Today's lesson is another transitional lesson as I try to introduce a new unit ("Objects in Motion") and allow time for students to prep for a summative evaluation on the previous unit ("Electromagnetics"). The Objects in Motion lessons constitute a long progression towards the HS-PS2-1 Performance Expectation:
|Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.|
To successfully address this expectation, students naturally need to be conversant with concepts like position, velocity, and acceleration.
I begin today's lesson by sharing an image of the double slit experiment, familiar to my students from their recent Four Big Ideas investigation. The mathematics that is associated with this experiment is a bit challenging and, though each team wrestled with it during the investigation, it's not clear that every single student truly invested in that exercise. As it is featured in the electromagnetics mock quiz (and, therefore, quite possibly on the actual quiz) I want my students to look closely at a problem of this type.
The hardest part of this kind of problem is keeping a sense of clarity about the physical meaning of the variables. To help assist with that today, I provide the image as a way to decode the problem properly. I warn students that, while they'll have the equations on the quiz, the image will not be available to them. After reviewing the variables, I ask my students to try question #7 from the mock quiz.
Students take about ten minutes to work on the problem either on their own or in small collaborative groups. I circulate around the room and provide assistance or affirmation. For students who are moving quickly on this problem, I suggest looking at question #8 which is a related question. When most students seem done with their work, I take a few minutes to provide a solution at the Smartboard.
I provide a segment of time where students can continue to consider the questions on the mock quiz. I feel that, having tackled perhaps the most challenging question on the electromagnetics mock quiz, it is wise to allow time to explore some of the more familiar questions as reassurance. I addition, as this is one of very few tests of this year, I want my students to be fully supported. Finally, and as an example of the support I wish to provide, I can alert my students to the fact that, though they have access to a set of solutions for the mock quiz, the solutions document is a bit incomplete. The first question asks students to sketch waves based on their equations for which I have not shown solutions in the electronic document. With that in mind, I ask students to come to the board to show some solutions to those problems. Here you can see two students providing that service for their classmates:
Their efforts are available here.
During this block of time, students are free to work on whichever questions they would like and may work by themselves or with others. After about 25 minutes, I ask students to store their papers and turn their attention to the board for a group discussion that will launch our new unit.
As students finish their in-class preparation for the upcoming test, I inform them that we are starting a new unit of Physics and to start a new section in their notebooks. We being our study of "Objects in Motion" with an on-line simulation. Though there are many simulations to choose from, I use an Explorelearning Gizmo to get students to think about the relationship between runners and their position versus time profiles. The first image I share is simple and provides us an opportunity to look closely at the axes and think about the meaning of the graph. I ask students to make any observations they can about this graph and then run the simulation to check our intuition.
Students naturally begin to develop their own questions. For example, one common question is whether or not the runner can go backwards. I show the following image which allows me the chance to underscore the physical meaning of the slope in these graphs. This is, of course, the critical insight that students need to make in this unit: the slope of a position versus time graph provides the velocity of an object. A similar statement will be made soon regarding the relationship between velocity and acceleration.
I continue to explore student thinking using this simulator by posing different challenges. I ask, for example, "Can you design a profile that has the runner going backwards twice and winding up 10 meters short of the finish line?" Students come to the board to manipulate the profile and we check for accuracy. At some point, to enrich the scenarios, I show students that it's possible to have two runners square off in a race.
Here, a student is at the board trying to implement the following challenge: the blue runner needs to win the race despite going backwards twice during the event.
This mode of instruction continues until there are about five minutes left in class. At that time, I ask my student to reflect on this activity with a short writing exercise.
In the final few minutes of class, I want to give students a chance to consolidate their learning and provide me with a bit of formative assessment. I ask students to do a "3-2-1" writing exercise on a small piece of paper.
This simple exercise gives me a lot of information and allows students the chance to distill their learning in a short amount of time. I collect these papers before the end of class.
Here are some sample responses. The questions and comments range in interest and complexity. The one theme, seen here in part but evident in the larger set of responses, is that "direction" will be an important aspect of our study. I think that's a good takeaway message as it captures the essence of the vector quantities that are the core of this unit.