Standards for Mathematical Practices

The Standards for Mathematical Practice describe the behaviors of Mathematically Proficient Students. The "practices" describe varieties of expertise that mathematics teachers at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

 

Possible "I can" statements for SMPs

1. I can solve problems in different ways without giving up.
2. I can think about numbers in many ways.
3. I can explain my thinking and listen to others’ thinking.
4. I can show my thinking.
5. I can use tools and know when to use them.
6. I can use correct words and check my work.
7. I can look for patterns.
8. I can use shortcuts that I understand.

 

• Full Description of Practices Download Full Description of Practices
  (pdf)
• Child-Friendly Standards for Mathematical Practices Download Child-Friendly Standards for Mathematical Practices
  (pdf)
• Another Version of Classroom Posters Download Another Version of Classroom Posters
  *NEW* (RESA School District Wayne, MI)
• Additional Version of Classroom Posters Download Additional Version of Classroom Posters
  (The Math Learning Center)
• Parent-Friendly Standards for Mathematical Practices Download Parent-Friendly Standards for Mathematical Practices
  (pdf)
• HCPSS Standards for Mathematical Practices Look-Fors Download HCPSS Standards for Mathematical Practices Look-Fors
  (pdf)
• Abbreviated Walkthrough Tool SMPs Download Abbreviated Walkthrough Tool SMPs

 

Practice #1: Make Sense of Problems and Persevere In Solving Them

Students:	Because Teachers:
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	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

 

Practice #2: Reason Abstractly and Quantitatively

Students:	Because Teachers:
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	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:	Because Teachers:
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 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:	Because Teachers:
Apply prior knowledge to new problems and reflect Use representations to solve real life problems Apply formulas and equations where appropriate	Pose problems connected to previous concepts Provide a variety of real world connections Use intentional representations

 

 

Practice #5: Use Appropriate Tools Strategically

Students:	Because Teachers:
Select and use tools strategically (and flexibly) to visualize, explore, and compare information Use technological tools and resources to solve problems and deepen understanding	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:	Because Teachers:
Calculate accurately and efficiently Explain their thinking using mathematics vocabulary Use appropriate symbols and specify units of measure	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:	Because Teachers:
Look for, develop, and generalize relationships and patterns Apply reasonable thoughts about patterns and properties to new situations	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:	Because Teachers:
Look for methods and shortcuts in patterns and repeated calculations Evaluate the reasonableness of results and solutions	Provide tasks and problems with patterns Ask about answers before and reasonableness after computations

 

Other Standards for Mathematical Practices Resources

• Illustrative Mathematics Project Links to an external site.

 

 

 

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