My goal for this lesson is for students to observe and develop a model for constant velocity motion using constant velocity carts that I call dune buggies. I start out the unit with a lab so that we can develop the graphical, written and mathematical models from a experience of constant velocity motion with the dune buggies. Students start out the lab by asking questions about a situation that they observe. Then they develop an investigation and produce a model from the data that they collect that we discuss as a class.
To start class, I tell them that we are going to do another paradigm lab to start the unit. In each unit in the AMTA Modeling Curriculum, the unit starts out with a lab that helps to define a model for the unit that is written, graphical, diagrammatical and mathematical. Each unit starts out with one of these labs to provide students with the background they need to solve problems and work through situations during the units.
I tell students that they need to make observations about the motion of a dune buggy. (The buggy is a motorized car that moves at a constant velocity.) I turn on the dune buggy and allow it to move across the table. I must make sure that it travels in a straight line! When the students have observed the motion for about 15-20 seconds, I ask them what observations they can make that are quantifiable or measurable. As a class, we come up with a list of measurable observations and the corresponding tools we would need to measure these observations. If no students mention it, I let the cart move again and ask them to observe the speed of the cart. Then I lead them to see that it moves at a constant speed (that is, that it travels equal distances in equal time intervals).
Once all of the measurable observations that the students come up with are listed, I start going through each observation and cross out any that appear unreasonable to students. I ask students if we have the appropriate tools to directly measure the variables they put on the board. By the end of the discussion we should be focused on two variables: position and time. If my students don't come up with position, which they usually don't, I tell them there are two other things we talk about related to distance that are more accurate: position and displacement. I tell them to be the most accurate for this experiment we only look at the position of the object.
When we decide that position and time are the variables, I then ask my students which should be the independent variable and which should be the dependent variable. They should come up with time as the independent variable and position as the dependent variable. In this lab, either measurement could be independent, but since in physics the convention on position vs. time graphs is to have time on the x-axis, I want to follow that.
After the pre-lab discussion where we have decided on the independent variable (time) and dependent variable (position), I ask them what tools they need to complete the lab. The class comes to the conclusion that each group needs a dune buddy, meter sticks and a stopwatch, which I provide for them. I remind them that the goal for this lab is to find out more quantitative information about the motion of the dune buggy.
In this lab, I assign students by the numbers on their tables (seat #1-4 at each table) to have jobs during the lab. The jobs are: (1) Buggy Controller (2) Data Collector (3) Time Reader and (4) Data Recorder. The Buggy Controller is in charge of starting the Buggy at the beginning of each trial in the same location each time. The Data Collector walk alongside the buggy and records the position at each designated instant of time. The Time Reader states the pre-designated time intervals so the Data Collector knows when to record data. The Data Recorder is in charge of inputting data into a Plotly data table.
Before students start the lab, I tell them to make sure to collect at least 6 data points per trial, which requires them to have 6 pre-designated time instances. I prompt students to choose their time intervals that they would like to record whether it is 0.5 seconds or 1 second or even 2 seconds. I ask the Data Recorder to open to Plotly on their chromebook and enter the points that their group have chose. After they have chose their times (independent variable), I tell them that it is important to average our dependent variable (position) data instead of taking just one trial. So instead of just 1 trial, students should average the results from 3 trials. When they graph I ask them to plot the time and average of the position at time instance. The last thing I mention to students is that they must choose a starting position. I try to have groups choose different starting points other than 0 meters so that we can identify the y-intercept as initial position later on. Once I tell students these things I allow them to choose any point in the room or hallway to set up with their dune buggy and meter tape.
When students are completed with their data collection, I have them create a graph of their data in Plotly. Similar to the first lab in this class, I have students complete the Lab Summary as a group prior to the whiteboard session so they have all of the information submitted to me as a group before the students discuss it as a class. The lab summary includes their mathematical, graphical and written representation of their data. I do the lab summary so students have a chance to analyze their data prior to the whiteboard session. I like for students to have everything they need with respect to the data during the whiteboard session so I have them complete the lab summary first. Here is a Student Copy of the Dune Buggy Lab.
I give students time to create their whiteboard that they are presenting to the class. Each group should have their own graphs and mathematical models on their whiteboards. Since they completed the data collection and lab summary, they should be able to put together the graph and mathematical model pretty quickly as a group. Students should include the graph sketch and the equation with substituted variables:
Position = (slope in m/s)(time) + (y-intercept in m)
As students are working on their whiteboards, I walk around to gain insight into what questions I will need to focus on during the whiteboard discussion session. For example, if many students have incorrect units, I know I need to ask a question about how they determined units for slope and y-intercept.
When students are done creating their summary on the whiteboard, I have them sit in a circle with all of their whiteboards facing the center of the room (so all groups can see). Then I go through leading a discussion about the experiment. I ask the questions to the whole class and students raise their hands to answer. A number of questions ask them to look at the graphs of the entire class before saying an answer. If my students are not supplying answers, I may ask them to tell a partner what they think about that question. When I have them share out then I will ask them to tell me what their partner said. I try to get each group to participate in some way by answering questions.
Questions to lead the discussion:
- Experimental Procedure- I ask students these questions to refer back to where we started and to give the discussion some context.
What was your independent variable? Dependent variable?
What does it mean that we controlled variables?
How did you control your variables?
How do you know if you collected enough data?
- Graph Analysis Questions-When I ask these questions, I ask students to look at many groups data and compare it to their own data before answering the questions.
What do we see in common with all of our graphs? (focus on axis labels, units, variables in the right place, etc.)
What does the straight-line graph tell you about the car’s motion?
What does the slope mean in terms of this experiment? (For every statement…)
Why do different groups have different values for their slopes?
What would a larger slope look like if it were added to your board?
What does the y-intercept mean in terms of the car’s motion?
For homework, I have my students watch a video that I put together about the multiple representations of motion. I have them watch this so they have a first exposure to hearing the language and seeing the images that they will be looking at throughout the unit with Position-Time graphs, Velocity-Time graphs and Motion Maps. I want them to be able to participate in mini-lesson the next day so it is more of a discussion between the students and I instead of a lecture.