Standards of Mathematical Practices - One Standard at a Time

Mathematical Practices are embedded in every math lesson we teach.  The Standards for Mathematical Practice describe varieties of expertise that math educators at all levels (K-12) should seek to develop in their students.  These practices rest on important "processes and proficiencies" with longstanding importance in mathematics education. 

Mathematical Practice #2

Reason abstractly and quantitatively.

What should students be able to do?

• Make sense of quantities and their relationships.
• Decontextualize (represent a situation symbolically and manipulate the symbols) and contextualize (make meaning of the symbols in a problem) quantitative relationships. 
• Understand the meaning of quantities and are flexible in the use of operations and their properties.
• Create a logical representation of the problem.
• Attends to the meaning of quantities, not just how to compute them.

Questions the Teacher Can Ask to Develop Mathematical Thinking:

• What do the numbers used in the problem represent?
• What is the relationship of the quantities?
• How is ________ related to ________?
• What is the relationship between ________ and ________?
• What does ________ mean to you?  (e.g., symbol, quantity, diagram)
• What properties might we use to find a solution?
• How did you decide in this task that you needed to use...?
• Could we have used another operation of property to solve this task?  Why or why not?