1 new york state mathematics core curriculum 2005
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Curriculum, Instruction and Curriculum, Instruction and Instructional TechnologyInstructional Technology
Anne SchianoAnne Schiano
Assistant DirectorAssistant Director
aschiano@mail.nysed.gov
(518) 474-5922
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Board of Regents Approves Board of Regents Approves
NYS Learning Standard inNYS Learning Standard in
MathematicsMathematics
andand
NYS MathematicsNYS Mathematics
Core CurriculumCore Curriculum
20052005
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Mathematics, Science, and TechnologyMathematics, Science, and Technology
Learning Standard 3: MathematicsLearning 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 3Standard 3
The Three ComponentsThe Three Components
•Conceptual Understanding consists of those relationships constructed internally and connected to already existing ideas.
•Procedural Fluency is 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 3Standard 3
Process and Content StrandsProcess and Content Strands
The Five Process Strands The Five Content Strands
Problem SolvingNumber Sense and
Operations
Reasoning and Proof Algebra
Communication Geometry
Connections Measurement
Representation Statistics and Probability
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The Five Content StrandsThe 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 Number Sense and Operations StrandStrand
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 StrandAlgebra 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 StrandGeometry 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 StrandMeasurement 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 StrandStatistics 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 StrandsThe 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 StrandProblem 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 StrandReasoning 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 StrandCommunication 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 StrandConnections 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 StrandRepresentation 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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Number Sense and Operations Number Sense and Operations BandsBands
•Number Systems
•Number Theory
•Operations
•Estimation
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Algebra BandsAlgebra Bands
•Variables and Expressions
•Equations and Inequalities
•Patterns, Relations, and Functions
•Coordinate Geometry
•Trigonometric Functions
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Geometry BandsGeometry Bands
•Shapes
•Geometric Relationships
•Transformational Geometry
•Coordinate Geometry
•Constructions
•Locus
•Informal Proofs
•Formal Proofs
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Measurement BandsMeasurement Bands
•Units of Measurement
•Tools and Methods
•Units
•Error and Magnitude
•Estimation
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Statistics and Probability BandsStatistics and Probability Bands
•Collection of Data
•Organization and Display of Data
•Analysis of Data
•Predictions from Data
•Probability
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Prekindergarten 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
PerformanceIndicator
Strand
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Prekindergarten 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
BandPerformance
Indicator
Strand
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Performance Indicator GuidePerformance 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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