Element 2b - Reason abstractly, reflectively, and - Reason abstractly, reflectively, and - Reason abstractly, reflectively, and quantitatively with attention to units, quantitatively with attention to quantitatively with attention to units, Reason abstractly, reflectively, constructing viable arguments and constructing viable arguments and constructing viable arguments and and quantitatively with attention proofs, and critiquing the reasoning proofs, and critiquing the reasoning proofs, and critiquing the reasoning of to units, constructing viable of others. of others. others. arguments and proofs, and - Represent and model generalizations - Represent and model generalizations - Represent and model generalizations critiquing the reasoning of using mathematics. using mathematics. using mathematics. others; represent and model generalizations using - - - Recognize structure and express Recognize structure and express Recognize structure and express mathematics; recognize structure regularity in patterns of regularity in patterns of mathematical regularity in patterns of mathematical and express regularity in patterns mathematical reasoning. reasoning. reasoning. of mathematical reasoning; use multiple representations to model Use multiple representations to Use multiple representations to model Use multiple representations to model and describe mathematics; and model and describe mathematics. and describe mathematics. and describe mathematics. utilize appropriate mathematical vocabulary and symbols to - Use appropriate mathematical - Use appropriate mathematical - Use appropriate mathematical communicate mathematical ideas vocabulary and symbols to vocabulary and symbols to vocabulary and symbols to to others. communicate mathematical to communicate mathematical ideas to communicate mathematical ideas to others. others. others. - Demonstrate an appreciation for mathematical and inquiry. Element 2c - Formulate, represent, analyze, and - Formulate, represent, analyze, and - Formulate, represent, analyze, interpret mathematical models interpret mathematical models interpret, and validate mathematical Formulate, represent, analyze, derived from real-world contexts or derived from real-world contexts or models derived from real-world and interpret mathematical mathematical problems. mathematical problems. contexts or mathematical problems. models derived from real-world - Demonstrate flexibility in contexts or mathematical mathematical modeling when problems. confronted with different purposes or contexts. Element 2d - Organize mathematical thinking. - Organize mathematical thinking. - Organize mathematical thinking. - Use the language of mathematics to - Use the language of mathematics to - Use the language of mathematics to Organize mathematical thinking express ideas precisely, both orally express precisely, both orally express ideas precisely, both orally and use the language of
Element 2b Reason abstractly, reflectively, and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others; represent and model generalizations using mathematics; recognize structure and express regularity in patterns of mathematical reasoning; use multiple representations to model and describe mathematics; and utilize appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. - Reason abstractly, reflectively, and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to model and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical to others. - Reason abstractly, reflectively, and quantitatively with attention to constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to model and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. - Reason abstractly, reflectively, and quantitatively with attention to units, constructing viable arguments and proofs, and critiquing the reasoning of others. - Represent and model generalizations using mathematics. - Recognize structure and express regularity in patterns of mathematical reasoning. Use multiple representations to model and describe mathematics. - Use appropriate mathematical vocabulary and symbols to communicate mathematical ideas to others. - Demonstrate an appreciation for mathematical and inquiry. Element 2c Formulate, represent, analyze, and interpret mathematical models derived from real-world contexts or mathematical problems. - Formulate, represent, analyze, and interpret mathematical models derived from real-world contexts or mathematical problems. - Formulate, represent, analyze, and interpret mathematical models derived from real-world contexts or mathematical problems. - Formulate, represent, analyze, interpret, and validate mathematical models derived from real-world contexts or mathematical problems. - Demonstrate flexibility in mathematical modeling when confronted with different purposes or contexts. Element 2d Organize mathematical thinking and use the language of - Organize mathematical thinking. - Use the language of mathematics to express ideas precisely, both orally - Organize mathematical thinking. - Use the language of mathematics to express precisely, both orally - Organize mathematical thinking. - Use the language of mathematics to express ideas precisely, both orally