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K12MATH009: Algebra I

Unit 4: Data   Suppose you belong to a gym that has posters displayed to help members focus on reaching their peak heart rate during workouts. Age is given in years, and peak heart rate is in beats per minute (BPM). This would make it very easy to determine what your peak heart rate should be if your age is listed. However, if your age is not listed, a data display or a line of best fit would be beneficial in determining this information.
 
This unit addresses data displays and fitting lines to data.

Unit 4 Time Advisory
Completing this unit should take you approximately 3.25 hours.

☐    Subunit 4.1: 1.25 hours

☐    Subunit 4.2: 1 hour

☐    Subunit 4.3: 1 hour
 

☐    Subunit 4.3.1: 15 minutes
 

☐    Subunit 4.3.2: 45 minutes

Unit4 Learning Outcomes
Upon successful completion of this unit, you will be able to:
- distinguish between correlation and causation. - compute using technology the correlation coefficient. - fit a function to data.

Standards Addressed (Common Core):
- CCSS.Math.Content.HSS-ID.A.3 - CCSS.Math.Content.HSS-ID.B.6 - CCSS.Math.Content.HSS-ID.B.6b - CCSS.Math.Content.HSS-ID.C.7 - CCSS.Math.Content.HSS-ID.C.8 - CCSS.Math.Content.HSS-ID.C.9 - CCSS.Math.Content.HSA-CED.A.2 - CCSS.Math.Content.HSA-REI.D.10 - CCSS.Math.Content.HSF-IF.B.6 - CCSS.Math.Content.HSF-LE.B.5

4.1 Scatter Plots and Correlation   Data is all around us. We see it on the television and in the papers. It is used in a variety of situations. One way to display data is through a scatter plot. In subunit 4.1, you will learn what a scatter plot is and what the possible relationships are among the given data.

  • Activity: Georgia Virtual Learning’s “Scatter Plots” Link: Georgia Virtual Learning’s “Scatter Plots” (HTML)
     
    Instructions: Please click on the link above and then click on tab 8 and read the article and view the examples. Toward the end of this site, there is an icon that says “Quiz Group.” Click on that and a self-quiz will pop up on the screen. When complete, there is a “Check Answers” button and the quiz will be scored. The correct answers will be given and you can also hit the “Retry” button to take the quiz again.
     
    Completing this activity should take approximately 15 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Explanation: Sophia’s “Scatter Plots” Link: Sophia’s “Scatter Plots” (Flash)

    Instructions: Watch the “Scatter Plots” tutorial, pausing to take notes as needed.
     
    Watching the video should take approximately 5 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Checkpoint: Better Lesson’s “Scatter Plots and Correlation” Link: Better Lesson’s “Scatter Plots and Correlation” (HTML)
     
    Instructions: After watching the previous video, complete the guided practice on the worksheet. Watch the video again if you need to.
     
    Completing the guided practice should take approximately 25 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Explanation: NASA.gov’s “Space Shuttle Ascent: Mass vs. Time” Link: NASA.gov’s “Space Shuttle Ascent: Mass vs. Time” (PDF)
     
    Instructions: Read the Background, Instructional Objectives, and complete exercise number 7 in the Regression Equations section, making sure to pay attention to table above it (Table 3: STS-125 Atlantis Ascent data (total mass) ) and the description of the problem.  
     
    Reading these sections and completing exercise 7 should take approximately 30 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.2 Line of Best Fit   Since a scatter plot is not exactly linear, a line of best fit has to be drawn. What line would best model the data? Depending upon the data, sometimes the line is a good fit and sometimes it is a bad fit. In subunit 4.2, you will use the graphing utility to determine the line of best fit.

  • Explanation: Sophia’s “Line of Best Fit” and College of the Redwoods’ “Line of Best Fit” Link: Sophia’s “Line of Best Fit” (Flash) and College of the Redwoods’ “Linear Functions” (PDF)
     
    Instructions: Watch the “Line of Best Fit” Tutorial and Read Section 3.5 of College of the Redwoods’ Algebra Text (p. 313-319), and choose one of the exercises on page 321-325 to solve manually, and using your calculator. Check your answer on pg. 326-7.
     
    Watching the tutorial should take approximately 5 minutes. Reading the section should take approximately 40 minutes. Working through the exercise and checking your answer should take approximately 15 minutes.
     
    Standards Addressed (Common Core):

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

4.3 Residuals   At the fair, you can always find the game where a person guesses your weight. Usually the guess is not accurate. How far off the actual weight is from the prediction is part of the residual concept. In this unit, you will explore the concept of residuals.

4.3.1 Graphic Display of Residuals   - Explanation: LawrenceAcademy Math’s “What is a Residual” Link: LawrenceAcademy Math’s “What is a Residual” (YouTube)
 
Instructions: Please click on the link above watch the video, pausing to take notes.
 
Watching this video and pausing to take notes should take approximately 15 minutes.
 
Standards Addressed (Common Core):

-   [CCSS.Math.Content.HSS-ID.B.6b](http://www.corestandards.org/Math/Content/HSS/ID/B/6/b)
-   [CCSS.Math.Content.HSS-ID.C.9](http://www.corestandards.org/Math/Content/HSS/ID/C/9)

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.

4.3.2 Recognizing Patterns in Residual Plots   - Explanation: Sophia’s “Residuals” and Better Lesson’s “Modeling Using Residuals” Link: Sophia’s “Residuals” (Flash) and Better Lesson’s “Modeling Using Residuals” (PDF)
 
Instructions: Watch “Residuals” and take notes. Read carefully through the activity and try one of the exercises on your own.
 
Watching the tutorial and taking notes should take approximately 25 minutes. Reading through the activity and trying the exercise should take approximately 20 minutes.
 
Standards Addressed (Common Core):

-   [CCSS.Math.Content.HSS-ID.B.6b](http://www.corestandards.org/Math/Content/HSS/ID/B/6/b)
-   [CCSS.Math.Content.HSS-ID.C.9](http://www.corestandards.org/Math/Content/HSS/ID/C/9)

Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.