U.S. National Standards
N.1. Number and Operations (NCTM)
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.4. 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.
1.2. Understand meanings of operations and how they relate to one another.
1.2.1. Understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations.
1.2.2. Understand the effects of adding and subtracting whole numbers.
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)
2.2. Represent and analyze mathematical situations and structures using algebraic symbols.
2.2.2. Use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations.
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 2 Curriculum Focal Points (NCTM)
11.2. Number and Operations and Algebra: Developing quick recall of addition facts and related subtraction facts and fluency with multi-digit addition and subtraction
11.2.1. Children use their understanding of addition to develop quick recall of basic addition facts and related subtraction facts. They solve arithmetic problems by applying their understanding of models of addition and subtraction (such as combining or separating sets or using number lines), relationships and properties of number (such as place value), and properties of addition (commutativity and associativity). Children develop, discuss, and use efficient, accurate, and generalizable methods to add and subtract multi-digit whole numbers. They select and apply appropriate methods to estimate sums and differences or calculate them mentally, depending on the context and numbers involved. They develop fluency with efficient procedures, including standard algorithms, for adding and subtracting whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.
N.12. Connections to the Grade 2 Focal Points (NCTM)
12.1. Number and Operations: Children use place value and properties of operations to create equivalent representations of given numbers (such as 35 represented by 35 ones, 3 tens and 5 ones, or 2 tens and 15 ones) and to write, compare, and order multi-digit numbers. They use these ideas to compose and decompose multi-digit numbers. Children add and subtract to solve a variety of problems, including applications involving measurement, geometry, and data, as well as nonroutine problems. In preparation for grade 3, they solve problems involving multiplicative situations, developing initial understandings of multiplication as repeated addition.