A1-F-3-1

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A1.F.3.1 Identify and generate equivalent representations of linear equations, graphs, tables, and real-world situations.

In a Nutshell

Students will move between different representations of linear functions. Given one form of a linear function, such as a table, words, equation, or graph, students will be able to transfer to any other form. Tables, graphs and equations are used to find and interpret solutions to real-world linear situations.

Student Actions	Teacher Actions
Students explore and create more than one representation (equations, graphs, tables, verbal explanations) of each linear function they explore to develop a deep and flexible conceptual understanding.. Students develop mathematical reasoning by using real world concrete situations to explore the meaning of linear functions and relate mathematical representations and graphs to real-world situations. Students develop the ability to communicate mathematically by identifying the independent variable and dependent variable in situations and justifying their reasoning to their peers and teachers. Students will relate mathematical representations and graphs to real-world situations.	Implement tasks that promote reasoning and problem solving by providing students with multiple representations of functions to solve problems. Build procedural fluency from conceptual understanding by exposing students to a variety of representations and asking them to create different representations based on those. Elicit and use evidence of student thinking by asking students to highlight features of functions in each representation. Pose purposeful questions that check for the student’s understanding of the meaning of slope and y-intercept of linear functions represented in various representations.
Key Understandings	Misconceptions
Write a linear equation in multiples forms such as Standard, General, Slope-Intercept, or Point-Slope. Identify the slope as a rate of change in a real-world linear situation and the y-intercept as the initial condition when time is zero. Interpret the slope from a table or a graph to transfer to other forms. Understand and create many different representations of functions including tables, graphs, equations and verbal representations.	When given a table representation of a linear function with the first entry pair of the table not being "when x = 0," students sometimes give the first y value given as the y-intercept and not the y-value associated to x = 0. When given a table that doesn't have consecutive x-values, students sometimes will calculate the slope wrong.