Analyzing Bivariate Data

5 min

Narrative

The purpose of this Warm-up is for students to interpret the rate of change of a function to describe a trend (MP2). It is used to help students recall the role of slope in showing associations for data that can be fit with a linear model in anticipation of looking for associations in this lesson.

Launch

Give students 2 minutes of quiet work time followed by a whole-class discussion. Remind students that the phrase “rate of change” is the interpretation of the slope of a line for the situation

Student Task

A researcher found an association between a dog’s stride length and its speed: the longer a dog’s steps, the faster it goes. The predicted speed in meters per second, ss, as a function of step length in meters, ll, is

s=4l−1.6\displaystyle s = 4l-1.6

What does the rate of change of the function tell you about the association between stride length and speed?

Sample Response

For every 1 meter increase in a dog's step length, its speed increases by 4 meters per second.

Synthesis

Ask students to share what the rate of change of this function tells them about the trend. Record and display their responses for all to see. To include more students in the conversation, consider asking some of the following questions:

  • “Does anyone agree or disagree with this reasoning? Why?”
  • “Did anyone reason about the rate of change in a different way?”
  • “Did anyone reason about the rate of change in the same way but would describe the trend differently?”
  • “Does anyone want to add on to ‾\underline{\hspace{.5in}}’s reasoning?”
Standards
Building Toward
  • 8.SP.3·Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. <em>For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.</em>
  • 8.SP.A.3·Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. <span>For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.</span>

15 min

15 min