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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.
1.3. 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.11. Grade 1 Curriculum Focal Points
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
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.
12.2. Measurement and Data Analysis: Children strengthen their sense of number by solving problems involving measurements and data. Measuring by laying multiple copies of a unit end to end and then counting the units by using groups of tens and ones supports children's understanding of number lines and number relationships. Representing measurements and discrete data in picture and bar graphs involves counting and comparisons that provide another meaningful connection to number relationships.
12.3. Algebra: Through identifying, describing, and applying number patterns and properties in developing strategies for basic facts, children learn about other properties of numbers and operations, such as odd and even (e.g., 'Even numbers of objects can be paired, with none left over'), and 0 as the identity element for addition.
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.
3.4.4. 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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