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A1-F-1-4

Page history last edited by Brenda Butz 6 years, 3 months ago

A1.F.1.4 Given a graph modeling a real-world situation, read and interpret the linear piecewise function (excluding step functions).

In a Nutshell

Students will recognize piecewise functions as functions represented by a combination of equations, each corresponding to a specific part of the domain.

Student Actions	Teacher Actions
Students will develop mathematical reasoning as they learn to accurately read graphs and interpret the domain and range of each piece of the function. Students will use the graph to interpret the y-values that apply to each piece of the function and generalize the relationship to the real-world situation. Students will communicate mathematically as they justify their interpretation to teachers and peers, and demonstrate their understanding of the pieces of the graph in the context of mathematical problems and real-world situations.	Provide the students the opportunity to use and connect mathematical representations of various real-world models including data sets, verbal interpretations and piecewise functions. Guide students while they build procedural fluency as they learn to read only a segment of a linear graph and interpret and express the boundaries of each piece of the function as it relates to real-world situations. Pose purposeful questions to students about what they notice on the graph about the domain, range and the pieces how they relate to a real-world situation. “Why do you think the graph changes at that point?” “What is happening at that point?” “At what point does graph change? Why do you think it does that?”
Key Understandings	Misconceptions
Piecewise linear function is a real-valued function defined on the real numbers or a segment thereof, whose graph is composed of straight-line sections.	Students confuse or can not identify the part of the domain which corresponds to each piece of the function. Students interchange the domain and range of each piece(s). Students tend to think that a piece-wise linear function has only one linear function because of its name. They fail to realize that two or more distinct lines are needed to represent a real-world situation. Students may not understand the meaning of a horizontal line, not recognizing that there is no slope and no change in the x values along that line.