Reflection: Connection to Prior Knowledge Describing Scatterplots - Section 4: Closing Discussion and Assignment

The applied nature of statistics makes it an excellent content area to expand students’ knowledge of graphs and equations. I find that my students have had a fairly good introduction to writing equations of lines in Algebra 1. Even if they are rusty today, after a skill refresher they can usually calculate slope and either use slope-intercept or point-slope formulas to write an equation of a line. They may not, however, have had such a solid foundation of the meaning of these graphs. Now, after having studied many other function types and numerous application models all year, is a good time to remind them that:

• Ordered pairs always have the form (independent variable, dependent variable), commonly (x, y), and in the case of applications are packed with information about two things in relation to one another.

• The y-intercept is the resulting output when the input is zero. In many applications, this is the ‘starting value’ or at least a value that supplies important information.

• The x-intercept is the value required to give an output of zero. It is just as important as the y-intercept.

• The slope and the rate of change are the same thing. The rate is always “change of dependent variable” compared to “change of independent variable.” In an application, the rate can be described in the same units as the variables (eg. miles/hour for a graph showing distance in miles on the vertical axis and time in hours on the horizontal).

• Changing a fractional slope to a decimal is the same as converting a regular rate to a unit rate. In other words, if m=⅗ we could say that’s a rate of 3 miles per every 5 hours or a rate of 0.6 miles per hour.

Interpreting Graphs
Connection to Prior Knowledge: Interpreting Graphs

Describing Scatterplots

Unit 7: Statistics: Two Variables
Lesson 3 of 4

Big Idea: The appearance of a scatter plot can tell us a lot about the relationship between the variables on the axes.

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Standards:
Subject(s):
Math, Statistics, Linear and Nonlinear Equations, bivariate data, residual plots, Line of Best Fit, correlation, Algebra 2, Linear Regression, Residuals
85 minutes

Colleen Werner

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