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PA-A-2-3

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

PA.A.2.3 Identify graphical properties of linear functions including slope and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

In a Nutshell

Extending the understanding of linear data, students will be able to find the rate of change between two points, given a graph, table of values or two ordered pairs. In addition to finding the rate of change and identifying it as the slope of a line, students will be able to determine the initial value of the relation as the y-intercept, when the x value is zero. Students will find that proportional relationships produce an output of zero when the input is zero, stating that the y-intercept of a proportional relationship is at y=0.

Student Actions	Teacher Actions
Develop a Deep and Conceptual Understanding when identifying the slope and y-intercepts of a linear function both graphically and written in slope-intercept form. Develop Ability to Make Conjectures, Model and Generalize by exploring input/output tables of proportional relationships and their equations. When 0 is the input, 0 is also the output in a data table. On a graph this is realized as the y-intercept is at the origin. The generalization is that the y-intercept of a proportional relationship is at y=0. Develop Accurate and Appropriate Procedural Fluency when analyzing the constant of proportionality (unit rate or slope) when given a proportional relationship. Develop a Deep and Conceptual Understanding of what slope means in the context of real life examples both graphically and in linear equations formats.	Use and connect mathematical representations by allowing for multiple methods of calculating slope both graphically and mathematically. Pose purposeful questions that allow students to view slope in a contextual problem as a rate of change between 2 variables; instead of, only a value that can be written as a fraction. Implement meaningful tasks that promote reasoning and problem solving by giving students ample examples of linear equations and their graphs to explore proportional vs non-proportional relationships. Allow students to look for patterns to discover why graphs are classified as either proportional or nonproportional.
Key Understandings	Misconceptions
Identify the slope and y-intercept of a linear function; Interpret the slope and y-intercept in the context of the given situation; Know how to calculate the constant of proportionality (unit rate or slope) given a proportional relationship; Be able to describe what makes a relationship proportional and identify them when given the data in a table, equation, or graph.	Students get confused about which value is the y-intercept in the sequence. 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 wrong.