Student Actions

Teacher Actions

• Develop Mathematical Reasoning when you explore and create more than one representation of each linear function explored (table, graph, equation, verbal description).

• Develop Mathematical Reasoning when using real world concrete situations to explore the meaning of linear functions.

• Develop a Deep and Flexible Conceptual Understanding working with a variety of arithmetic and geometric sequences and connecting them to tables, graphs, and equations.

• Develop Ability to Communicate Mathematically when using graphing technologies to explore the effect of changing the m value (coefficient) in the equation and discuss your results with a partner or in a class discussion.

    

• Use and connect mathematical representation by giving students multiple opportunities to experience the translation between graph, table, equation, and situation through a variety of tasks.

• Implement meaningful tasks that promote reasoning and problem solving by putting students in situations where they must use multiple representations of functions to solve problems.

• Facilitate meaningful mathematical discourse by exposing students to a variety of tables that may or may not have x values(input values)  that increase by one or change by a constant amount, and allowing them to reach an understanding of the data.

• Elicit and use evidence of student thinking by requiring students to not only solve problems involving functions, but to justify their solutions and represent them in a variety of ways.

   

Key Understandings

Misconceptions

• Recognize linear relationships as they are expressed in a variety of formats;

• Given one form of a linear function, such as a table, verbal description, equation, or graph, be able to transfer to any other form;

• Students should be able to connect the sequence to the function that represents the sequence.

• 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 calculating slope from a graph, students sometimes will not pay attention to the "direction" of the rise or the run which will sometimes cause the sign of the slope to be incorrect.

• When given a table that doesn't have consecutive x-values, students sometimes will calculate the slope incorrectly. They will only pay attention to the change in y.

• Students sometimes jump to conclusions and try to determine the pattern of the sequence by just looking at the first two terms.