TABLE 5.2 Table of Standards and Expectations for School Mathematics

Number and operations

  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems

  • Understand meanings of operations and how they relate to one another

  • Compute fluently and make reasonable estimates


  • Understand patterns, relations, and functions

  • Represent and analyze mathematical situations and structures using algebraic symbols

  • Use mathematical models to represent and understand quantitative relationships

  • Analyze change in various contexts


  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems

  • Apply transformations and use symmetry to analyze mathematical situations

  • Use visualization, spatial reasoning, and geometric modeling to solve problems


  • Understand measurable attributes of objects and the units, systems, and processes of measurement

  • Apply appropriate techniques, tools, and formulas to determine measurements

Data analysis and probability

  • Formulate questions that can be addressed with data, and collect, organize, and display relevant data to answer them

  • Select and use appropriate statistical methods to analyze data

  • Develop and evaluate inferences and predictions that are based on data

  • Understand and apply basic concepts of probability

Problem solving

  • Build new mathematical knowledge through problem solving

  • Solve problems that arise in mathematics and in other contexts

  • Apply and adapt a variety of appropriate strategies to solve problems

  • Monitor and reflect on the process of mathematical problem solving

Reasoning and proof

  • Recognize reasoning and proof as fundamental aspects of mathematics

  • Make and investigate mathematical conjectures

  • Develop and evaluate mathematical arguments and proofs

  • Select and use various types of reasoning and methods of proof


  • Organize and consolidate mathematical thinking through communication

  • Communicate mathematical thinking coherently and clearly to peers, teachers, and others

  • Analyze and evaluate the mathematical thinking and strategies of others

  • Use the language of mathematics to express mathematical ideas precisely

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