A2-F-1-8

Student Actions

Teacher Actions

• Students will develop a productive mathematical disposition that piecewise functions are sensible, useful and worthwhile in representing real-world situations.

• Students will develop a deep conceptual understanding of piecewise functions as different functions together as one unit with different domain and range.

• Students will develop accurate and appropriate procedural fluency for graphing piecewise functions.

• Students will develop deep and flexible conceptual understanding of critical points and key characteristics of a piecewise function by analyzing a given a graph.

• Focus students’ attention on the structure and/or essential features of piecewise functions.

• Ask questions that go beyond simply producing a graph to probing thinking and requiring explanation.

• Provide students with opportunities  through a variety of activities to practice of graphing piecewise functions.

• Provide students with opportunities to use their own reasoning, strategies and methods for graphing and interpreting piecewise functions. Allow students time to collaborate, discuss and defend their reasoning, strategies, and methods.

• Allow students time to discover real world problems that are represented by piecewise functions. Give students choice on how to present their findings.

Key Understandings

Misconceptions

• Graph a function only over the defined domain interval. 
• Graph all pieces of a given piecewise function on the same coordinate grid to make up the entire graph. 
• Understand that a graph is increasing if it is rising from left to right; a graph is decreasing if it is falling left to right; and a graph is constant if it is horizontal.

• Understand that a piecewise function may contain all of the following: increasing, decreasing and horizontal intervals.

• Students fail to restrict the domain of each piece of the function or restrict it incorrectly.
• Students try to connect all the pieces of the function whether or not they should.
• Students give the intervals of the range where the function is increasing, decreasing, or constant, instead of the intervals of the domain.

• Students fail to indicate if there are discontinuities in the domain or range.