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PA-A-1-2

Page history last edited by Tashe Harris 6 years, 2 months ago

PA.A.1.2 Use linear functions to represent and explain real-world and mathematical situations.

In a Nutshell

Students should be able to interpret a given scenario and write a linear equation that reflects the relationship. Once students produce their linear equation, students will be able to predict additional information that can be applied to the original problem. Students should be able to describe the rate of change of the linear relationship within the context of a given situation.

Student Actions	Teacher Actions
Develop Ability to Communicate Mathematically when writing a linear equation from a situation. Graph the equation and include a title, both axis labels, and describe the rate of change(slope) as the change in the y-values in relationship to the change in x-values. (Example: Time vs Words Read). Develop Strategies for Problem Solving when describing the graph of a line without a title or axis labels, and connecting a real life situation that the graph could be modeling. Title and label the graph and describe what the slope (rate of change) and y-intercept mean in context to the situation that you have created. Develop Ability to Make Conjectures, Model, and Generalize when Analyzing linear graphs to make predictions. Extend the graph and verify your accuracy	Use and Connect vocabulary understanding by continually referring to slope in context and pose purposeful questions using slope as the rate of change. This will allow the students to begin making that same connection that slope is rate of change. Implement meaningful tasks that promote reason and understanding by providing students with several real-world and mathematical situations to be turned into a linear functions. Pose purposeful questions that allow students to examine relationships between linear functions and their graphs in context.
Key Understandings	Misconceptions
Draw reasonable conclusions about a situation being modeled. Know what slope represents in context of the problem. Understand the y-intercept in context of the problem. Understand that slope is synonymous with rate of change.	Students may have a difficult time recognizing the y-intercept and the relation it has to the real-world context. Some students will not make the connection of the slope and what it is measuring in the context of the problem. For instance, if the graph is labeled wages on the y-axis and hours on the x-axis they may not connect that the slope is the wages per hour wages/hours.