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PA-A-1-3

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

PA.A.1.3 Identify a function as linear if it can be expressed in the form y=mx + b or if its graph is a straight line.

In a Nutshell

Students will be able to take sets of data and create graphs, recognizing that the rate of change is the same between any two points on the line. Also, students will be able to identify the slope and y-intercept of the data or line and write the slope-intercept equation that represents the data or line. As students find the slope-intercept equation, they will be able to produce additional data that corresponds to the original data and will be on the original line. Students will also be able to apply the knowledge of linear function to identify them when given a graph.

Student Actions	Teacher Actions
Develop Ability to Make Conjectures, Model and Generalize when given functions graphed on a coordinate plane, identify that linear functions produce straight lines. Develop Accurate and Procedural Understanding when identifying the parts of the equation y=mx+b and how each part is represented on a graphed line. Develop Accurate and Procedural Understanding when given graphed linear functions, derive the equation for the lines by substituting the slope in for m and the y-intercept in for b in the slope-intercept form equation of a line: y=mx+b. Develop Accurate and Procedural Understanding when evaluating an equation in slope-intercept form, creating a line by plotting the y-intercept, and using the slope to create other point on the line. Develop Mathematical Reasoning as students discuss and explore how the slope and y-intercept of the line plotted is the same as the original linear equation. Develop a Deep and Flexible Understanding by measuring the slope between multiple pairs of points on the line to verify that the slope is always the same because the rate of change for linear functions are always equivalent fractions.	Implement meaningful tasks that promote reason and understanding by providing activities where students identify graphs of function that produce lines and classify them as linear or nonlinear functions. Pose purposeful questions when students are looking at graphs of linear functions, have students develop ways of describing the lines. Build procedural fluency from conceptual understanding when introducing the slope-intercept form as an equation that is used to describe the line, when using slope and the y-intercept. Allow students to also explore lines that do not have a y-intercept (vertical lines). Ask purposeful questions to students on how each equation represents the line that it produces by examining the key concepts of slope and y-intercept. Build conceptual understanding by examining slope, have students find the slope between multiple pairs of points and discuss how and why one slope represents the entire line with context when applicable. Build procedural fluency from conceptual understanding by using a matching activity where students have to match linear equations with the corresponding data tables of points, slope, y-intercept, and graphs. With each match, students must provide justification of their choices.
Key Understandings	Misconceptions
A straight line is a function if it can be written in the form y=mx +b A straight line, that is graphed, is a function and can be written as y=mx+b m represents slope (rate of change) in the slope-intercept form of a linear equation b represents the y-intercept in the slope-intercept form of a linear equation.	Students may think that an equation is already in slope intercept when it is not in the exact format of y=mx+b ( Ex: 5x +50 = y) Students may confuse the slope and the y-intercept in the equation y=mx + b.