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N.1. Number and Operations
1.1. Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.1.1. Count with understanding and recognize 'how many' in sets of objects.
1.1.2. Use multiple models to develop initial understandings of place value and the base-ten number system.
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.
1.1.6. Understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2.
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.
1.2.3. Understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally.
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.
1.3.3. Use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.
N.11. Grade 2 Curriculum Focal Points
11.1. Number and Operations: Developing an understanding of the base-ten numeration system and place-value concepts
11.1.1. Children develop an understanding of the base-ten numeration system and place-value concepts (at least to 1000). Their understanding of base-ten numeration includes ideas of counting in units and multiples of hundreds, tens, and ones, as well as a grasp of number relationships, which they demonstrate in a variety of ways, including comparing and ordering numbers. They understand multi-digit numbers in terms of place value, recognizing that place-value notation is a shorthand for the sums of multiples of powers of 10 (e.g., 853 as 8 hundreds + 5 tens + 3 ones).
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.
11.3. Measurement: Developing an understanding of linear measurement and facility in measuring lengths
11.3.1. Children develop an understanding of the meaning and processes of measurement, including such underlying concepts as partitioning (the mental activity of slicing the length of an object into equal-sized units) and transitivity (e.g., if object A is longer than object B and object B is longer than object C, then object A is longer than object C). They understand linear measure as an iteration of units and use rulers and other measurement tools with that understanding. They understand the need for equal-length units, the use of standard units of measure (centimeter and inch), and the inverse relationship between the size of a unit and the number of units used in a particular measurement (i.e., children recognize that the smaller the unit, the more iterations they need to cover a given length).
N.12. Connections to the Grade 2 Focal Points
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.
12.2. Geometry and Measurement: Children estimate, measure, and compute lengths as they solve problems involving data, space, and movement through space. By composing and decomposing two-dimensional shapes (intentionally substituting arrangements of smaller shapes for larger shapes or substituting larger shapes for many smaller shapes), they use geometric knowledge and spatial reasoning to develop foundations for understanding area, fractions, and proportions.
12.3. Algebra: Children use number patterns to extend their knowledge of properties of numbers and operations. For example, when skip counting, they build foundations for understanding multiples and factors.
2.1. Understand patterns, relations, and functions.
2.1.1. Sort, classify, and order objects by size, number, and other properties.
2.1.2. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
2.1.3. Analyze how both repeating and growing patterns are generated.
2.2. Represent and analyze mathematical situations and structures using algebraic symbols.
2.2.1. Illustrate general principles and properties of operations, such as commutativity, using specific numbers.
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.
3.1. Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
3.1.1. Recognize, name, build, draw, compare, and sort two- and three-dimensional shapes.
3.1.2. Describe attributes and parts of two- and three-dimensional shapes.
3.2. Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
3.2.1. Describe, name, and interpret relative positions in space and apply ideas about relative position.
3.2.2. Describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance.
3.2.3. Find and name locations with simple relationships such as 'near to' and in coordinate systems such as maps.
3.3. Apply transformations and use symmetry to analyze mathematical situations.
3.3.2. Recognize and create shapes that have symmetry.
3.4. Use visualization, spatial reasoning, and geometric modeling to solve problems.
3.4.3. Relate ideas in geometry to ideas in number and measurement.
3.4.4. Recognize geometric shapes and structures in the environment and specify their location.
4.1. Understand measurable attributes of objects and the units, systems, and processes of measurement.
4.1.1. Recognize the attributes of length, volume, weight, area, and time.
4.1.2. Compare and order objects according to these attributes.
4.1.3. Understand how to measure using nonstandard and standard units.
4.1.4. Select an appropriate unit and tool for the attribute being measured.
4.2. Apply appropriate techniques, tools, and formulas to determine measurements.
4.2.3. Use tools to measure.
N.5. Data Analysis and Probability
5.2. Select and use appropriate statistical methods to analyze data.
5.2.1. Describe parts of the data and the set of data as a whole to determine what the data show.
5.3. Develop and evaluate inferences and predictions that are based on data.
5.3.1. Discuss events related to students' experiences as likely or unlikely.
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