U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.3. Develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections.
1.1.4. Develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers.
1.1.5. Connect number words and numerals to the quantities they represent, using various physical models and representations.
1.3. Compute fluently and make reasonable estimates.
1.3.1. Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
1.3.2. Develop fluency with basic number combinations for addition and subtraction.
N.2. Algebra (NCTM)
2.3. Use mathematical models to represent and understand quantitative relationships.
2.3.1. Model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols.
N.11. Grade 1 Curriculum Focal Points (NCTM)
11.1. Number and Operations and Algebra: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts
11.1.1. Children develop strategies for adding and subtracting whole numbers on the basis of their earlier work with small numbers. They use a variety of models, including discrete objects, length-based models (e.g., lengths of connecting cubes), and number lines, to model 'part-whole,' 'adding to,' 'taking away from,' and 'comparing' situations to develop an understanding of the meanings of addition and subtraction and strategies to solve such arithmetic problems. Children understand the connections between counting and the operations of addition and subtraction (e.g., adding two is the same as 'counting on' two). They use properties of addition (commutativity and associativity) to add whole numbers, and they create and use increasingly sophisticated strategies based on these properties (e.g., 'making tens') to solve addition and subtraction problems involving basic facts. By comparing a variety of solution strategies, children relate addition and subtraction as inverse operations.
11.2. Number and Operations: Developing an understanding of whole number relationships, including grouping in tens and ones
11.2.1. Children compare and order whole numbers (at least to 100) to develop an understanding of and solve problems involving the relative sizes of these numbers. They think of whole numbers between 10 and 100 in terms of groups of tens and ones (especially recognizing the numbers 11 to 19 as 1 group of ten and particular numbers of ones). They understand the sequential order of the counting numbers and their relative magnitudes and represent numbers on a number line.
N.12. Connections to the Grade 1 Focal Points (NCTM)
12.1. Number and Operations and Algebra: Children use mathematical reasoning, including ideas such as commutativity and associativity and beginning ideas of tens and ones, to solve two-digit addition and subtraction problems with strategies that they understand and can explain. They solve both routine and nonroutine problems.