Math
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Unit One
Mathematical Practice #2: Reason Abstractly and Quantitatively
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability todecontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents, and the ability to contextualize—to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. |
Unit Two
Mathematical Practice #1: Make Sense of Problems and Persevere in Solving Them
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. Students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others so solving complex problems and identify correspondences between different approaches. Mathematical Practice #8: Express Regularity in Repeated Expression Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. They continually evaluate the reasonableness of the intermediate results. |
Unit Three
Mathematical Practice #3: Construct Viable Arguments and Critique the Reasoning of Others.
Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They can build a logical progression of statements to explore the truth of their conjectures. They can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They can compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. | ||||||||
Unit Four
Mathematical Practice #4: Model with Mathematics
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. |
Unit Five
Mathematical Practice #7: Make Use of Structures
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. |
Unit Six
Mathematical Practice #6: Attend to Precision
Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently and express numerical answers with a degree of precision appropriate for the problem context. | ||||||