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An Exploration of Direct Variation and Linear Regression

Published on 09/30/2005

Activity Overview

Learning Concepts

  • Review of Direct Variation
  • Properties of direct variations
  • Finding the constant of variations from data sets
  • Find missing values in data sets both numerically and algebraically
  • Graphing Equations of Direct Variation
  • Lines of Best Fit and Linear Regression with Meaningful Data Sets
  • Before the Activity

    Send the students DirectVariation.edc which contains a four question set that reviews the important characteristics of a direct variation and has students use pattern recognition skills to find the missing values using k.

    During the Activity

    1. Have students take measurements of their actual heights and kneel height. While students are taking measurements, start Activity Center and load DirectVari.act.
    Have students submit data via TI-Navigator™ 2.0 by logging in using NavNet and going to Activity Center. When the teacher starts the activity, the students will be prompted to send data in L1 and L2.
    Tell students to enter their height (in inches) in L1 and their kneel height (in inches) in L2. Points will appear on the graph screen as they send their data.
    If students make a mistake, they may reenter their data, until the activity is stopped. Note: Students will be able to enter more than one data point if desired. As an extention, students could be asked to collect data at home from three or four family members to make the data set larger and more varied.
    Stop the activity once all data has been collected.
    2. Load the activity settings, SpaghettiFit.act. This will put a 10 x 10 grid on the graph. Have the students use this grid view to determine the equation of a line using two points. Once students have their equations, have them submit their equations by starting the activity.
    This will allow the students to see how their line fit the data that they submitted earlier. This begs the question: Is the class data set a direct variation?
    3. Save the data list generated by the class. You can send the list to the students to perform a linear regression, either with file transfer or by sending the lists via activity center. The teacher will now review with students how to perform the steps for a linear regression to compare the actual regress line with their estimates for a line of best fit.

    After the Activity

    Follow-Up Force send to students L1, L2, and Crickets.edc. This is the students homework assignment. This LearningCheck document asks the students to work with a classic data set to perform a linear regression and interpret results, taking into account the context of a problem. Students will answer the questions at home, and the responses will be collected during the next class and reviewed.