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Math Bookmarks Mathematics Mathematics Bookmarks Bookmarks Standards Reference to Support Standards Reference to Support Planning and Instruction Planning and Instruction http://commoncore.tcoe.org http://commoncore.tcoe.org 2nd Grade 2nd Grade 2nd Grade – CCSS for Mathematics 2nd Grade – CCSS for Mathematics Grade-Level Introduction Grade-Level Introduction In Grade 2, instructional time should focus on four critical In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) areas: (1) extending understanding of base-ten notation; (2) building fluency with addition and subtraction; (3) using building fluency with addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing standard units of measure; and (4) describing and shapes. analyzing shapes. (1) Students extend their understanding of the base-ten (1) Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including number relationships involving these units, including comparing. Students understand multi-digit numbers comparing. Students understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones). hundreds + 5 tens + 3 ones). (2) Students use their understanding of addition to develop (2) Students use their understanding of addition to develop fluency with addition and subtraction within 100. They fluency with addition and subtraction within 100. They solve problems within 1000 by applying their solve problems within 1000 by applying their understanding of models for addition and subtraction, understanding of models for addition and subtraction, and they develop, discuss, and use efficient, accurate, and they develop, discuss, and use efficient, accurate, and generalizable methods to compute sums and and generalizable methods to compute sums and differences of whole numbers in base-ten notation, differences of whole numbers in base-ten notation, using their understanding of place value and the using their understanding of place value and the properties of operations. They select and accurately properties of operations. They select and accurately apply methods that are appropriate for the context and apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and the numbers involved to mentally calculate sums and differences for numbers with only tens or only differences for numbers with only tens or only hundreds. hundreds. (3) Students recognize the need for standard units of (3) Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that other measurement tools with the understanding that linear measure involves an iteration of units. They linear measure involves an iteration of units. They recognize that the smaller the unit, the more iterations recognize that the smaller the unit, the more iterations they need to cover a given length. they need to cover a given length. (4) Students describe and analyze shapes by examining (4) Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and make other shapes. Through building, drawing, and analyzing two- and three-dimensional shapes, students analyzing two- and three-dimensional shapes, students develop a foundation for understanding area, volume, develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later grades. congruence, similarity, and symmetry in later grades. http://commoncore.tcoe.org/licensing http://commoncore.tcoe.org/licensing 2nd edition 6/19 2nd edition 6/19 2nd Grade – CCSS for Mathematics 2nd Grade – CCSS for Mathematics FLUENCY FLUENCY In kindergarten through grade six there are individual content In kindergarten through grade six there are individual content standards that set expectations for fluency with computations standards that set expectations for fluency with computations using the standard algorithm (e.g., “fluently” multiply multi- using the standard algorithm (e.g., “fluently” multiply multi- digit whole numbers using the standard algorithm digit whole numbers using the standard algorithm (5.NBT.5▲). Such standards are culminations of (5.NBT.5▲). Such standards are culminations of progressions of learning, often spanning several grades, progressions of learning, often spanning several grades, involving conceptual understanding (such as reasoning about involving conceptual understanding (such as reasoning about quantities, the base-ten system, and properties of operations), quantities, the base-ten system, and properties of operations), thoughtful practice, and extra support where necessary. thoughtful practice, and extra support where necessary. The word “fluent” is used in the standards to mean The word “fluent” is used in the standards to mean “reasonably fast and accurate” and the ability to use certain “reasonably fast and accurate” and the ability to use certain facts and procedures with enough facility that using them facts and procedures with enough facility that using them does not slow down or derail the problem solver as he or she does not slow down or derail the problem solver as he or she works on more complex problems. Procedural fluency works on more complex problems. Procedural fluency requires skill in carrying out procedures flexibly, accurately, requires skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Developing fluency in each efficiently, and appropriately. Developing fluency in each grade can involve a mixture of just knowing some answers, grade can involve a mixture of just knowing some answers, knowing some answers from patterns, and knowing some knowing some answers from patterns, and knowing some answers from the use of strategies. answers from the use of strategies. Explanations of Major, Additional and Supporting Cluster- Explanations of Major, Additional and Supporting Cluster- Level Emphases Level Emphases Major3 [m] clusters – areas of intensive focus where Major3 [m] clusters – areas of intensive focus where students need fluent understanding and application of the students need fluent understanding and application of the core concepts. These clusters require greater emphasis than core concepts. These clusters require greater emphasis than the others based on the depth of the ideas, the time that they the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics take to master, and/or their importance to future mathematics or the demands of college and career readiness. The ▲ or the demands of college and career readiness. The ▲ symbol will indicate standards in a Major Cluster in the symbol will indicate standards in a Major Cluster in the narrative. narrative. Additional [a] clusters – expose students to other subjects; Additional [a] clusters – expose students to other subjects; may not connect tightly or explicitly to the major work of may not connect tightly or explicitly to the major work of the grade the grade Supporting [s] clusters – rethinking and linking; areas where Supporting [s] clusters – rethinking and linking; areas where some material is being covered, but in a way that applies some material is being covered, but in a way that applies core understanding; designed to support and strengthen areas core understanding; designed to support and strengthen areas of major emphasis. of major emphasis. *A Note of Caution: Neglecting material will leave gaps in *A Note of Caution: Neglecting material will leave gaps in students’ skills and understanding and will leave students students’ skills and understanding and will leave students unprepared for the challenges of a later grade. unprepared for the challenges of a later grade. California Mathematics Framework, adopted by the California Mathematics Framework, adopted by the California State Board of Education November 6, 2013, California State Board of Education November 6, 2013, http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.a http://www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.a sp sp http://commoncore.tcoe.org/licensing http://commoncore.tcoe.org/licensing 2nd edition 6/19 2nd edition 6/19 2nd Grade – CCSS for Mathematics 2nd Grade – CCSS for Mathematics Mathematical Practices Mathematical Practices 1. Make sense of problems and persevere in solving them. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of 3. Construct viable arguments and critique the reasoning of others. others. 4. Model with mathematics. 4. Model with
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