Innovation for 21st Century Teaching & Learning Partnership

Graphing Motion*

Teacher Version(.doc)

Student Version(.doc)

• Grade Level(s):  6th, 7th, and 8th
• Primary Focus: Science; NC Standard Course of Study Areas: 7th: 6.03, 6.05
  • (Key Concepts: Distance vs. Time graph, velocity, and velocity vs. time graph)
• Secondary Focus: Math; NC Standard Course of Study Areas: 6th: 1.07, 2.01, 5.04; 7th: 1.03, 4.01; 8th: 1.02, 4.01; Algebra: 4.01
  • (Key Concepts: Rate, Rate of Change, Scale and Linear)
• Technology Focus Areas: Calculators, Probeware, Data Visualization; NC Standard Course of Study Areas: 6th: 3.01, 3.03, 3.06; 7th: 1.10, 3.01, 3.02; 8th: 2.06, 3.01
• Essential Question: Why do most roller coaster tracks start out with a big hill?  Why might one coaster with the same height hill as another coasters be faster or slower?
• Summary of Activity:  Working in groups of two, three, or four, students will record their own motion using the motion detector to create distance vs. time and velocity vs. time graphs first free form and then attempt to match their motion with randomly generated graphs.
• Cognitive Teaching Strategies:  Velocity graphs are often non-intuitive for students because the shape of the graph does not resemble the path of the object.  Work with students to help them gain this understanding and how the rate of change in the velocity relates to the increases and decreases of the graph.  Also work with students to help them understand the relationship between a position graph and a velocity graph.  In other words, given a position graph, what would the resulting velocity graph look like?  Helping students gain an intuitive feel for these concepts will help them understand the more formal Calculus when presented later in the high school curriculum.
• Materials:
  • Go! Motion Detectors (1 per group)
  • TI graphing calculator (1 per group)
  • GM-CALC cables(1 per group)
  • Document camera
  • Masking tape
  • Meter stick
  • Graph paper
  • Stopwatch (or try the Shodor Online Stopwatch)
  

Part I: Distance vs. Time Graphs

1. Fasten the Go! Motion detector to a tabletop facing an area free of furniture and other objects. The motion detector should be at a height of about 15 cm above waist level.
2. Use short strips of masking tape on the floor to mark the 1 m, 2 m, 3 m, and 4 m distances from the motion detector.
3. Plug in the cable to the calculator and the motion detector. Firmly press in the cable ends. Ensure the sensitivity switch is set towards the person / ball icon.
4. Have students turn on the calculator and press the APPS key. Scroll to the Easy Data application and press.
5. If students have not yet used the application explain the settings and how to change the sample interval size, total number of samples and experiment length.  (You may wish to point out how the three of these are related).  For the first experiment have students set the sample interval to 0.05, the number of samples to 200.  (Note this automatically changes the experiment length to 10).  For more information on using Easy Data, refer to the Easy Data Instructions.
6. Explore making distance vs. time graphs.  Put students in groups of 2, 3, or 4 depending on space and number of calculators / motion detectors available.  Explain the procedure to the students by modeling an example.
7. Stand at the 1.0 m mark, facing away from the motion detector.
8. Signal your partner to select START.
9. Slowly walk to the 2.5 m mark and stop.
10. Sketch your graph on graph paper and be sure to include the scale and axis labels.  You may need to use the ANALYZE->Statistics option in order to find the min and max values on the graph.
11. Write a few sentences that describe the motion of the person walking corresponding to the graph.
12. Repeat Step 6 at least two more times but using different paces both slowing down and speeding up during the walk to the detector.  Be sure each time to copy the graph on paper then writing a description.
13. After each group has copied several graphs on paper call groups up to share their graphs and descriptions with the rest of the class using the document camera.

Part II: Matching Distance vs. Time Graphs

1. Have each group sketch at least one graph.  Remind them to label their axes.
2. On a separate piece of paper the group should write a description of their graph.
3. Swap the graphs (not the description) with another group and try to recreate the graph with the motion detector.  The group should also write a description of the motion.
4. Once the graph is completed the groups should compare their descriptions. 
5. As a class discuss how successful each of the groups were at both recreating the graph and the accuracy of the description.

Part III: Velocity vs. Time Graphs

1. Lead a discussion on velocity and its relationship to distance.  Draw a sample velocity vs. time graph and have students qualitatively describe the motion.
2. Explore making velocity vs. time graphs. 
   1. Take a starting position at the 1 m mark in front of the Motion Detector.
   2. Signal your partner to select START.
   3. Stand still for one second, and then walk to the 3 m mark (away from the Motion Detector) at constant velocity.
   4. Stand still for one second then walk backwards to the 1 m mark (toward the Motion Detector) at constant velocity.
   5. When data collection ends,use   and   to select VELOCITY from the SELECT GRAPH menu.
   6. Sketch your velocity vs. time graph on graph paper and be sure to include the scale and axis labels.  You may need to use the ANALYZE->Statistics option in order to find the min and max values on the graph.
   7. Write a few sentences that describe the motion of the person walking corresponding to the graph.
3. Repeat Step 2 at least two more times but using different paces both slowing down and speeding up during the walk to the detector.  Be sure each time to copy the graph on paper then writing a description.
4. After each group has copied several graphs on paper call groups up to share their graphs and descriptions with the rest of the class using the document camera.

Part IV: Matching Velocity vs. Time Graphs

1. Have each group sketch at least one graph.  Remind them to label their axes.
2. On a separate piece of paper the group should write a description of the motion of their graph.
3. Swap the graphs (not the description) with another group and try to recreate the graph with the motion detector.  The group should also write a description of the motion.
4. Once the graph is completed the groups should compare their descriptions. 
5. As a class discuss how successful each of the groups were at both recreating the graph and the accuracy of the description.

Instructional Strategies:

 The Easy Data program auto scales the graph to fit the data collected.  This can be confusing for students if they attempt to create a graph with little variation along the y-axis as the graph appear to have a good deal of variation due to the zoomed window size.  There are several ways you can deal with this situation:

• This can be a great opportunity to teach about scale!  Be sure students look at the scale of the graphs using the trace feature.
• Have them look at the data outside of the EasyData program by storing the data in the calculator’s lists and use the StatPlot function.
• Import the data into LoggerPro or another computer graphing program.
  

Additional Resources for this Lesson:

• The SimCalc Project out of the University of Massachusetts, Dartmouth has their own software freely available for use with the TI Calculators along with a variety of lesson plans to help middle school aged students grasp the concepts of distance and velocity graphs.
• Nova has a very good video entitled “Roller Coasters” that could be shown in conjunction with this lab.
• The Physics Classroom provides information and examples on motion and other physics concepts.  www.thephysicsclassroom.com

Re-teaching and Enrichment Strategies:

• Have students write a description of motion with position or velocity (or one of each) and swap the description with another group.  The other group should then try to create a graph matching that description.
• Have each group create a position graph using the motion detector and copy down the resulting graph.  Have them describe in writing what the same motion would look like as a velocity graph.

* Adapted from Brueningsen, C., Bower, B., Antinone, L., Kerner, E., Gastineau, J. E., & Cortez, W. (2005). Real World Math Made Easy: Explorations. Dallas, TX: Texas Instruments Inc. & Volz, D., & Sapatka, S. (2000). Middle School Science with Calculators. Beaverton, OR: Vernier Software & Technology.