1. Introduction to Graphing Calculators Using Graphing Calculators to Describe Linear Motion in terms of Distance and Time University of Virginia Fall 2001

2. Participants/Authors University of Virginia: Student Albemarle Co. Middle School: Cooperating teacher Honors Math 6 Class

3. Module Goal Students will become more comfortable using technology to aid in learning mathematical concepts Module Objective  Students will learn the general properties of graphs and how to aid in describing distance vs. time relationships

4. Lesson 0: Introduction to Graphing Calculators (preliminary work) Objective: Students will learn how to use the following functions on the TI-83 graphing calculator: Entering and graphing equations Using table to analyze specific point on a graph Recognizing the meaning of MODE, FORMAT, and ZOOM settings in changing appearance of graph Activity: Informal manipulation of graphs. Students also learned what a sine graph looks like and applied settings to change appearance. Played on calculators for 2 lessons (plus additional work on using lists during “optional” lesson)

5. Lesson 1: Characteristics of Graphs Objective: Students will learn how coefficients affect the behavior/appearance of graphs Changing x-coefficients (slope) and constants (y-intercepts) Graphing linear, simple quadratics [and sine and cosine graphs] Activity: After working through a few equations together, students broke into groups complete exercises and discussion questionsexercises and discussion questions

6. Lesson 2: Review of Linear Equation Concepts (discussion) Objective: Students will be able to explain the concepts of slope and y-intercepts in terms of the x-coefficient and constant term in a linear equation y = m x + b Activity: Discussion to lead in to next lessons

7. Lesson 3: Linear Graphs as a Representation of Distance and Velocity vs. Time (discussion) Objective: Students will be able to describe the relationship between distance and time by observing a linear-type graph Observe and describe data collected by CBR unit What types of lines describe specific motions? (moving closer to, further away, or staying in one location in relation to CBR unit) Does the speed change when the line is straight? Activity: Discussion and demonstration of CBR unit to lead in to next lesson

8. Lesson 4: Distance Match Objective: Students will experiment with representing distance vs. time on the coordinate plane Learn to use CBR unit as a motion detector Learn to execute programs (applications associated with CBR and otherwise) Activity: CBR application programs have the ability to measure distance from the CBR unit and plot on the TI-83 calculator. Distance Match application allows students to observe real- time motion (as compared to linear-type graph generated by calculator) Students ran experiment in pairs with prompting from other students, using equipment themselves, completing guided questionaire and discussion questionsguided questionairediscussion questions

9. Lesson 5: Creating Scatter Plots and Introduction to Regression (supplementary) Objective: Students will learn to create scatter plots and do regressions using data entered into lists in calculator Will gain understanding of concept of regression (best fit line) and apply to different types of equations Will learn how to use linking function of calculator Extension of objective: Through experimenting with different types of regressions on the calculator, students can begin to identify different types of functions (quadratic, exponential, etc., …) Activity: Given sets of data collected with the CBR unit (representing different types of motion), Students entered each set of data into lists Created a scatter plot to show exact data “points” collected Performed regression and had calculator graph along side of scatter plot to investigate accuracy, predict future values completing guided questionnaireguided questionnaire

10. What the students were able to accomplish through this module Understanding of premises behind graphing functions Graphing linear equations by hand (making a table) Graphing by transforming the line y = x Applications of functions to real-life uses Change of variables to measurements (y = distance, x= time) Matching motion to graph Prediction of future measurements based on collected data Increased familiarity with the TI-83 graphing calculator Use of graphing utilities, CBR motion detector Use of application programs Use of linking function (to transfer data)

11. What the students were able to accomplish through this module (SOL technology and math correlations) C/T8.4: Processing, retrieval, transmission of electronic information (entire module) 6.21: Patterns in graphs 6.18: Analyze and interpret data in graph form 6.23: Use of tables to graph equations 7.21: Predict data behavior 8.13: Use information in graph to predict future data

12. How students were evaluated Classes led in discussion based format and through group learning projects during which students were observed and questioned for understanding of material Evaluation rubric provided for class teacher Evaluation rubric

13. What the teachers were able to accomplish through this module Exchange of ideas in using graphing calculators and CBR’s (or CBL’s) as a supplement to learning basic properties of linear (and other) graphs Discussion of CBR use versus CBL use (both types of probes for graphing calculators)

14. What the teachers were able to accomplish through this module Exchange of ideas in using graphing calculators and CBR’s (or CBL’s) as a supplement to learning basic properties of linear (and other) graphs Calculator use New methods of approaching the same type of problems (how to set up functions, programs on calculator) Applications to use with collections of data (regressions) Exposure to new resources related to use of graphing calculators in the math classroom Texas Instrument’s Educational Resources Homepage Getting Started with CBR, Texas Instruments ©1997 Getting Started with CBR Interpreting the Spread of AIDS in the US (Center for Technology and Teacher Education, Uva) Interpreting the Spread of AIDS in the US