Grade Level: 10

Subject: Coordinated Science
 

Learner Outcomes:

• Students will use the TI-83 graphing calculator to make agraph of X and Y data.
• Students will use the TI-83 graphing calculator to createa regression line, determine the regression equation, and determine theslope and y-intercept for the regression line.
• Students will use the regression equation and graphing calculatorto discover the relationship between the X and Y variables.
• Students will learn to how to convert from one temperaturescale to another by using a graph and regression equation instead of standardtemperature conversion equations.
• Students will learn the derivation of mathematical equationssuch as the temperature conversion equation.
• Students will develop problem-solving skills by determiningthe relationship between X and Y.

Materials: Pencil, Paper, and copyof the worksheet provided for the Internet site.
 
 

Technology Tools/Courseware: OneTI-83 graphing calculator per student
 
 

Teacher notes:

• Students should be familiar with the use of a TI-83 graphingcalculator.

• The worksheet should be printed out for each student.
• Only technical assistance for use of the calculator shouldbe provided. Students should be allowed to determine the relationship unaided,if possible.
• Students should work individually on the worksheet if enoughcalculators are available.
• Students should be cautioned to read carefully and followexactly the steps given in the worksheet.

Students will complete the following lesson. Part A mustbe completed before Part B. Print the following student handout and givea copy to each student or group.
 
 

_____CUT HERE_______________________________________________________________________

Record all data neatly on a separate sheet of paper.

 Part A

1. Press [MODE] and move the cursor to the left for allitems to return to the factory default settings. Press [2^nd],Y=], [4], [ENTER]. The screen will say Done. Press [Y=] and clear any equations.

2. Press [STAT], [1] and place the following data in lists 1and 2 (L1 and L2) of a TI-83 graphing calculator.

 

X	Y
-40	-40
75	167


 
3. Press [2nd] [Y=] to turn on Plot 1. Choose the scatter plot(the 1st Type). Be sure that the X-List is L₁, and the Y-Listis L₂. Press [ZOOM] and [9] to see the plot.
4. Determine the regression statistics for the graph that isformed. Record the regression statistics on a separate sheet ofpaper. Press [STAT], right arrow to CALC, and press [4]. Press [2^nd][1][,],[2^ND] [2] [,], [VARS], right arrow over to Y-VARS. Press[1], [1], [ENTER].
5. Press [GRAPH]. Use the [TRACE] key and the UP ARROW key tochoose the regression equation. Compare the values of X to the values ofY using the RIGHT and LEFT ARROW keys to analyze the regression line.
6. To find the corresponding value of Y if X = 37.0, use thearrow keys to come as close to the value as possible. Use [ZOOM] [2] and[ENTER]. Press [TRACE] and use the UP ARROW key to choose the regressionequation again. Repeat the process several times to get as close as possibleto 37.0. Be sure to reach the regression line each time by using theTRACE and UP ARROW keys. What is the corresponding value of Y whenX = 37.0?
7. Reset the calculator using [ZOOM] and [9]. With the calculatorin trace mode and on the regression equation, type 21.15 and press ENTER.What is the corresponding value of Y?
8. Type 37.0 and press [ENTER]. What is the corresponding Y-value?
9. Use the [WINDOW] menu to set Xmin = -40, Xmax = 150, andXscl = 1. Set Ymin = -40, Ymax = 3 10, and Yscl = 1. Press[GRAPH]. Withthe calculator in the trace mode and on the regression equation, type in100 for X and press [ENTER]. What is the corresponding Y-value?
10. From what was learned in steps 5-9, what do these two setsof data points represent? What is X? What is Y?
11.  Clear Lists 1 and 2 and the Y = equation. Enter thedata below in those lists:

12. Plot these data points and determine the regression statisticsfor the graph as in the previous example. (See step 4.) Record the regressionstatistics.
13. Press [GRAPH]. Use the [TRACE] key and the UP ARROW key tochoose the regression equation.
14. To find the corresponding value of Y when X = 310.15, usethe arrow keys to come as close as possible. Then press [ZOOM], [2], and[ENTER]. Remember that the [TRACE] and UP ARROW keys must be chosento reach the regression equation. Repeat the process to get closerto the value. What is the value for Y?
15. Use the[ WINDOW] key to set Xmin = 0, Xmax = 400, Xscl =1, Ymin = -460, Ymax = 270, and Yscl = 1. Press [GRAPH]. Choose [TRACE]and use the UP ARROW key to choose the regression equation. Type in 373.15for X and press [ENTER]. What is the corresponding Y-value?
16. Reset the calculator using [ZOOM], [9]. With the calculatorin trace mode and on the regression equation, type in 294.30 for X. Recordthe Y value.

17. Now type in 273.15 for X. What is the corresponding Y-value?
18. From what was learned from tracing the regression equationin steps 13-17, what do these two sets of data points represent? What isX? What is Y?
19. Describe an alternate method of converting between temperaturescales without the use of the standard formulas. (Be specific!)

Modifications:

• Seeing-impaired students worksheet should be printed on bluepaper.
• Exceptional children may require more time and possibly needa teacher’s aide for assistance during the activity (or paired with anotherstudent).
• Teacher may choose to use the LCD panel connection with thegraphing calculator to walk the students through the process.

Enrichment Activities: Studentwill be challenged to find two equivalent dates in the Gregorian and Jewishcalendars or the Gregorian and Chinese calendars, to plot the data, determinethe regression equation, and to convert ten random dates from one calendarto the other using the graph and regression equation.
 

Evaluation/Assessment:

• Teacher will closely observe and assess student proficiencyin use of the graphing calculator, following printed directions, and observing,theorizing, and drawing proper conclusions from data analysis.
• Teacher will grade the worksheet. Teacher will look for thecorrect regression data for each graph and the correct relationship betweeneach X and Y data set.

IGOs and other standards:

• Science Ten

• English Language Arts

• Applied Math I-II

          AM2.3, AM2.5, AM2.13, AM2.15, and AM2.16

• Algebra I-II

           A2.2, A2.21, A2.22

• Geometry and Applied Geometry

National Standards
 
 

Lesson 1

Lesson 2

Lesson 3

Lesson 4

Lesson 5