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New York State Mathematics Core Curriculum 2005 Curriculum, Instruction and Instructional Technology Anne Schiano Assistant Director aschiano@mail.nysed.gov (518) 474-5922 Board of Regents Approves NYS Learning Standard in Mathematics and NYS Mathematics Core Curriculum 2005

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## New York State Mathematics Core Curriculum 2005

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**Curriculum, Instruction and Instructional Technology**Anne Schiano Assistant Director aschiano@mail.nysed.gov (518) 474-5922**Board of Regents Approves**• NYS Learning Standard in • Mathematics • and • NYS Mathematics • Core Curriculum • 2005**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.**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.**Standard 3**• Process and Content Strands**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**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.**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.**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.**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.**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.**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**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.**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.**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.**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.**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.**Number Sense and Operations Bands**• Number Systems • Number Theory • Operations • Estimation**Algebra Bands**• Variables and Expressions • Equations and Inequalities • Patterns, Relations, and Functions • Coordinate Geometry • Trigonometric Functions**Geometry Bands**•Shapes •Geometric Relationships •Transformational Geometry •Coordinate Geometry •Constructions •Locus •Informal Proofs •Formal Proofs**Measurement Bands**• Units of Measurement • Tools and Methods • Units • Error and Magnitude • Estimation**Statistics and Probability Bands**• Collection of Data • Organization and Display of Data • Analysis of Data • Predictions from Data • Probability**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**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**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

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