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New York State Mathematics Core Curriculum 2005 Curriculum, Instruction and Instructional Technology Anne Schiano Assistant Director [email protected] (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 MathematicsCore Curriculum2005

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Curriculum, Instruction and Instructional Technology

Anne Schiano

Assistant Director

[email protected]

(518) 474-5922

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Board of Regents Approves

  • NYS Learning Standard in

  • Mathematics

  • and

  • NYS Mathematics

  • Core Curriculum

  • 2005

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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.

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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.

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Standard 3

  • Process and Content Strands

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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

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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.

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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.

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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.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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.

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Bands within the Content Strands

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Number Sense and Operations Bands

  • Number Systems

  • Number Theory

  • Operations

  • Estimation

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Algebra Bands

  • Variables and Expressions

  • Equations and Inequalities

  • Patterns, Relations, and Functions

  • Coordinate Geometry

  • Trigonometric Functions

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Geometry Bands


•Geometric Relationships

•Transformational Geometry

•Coordinate Geometry



•Informal Proofs

•Formal Proofs 

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Measurement Bands

  • Units of Measurement

  • Tools and Methods

  • Units

  • Error and Magnitude

  • Estimation

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Statistics and Probability Bands

  • Collection of Data

  • Organization and Display of Data

  • Analysis of Data

  • Predictions from Data

  • Probability

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Guide to Reading the Document

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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




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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)







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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