#### Strands

Standards for each grade are grouped together by content and process strands.

nysed.gov describe these two groups of strands as:

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#### Process Strands

The process strands (Problem Solving, Reasoning and Proof, Communication, Connections, and Representation) highlight ways of acquiring and using content knowledge. These process strands help to give meaning to mathematics and help students to see mathematics as a discipline rather than a set of isolated skills. Student engagement in mathematical content is accomplished through these process strands. Students will gain a better understanding of mathematics and have longer retention of mathematical knowledge as they solve problems, reason mathematically, prove mathematical relationships, participate in mathematical discourse, make mathematical connections, and model and represent mathematical ideas in a variety of ways.

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#### Content Strands

The content strands (Number Sense and Operations, Algebra, Geometry, Measurement, and Statistics and Probability) explicitly describe the content that students should learn. Each school’s mathematics curriculum developed from these strands should include a broad range of content. This broad range of content, taught in an integrated fashion, allows students to see how various mathematics knowledge is related, not only within mathematics, but also to other disciplines and the real world as well. The performance indicators listed under each band within a strand are intended to assist teachers in determining what the outcomes of instruction should be. The instruction should engage students in the construction of this knowledge and should integrate conceptual understanding and problem solving with these performance indicators. The performance indicators 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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#### 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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