Principles and Standards for School Mathematics
Number and Operations Standard
Understand numbers, ways of representing numbers, relationships among numbers, and number systems
Expectations (Pre-K - 2)
count with understanding and recognize "how many" in sets of objects;
develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
connect number words and numerals to the quantities they represent, using various physical models and representations;
Understand meanings of operations and how they relate to one another
Expectations (Pre-K - 2)
count with understanding and recognize "how many" in sets of objects;
develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
connect number words and numerals to the quantities they represent, using various physical models and representations;
understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;
Compute fluently and make reasonable estimates
Expectations (Pre-K - 2)
count with understanding and recognize "how many" in sets of objects;
develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections;
develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers;
connect number words and numerals to the quantities they represent, using various physical models and representations;
understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations;
develop fluency with basic number combinations for addition and subtraction;
use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
Represent and analyze mathematical situations and structures using algebraic symbols
Expectations (Pre-K - 2)
illustrate general principles and properties of operations, such as commutativity, using specific numbers;
use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
Use mathematical models to represent and understand quantitative relationships
Expectations (Pre-K - 2)
illustrate general principles and properties of operations, such as commutativity, using specific numbers;
use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.
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