The Standards for Mathematical Practice describe the behaviors of a proficient mathematician. The "practices" describe varieties of expertise that we seek to develop in students during 3rd grade math.
Practice #1: Make Sense of Problems and Persevere In Solving Them Students:Analyze and explain the meaning of the problem Actively engage in problem solving (Develop, carry out, and refine a plan) Show patience and positive attitudes Ask if their answers make sense Check their answers with a different method Because Teachers:Pose rich problems and/or ask open ended questions Provide wait-time for processing/finding solutions Circulate to pose probing questions and monitor student progress Provide opportunities and time for cooperative problem solving and reciprocal teaching ***
Practice #2: Reason Abstractly and Quantitatively Students:Represent a problem with symbols Explain their thinking Use numbers flexibly by applying properties of operations and place value Examine the reasonableness of their answers/calculations Because Teachers:Ask students to explain their thinking regardless of accuracy Highlight flexible use of numbers Facilitate discussion through guided questions and representations Accept varied solutions/representations ***
Practice #3: Construct Viable Arguments and Critique the Reasoning of Others Students:Make reasonable guesses to explore their ideas Justify solutions and approaches Listen to the reasoning of others, compare arguments, and decide if the arguments of others makes sense Ask clarifying and probing questions Because Teachers:Provide opportunities for students to listen to or read the conclusions and arguments of others Establish and facilitate a safe environment for discussion Ask clarifying and probing questions Avoid giving too much assistance (e.g., providing answers or procedures) ***
Practice #4: Model with Mathematics Students:Apply prior knowledge to new problems and reflect Use representations to solve real life problems Apply formulas and equations where appropriate Because Teachers:Pose problems connected to previous concepts Provide a variety of real world contexts Use intentional representations ***
Practice #5: Use Appropriate Tools Strategically Students:Select and use tools strategically (and flexibly) to visualize, explore, and compare information Use technological tools and resources to solve problems and deepen understanding Because Teachers:Make appropriate tools available for learning (calculators, concrete models, digital resources, pencil/paper, compass, protractor, etc.) Use tools with their instruction ***
Practice #6: Attend to Precision Students:Calculate accurately and efficiently Explain their thinking using mathematics vocabulary Use appropriate symbols and specify units of measure Because Teachers:Recognize and model efficient strategies for computation Use (and challenge students to use) mathematics vocabulary precisely and consistently ***
Practice #7: Look For and Make Use of Structure Students:Look for, develop, and generalize relationships and patterns Apply reasonable thoughts about patterns and properties to new situations Because Teachers:Provide time for applying and discussing properties Ask questions about the application of patterns Highlight different approaches for solving problems *** Practice #8: Look For and Express Regularity in Repeated Reasoning Students:Look for methods and shortcuts in patterns and repeated calculations Evaluate the reasonableness of results and solutions Because Teachers:Provide tasks and problems with patterns Ask about answers before and reasonableness after computations ***