1 New York State Mathematics Core Curriculum 2005.

1

New York State New York State MathematicsMathematics

Core CurriculumCore Curriculum20052005

2

Curriculum, Instruction and Curriculum, Instruction and Instructional TechnologyInstructional Technology

Anne SchianoAnne Schiano

Assistant DirectorAssistant Director

[email protected]

(518) 474-5922

3

Board of Regents Approves Board of Regents Approves

NYS Learning Standard inNYS Learning Standard in

MathematicsMathematics

andand

NYS MathematicsNYS Mathematics

Core CurriculumCore Curriculum

20052005

4

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.

5

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.

6

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

7

8

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

9

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.

10

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.

11

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.

12

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.

13

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.

14

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

15

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.

16

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.

17

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.

18

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.

19

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.

20

Bands within the Bands within the Content StrandsContent Strands

21

Number Sense and Operations Number Sense and Operations BandsBands

•Number Systems

•Number Theory

•Operations

•Estimation

22

Algebra BandsAlgebra Bands

•Variables and Expressions

•Equations and Inequalities

•Patterns, Relations, and Functions

•Coordinate Geometry

•Trigonometric Functions

23

Geometry BandsGeometry Bands

•Shapes

•Geometric Relationships

•Transformational Geometry

•Coordinate Geometry

•Constructions

•Locus

•Informal Proofs

•Formal Proofs 

24

Measurement BandsMeasurement Bands

•Units of Measurement

•Tools and Methods

•Units

•Error and Magnitude

•Estimation

25

Statistics and Probability BandsStatistics and Probability Bands

•Collection of Data

•Organization and Display of Data

•Analysis of Data

•Predictions from Data

•Probability

26

Guide to Reading Guide to Reading the Documentthe Document

27

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

28

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

29

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