MATHMATICAL PRACTICE

STUDENT LOOK FORS

TEACHER LOOK FORS

Mathematical Practice 1: Make sense of problems, and persevere in solving them.

Students are engaged in solving problems and high cognitive demand tasks.

Teachers provide adequate time with formative feedback for students to discuss problem pathways and solutions with peers.

Mathematical Practice 2: Reason Abstractly and quantitatively.

Students are able to contextualize or decontextualize problems.

Teachers provide access to and uses appropriate representations (manipulative materials, drawings, or on-line renderings) of problems and asks questions focused on determining student reasoning.

Mathematical Practice 3: Construct viable arguments, and critique the reasoning of others.

Students can understand and use prior learning in constructing arguments.

Teachers provide opportunities for students to listen to or read the conclusions and arguments of others  - as students discuss approaches and solutions to problems, the teacher encourages them to provide arguments for why particular strategies work and to listen and respond to the reasoning of others and asks questions to prompt discussions.

Mathematical Practice 4: Model with mathematics.

Students will analyze and model relationships mathematically (such as when using an expression or equation).

Teachers will provide contexts for students to apply the mathematics learned.

Mathematical Practice 5: Use appropriate tools strategically.

Students will have access to and use instructional tools to deepen understanding (for example, manipulative materials, drawings, and technological tools).

Teachers will provide and demonstrate appropriate tools (like manipulatives).

Mathematical Practice 6: Attend to precision.

Students will recognize the need for precision in response to a problem and use appropriate mathematics vocabulary.

Teachers will emphasize the importance of precise communication, including appropriate mathematical vocabulary, and emphasizes the importance of accuracy and efficiency in solutions to problems, including the use of estimation and mental mathematics when appropriate.

Mathematical Practice 7: Look for and make use of structure.

Students are to be encouraged to look for patterns and structure (for example, when using properties and composing and decomposing numbers within mathematics.

Teachers will provide time for students to discuss patterns and structures that emerge in a problem’s solution.

Mathematical Practice 8: Look for and express regularity in repeated reasoning.  

Students will reason about varied strategies and methods for solving problems and check for the reasonableness of their results.

Teachers will encourage students to look for and discuss regularity in their reasoning.

Source: Adapted from Kanold, Briars & Fennell, 2012.

go.solution-tree.com/commoncore for a reproducible version of this table.