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A1-F-1-3

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

A1.F.1.3 Write linear functions, using function notation, to model real-world and mathematical situations.

In a Nutshell

Students will understand the relationship between the variables in a linear function in order to write them in the form of f(x) = mx+b to model real-world and mathematical situations.

Student Actions	Teacher Actions
Students will develop a deep and flexible conceptual understanding of linear relationships to determine the dependent and independent variables in order to write a linear function in function notation for various situations. As students develop mathematical reasoning, they will communicate what the letter in the notation represents and explore how any letter can be used in function notation. Students explore and create more than one representation of each linear function they explore and can justify their reasoning.	Establish mathematics goals to focus learning by using prior exposure to function machines from previous grades. Use and connect mathematical representations when writing function examples, teachers should be deliberate to change the letter used to represent the function and not always use f(x). Build procedural fluency from conceptual understanding by exposing students to a variety of tables that don't always have x values that increase by one or change by constant amount. Provide students with a variety of representations of real-world functions and allow them to create a linear function. Encourage students to create more than one representation of a function.
Key Understandings	Misconceptions
The students will recognize the rate of change as the slope and the initial value as the y-intercept of the linear function to write the linear function f(x) = mx+b. Example: Uncle Jim gave Emily $50 on the day she was born and $25 on each birthday after that. The function f(x)=25x+50 represents the amount of money Jim has given after x years. The rate of change is $25 per year.	Students may consider an equation such as x=10 a linear function. This is a linear equation, but it is not a linear function because there are infinite output values for the input value of 10. There may be a misunderstanding about the notation f and f(x). The notation f is the name of the function (or rule) and f(x) is the output from the rule when x is the input. In the form f(x)=mx+b, students may switch the values and call m the y-intercept and b the slope. When students see f(x), they may initially think it means f times x. Students do not recognize the difference between a linear equation and a linear functions and leave the equation as y=.when asked to write a linear function.