This linear graphing lesson introduces students to initial values, rates, and slope-intercept form. It is designed to interest students and use knowledge that students already have. Through it, students will explore and discover how stories, graphing, and equations all relate.
In this activity:
First, students are given 3 stories about current pop stars to get them engaged and keep the lesson fun. The stories are straightforward. Students create graphs based on the stories.
Next, the stories are changed slightly (to include a new "initial value"). Students draw new graphs to illustrate the new story.
Then, through a series of questions, students compare the graphs. The questions provided are great for class discussions on topics of initial value, rate of change, and slope-intercept form.
Finally, students create their own stories, graphs, and equations.
Great to use as a partner activity!
Many students (in my experience) know how to interpret a basic graph. Use this knowledge and build on it. If they can relate a real world story to a graph and then to y=mx+b, they will have a better understanding of this concept. I created this lesson after seeing issues with relating graphs and equations. I have made the mistake of bogging kids down in the formula-mathy stuff. This activity relates all the math back to real world events!
In this download, you will receive in PDF format:
4 pages of student handouts
Common Core Standards:
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
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