Standard 1: Concepts and Procedures—Students can explain and apply mathematical concepts and interpret and carry out mathematical procedures with precision and fluency
Standard 1 Overview: This claim addresses procedural skills and the conceptual understanding on which developing skills depend. It is important to assess how aware students are of how concepts link together and why mathematical procedures work the way they do.
Standard 2: Problem Solving and Application—Students can solve a range of complex, well-posed problems in pure and applied mathematics, making productive use of knowledge and problem-solving strategies.
Standard 3: Communicating Reason—Students can clearly and precisely construct viable arguments to support their own reasoning and to critique the reasoning of others.
Standard 3 Overview: Standard 3 refers to a recurring theme in the Common Core State Standards Mathematics content and practice standards—the ability to construct and present a clear, logical, convincing argument. For older students, this may take the form of a rigorous, deductive proof based on clearly stated axioms. For younger students, this will involve more informal justifications. Assessment tasks that address this claim will typically present a claim and ask students to provide, for example, a justification or counterexample.
Standard 4: Modeling and Data Analysis—Students can analyze complex, real-world scenarios and can construct and use mathematical models to interpret and solve problems.
Standard 4 Overview: In the real world, problems do not come neatly “packaged.” Real-world problems are complex and often contain insufficient or superfluous data. Tasks designed primarily to assess standard 4 will involve formulating a problem that is tractable using mathematics; that is, formulating a model. This will usually involve making assumptions and simplifications. Students will need to select from the data at hand or estimate data that are missing. Students will identify variables in a situation and construct relationships between them. Once students have formulated the problem, they will tackle it (often in a decontextualized manner) before interpreting their results and then checking the results for reasonableness.
Standard 5: Attention to Detail
Standard 5 Overview: Students follow directions and use appropriate labels. They calculate accurately and efficiently.