Mathematical Practices
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 4th grade math.
The "practices" describe varieties of expertise that we seek to develop in students during 4th grade math.
Practice #1: Make Sense of Problems and Persevere In Solving Them
- Students:
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:
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:
Explain their thinking
Use numbers flexibly by applying properties of operations and place value
Examine the reasonableness of their answers/calculations
- Because Teachers:
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:
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:
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:
Use representations to solve real life problems
Apply formulas and equations where appropriate
- Because Teachers:
Provide a variety of real world contexts
Use intentional representations
Practice #5: Use Appropriate Tools Strategically
- Students:
Use technological tools and resources to solve problems and deepen understanding
- Because Teachers:
Use tools with their instruction
Practice #6: Attend to Precision
- Students:
Explain their thinking using mathematics vocabulary
Use appropriate symbols and specify units of measure
- Because Teachers:
Use (and challenge students to use) mathematics vocabulary precisely and consistently
Practice #7: Look For and Make Use of Structure
- Students:
Apply reasonable thoughts about patterns and properties to new situations
- Because Teachers:
Ask questions about the application of patterns
Highlight different approaches for solving problems
Practice #8: Look For and Express Regularity in Repeated Reasoning
- Students:
Evaluate the reasonableness of results and solutions
- Because Teachers:
Ask about answers before and reasonableness after computations