural Fluencyis the skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. • Problem Solving is the ability to formulate, represent, and solve mathematical problems.

6. Standard 3 • Process and Content Strands

8. The Five Content Strands Performance Indicators which: • define a broad range of content knowledge that students must master • are taught in an integrated manner • engage students in construction of knowledge • integrate conceptual understanding and problem solving • should not be viewed as a checklist of skills void of understanding and application

9. Number Sense and Operations Strand • Students will: • •understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems; • •understand meanings of operations and procedures, and how they relate to one another; • •compute accurately and make reasonable estimates.

10. Algebra Strand • Students will: • •represent and analyze algebraically a wide variety of problem solving situations; • •perform algebraic procedures accurately; • •recognize, use, and represent algebraically patterns, relations, and functions.

11. Geometry Strand •  Students will: • •use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes; • •identify and justify geometric relationships, formally and informally; • •apply transformations and symmetry to analyze problem solving situations; • •apply coordinate geometry to analyze problem solving situations.

12. Measurement Strand • Students will: • •determine what can be measured and how, using appropriate methods and formulas; • •use units to give meaning to measurements; • •understand that all measurement contains error and be able to determine its significance; • •develop strategies for estimating measurements.

13. Statistics and Probability Strand • Students will: • •collect, organize, display, and analyze data; • •make predictions that are based upon data analysis; • •understand and apply concepts of probability.

14. The Five Process Strands Performance Indicators which: • highlight ways of acquiring and using content knowledge • give meaning to mathematics as a discipline rather than a set of isolated skills • engage students in mathematical content as they solve problems, reason mathematically, prove mathematical relationships, participate in mathematical connections, and model and represent mathematical ideas

15. Problem Solving Strand • Students will: • •build new mathematical knowledge through problem solving; • •solve problems that arise in mathematics and in other contexts; • •apply and adapt a variety of appropriate strategies to solve problems; • •monitor and reflect on the process of mathematical problem solving.

16. Reasoning and Proof Strand • Students will: • •recognize reasoning and proof as fundamental aspects of mathematics; • •make and investigate mathematical conjectures; • •develop and evaluate mathematical arguments and proofs; • •select and use various types of reasoning and methods of proof.

17. Communication Strand • Students will: • •organize and consolidate their mathematical thinking through communication; • •communicate their mathematical thinking coherently and clearly to peers, teachers, and others; • •analyze and evaluate the mathematical thinking and strategies of others; • •use the language of mathematics to express mathematical ideas precisely.

18. Connections Strand • Students will: • •recognize and use connections among mathematical ideas; • •understand how mathematical ideas interconnect and build on one another to produce a coherent whole; • •recognize and apply mathematics in contexts outside of mathematics.

19. Representation Strand • Students will: • •create and use representations to organize, record, and communicate mathematical ideas; • •select, apply, and translate among mathematical representations to solve problems; • •use representations to model and interpret physical, social, and mathematical phenomena.

20. Bands within the Content Strands

21. Number Sense and Operations Bands • Number Systems • Number Theory • Operations • Estimation

22. Algebra Bands • Variables and Expressions • Equations and Inequalities • Patterns, Relations, and Functions • Coordinate Geometry • Trigonometric Functions

23. Geometry Bands •Shapes •Geometric Relationships •Transformational Geometry •Coordinate Geometry •Constructions •Locus •Informal Proofs •Formal Proofs 

24. Measurement Bands • Units of Measurement • Tools and Methods • Units • Error and Magnitude • Estimation

25. Statistics and Probability Bands • Collection of Data • Organization and Display of Data • Analysis of Data • Predictions from Data • Probability

26. Guide to Reading the Document

27. Prekindergarten Problem Solving Students will build new mathematical knowledge through problem solving.  PK.PS.1 Explore, examine, and make observations about a social problem or mathematical situation Major Understanding Strand Performance Indicator

28. Prekindergarten Number Sense and Operations Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems. Number Systems  PK.N.1 Count the items in a collection and know the last counting word tells how many items are in the collection (1 to 10) Major Understanding Strand Performance Indicator Band

29. Performance Indicator Guide • PK – Prekindergarten • K – Kindergarten • PS – Problem Solving • RP – Reasoning and Proof • CM – Communication • CN – Connections • R – Representation • N – Number Sense and Operations • A – Algebra • G – Geometry • M – Measurement • S – Statistics and Probability