MP1 Make sense of problems and persevere in solving them | - Students fearlessly take risks in problem solving
- Students initiate problem solving without intervention
- Teachers provide tasks that allow for problem solving instead of mimicking what the teacher demonstrates at the board.
- Teachers provide tasks that have multiple solutions or no solution
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MP2 Reason abstractly and quantitatively | - Students and teachers show and explain multiple strategies for solving problems
- Students make sense of mathematics within a context (i.e.: word problems)
- Teachers and students focus on the processes of solving more than answer finding
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MP3 Construct viable arguments and critique the reasoning of others | - Students explain and justify their work using known definitions, properties, conventions, theories, and etc.
- Teachers regularly provide opportunities for students to problem solve collaboratively (with partners, in small groups, and whole group discussions.)
- Teachers prompt students to defend their work and explain the work of others
- Teachers provide opportunities to assess the reasonableness of others’ work in an respectful manner.
- Teachers ask high order questions that focus on the processes of math more than answer finding.
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MP4 Model with Mathematics | - Students appropriately use tools such as diagrams, tables, graphs, flowcharts, and formulas, changing tools as reasonable to tackle the problem.
- Teachers encourage and demonstrate the flexible use of tools without fixating on a single algorithm for solving.
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MP5 Use appropriate tools strategically | - Conceptual tools such as estimation are integrated to assess reasonableness of student work and thought processes
- Physical and digital tools are used by the students to support learning and may include:
Elementary: ten frames/five frames, number bars/number tiles, number lines, fraction bars, fraction circles Secondary: algebra tiles, number lines, balance scales, coordinate grids |
| - Students use precise units, labels, and contexts.
- Students work toward mastery and accuracy.
- Students recognize when an estimation may be the most appropriate solution.
- Teachers use consistent, accurate, and appropriate terminology and processes and encourage students to do the same. (i.e.: “distribute terms” not “FOIL” in algebra 1)
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MP7 Look for and make use of structure | - Students draw on previous experience to solve new problems.
- Teachers encourage regular connections between and among mathematical concepts and use this information to solve new problems
- Teachers provide opportunities for students to represent the same concept in a multiple ways
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MP8 Look for and express regularity in repeated reasoning | - Students build automaticity by recognizing patterns and using efficient solving method
- Students regularly reflect on whether their methods and answers make sense.
- Teachers structure tasks and activities such that students discover mathematical concepts and generate the rules for algorithms
- Teachers prompt students to make sense of their methods and answers.
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This document is abbreviated from the extensive NCTM “Engaging in the Mathematical Practices (Look-Fors) to support administrators in easily identifying and supporting key components of effective mathematics instruction. As noted on the NCTM document, “All indicators are not necessary for providing full evidence of practice(s). Each practice may not be evident during every lesson.” As such, this tool is not to be used for evaluative purposes.