Throughout this unit students have learned the fundamentals of rotational motion, including angular kinematics, centripetal acceleration, and Kepler's laws (HS-PS2-4). Today the goal is for students to apply that knowledge in preparation for a unit exam. The lesson starts with a delayed warm-up before students collaboratively solve problems (SP5). Students then share their solutions (SP6 & SP8), and we close by returning to the warm-up that started our lesson.
When students walk into the classroom I have a warm-up projected for them on the front board. As soon as our bell rings, I read the problem aloud and then give students time to try and solve it. My reading the problem reinforces that class has started and gets any straggling students focused. I allow collaboration during the work time, since I think it's important that students get to talk through their thought processes. It is also an expectation that students show these thought processes (even if they use a calculator) with written work in their science notebooks. They will return to their ideas later in the lesson.
I walk around during this time to informally assess student's work and conversations, but I do not tell a student if their answer is right or wrong. We will review the solution as our closure and I want students to get comfortable with not having immediate feedback. It's my goal that this delayed feedback forces students to double check their answers or possibly amend their answers during class.
I choose this problem because it grabs students attention with the reference to a black hole. The problem also goes back to one of the first topics we covered in this unit: the relationship between linear and rotational motion. In recent lessons, we've been focusing on planetary motion, but students need to remember those concepts we covered earlier in our unit on rotational motion. Now that students have had this content refresher, they are ready to move into actively solving review problems in small groups.
Today's class uses my collaborative solution & teaching Strategy as way for students to review rotational motion. Students are each given a different problem from a rotational motion practice test. These problems are problems that I feel are most representative of the test questions and offer students a good opportunity to review all of the concepts learned throughout this unit. To save time, students stay at their lab tables and I give each group one or two (depending on the difficulty) of the problems with its answer. Students always get excited when they see that the answer is given, but my goal in this activity is to see how students arrive at that answer. The majority of possible points on the free response portion of an AP exam comes from justification of the answer, so that justification process is the emphasis of our activity today.
The problem(s) that each group receives is random: I literally walk down the center aisle and give the group whichever problem is on the top stack of my pile. My expectation is that students take about 10 minutes and actively work together to write down the solution on the paper I pass out to them. Without giving the students too many details, I tell them to be prepared to not only show, but also explain, their solutions. Also, I encourage students to use pen as they work. Using pen keeps them from erasing, so even if they make a mistake or change their thinking I can see evidence of their entire process.
As students are working at their lab tables, I walk around and ensure that everyone is engaged in the discussion and thinking critically about their assigned problem. I am willing to give students hints as I observe, but my feeling is that by this point in the rotational motion unit students should be able to independently work through these problems.
After the collaborative work time is over, I share with students that they are presenting their solutions to the rest of the class. Each group comes forward, puts their problem with the solution under the document camera, and explains that solution to the rest of the class. The goal of this activity is to show students the variety of problems that are on the rotational motion test.
Because my students are sometimes shy, I ask for a group to volunteer to go first. There is always at least one group that wants to get the presentation out of the way, so I choose them and applaud them for being so willing. These first group of students walk to the front of the room and place the problem with their solution under the document camera. One person from the group reads the problem aloud so the entire class becomes familiar with that problem. A second student explains any drawn diagrams and the list of given information. Finally, a third student from the group verbalizes the solution written on the paper. Once the solution is appropriately provided, I ask the class if they have any questions for the group. If someone from the class does need to ask a clarifying question, or if I need to ask a clarifying question throughout the solution sharing, I expect that group members who haven't yet participated to answer these questions.
Once that first group is finished, they pick which group shares next. This group comes forward with their problem and solution, shares, and appropriately answers questions as the last group did. The process repeats itself until all problems have been shared. If students pay attention and take good notes throughout this activity, they now have a great study resource of new questions with solutions.
It's now time for me to relieve the students' curiosity and share the answer to our warm-up. They should still have their work from the warm-up activity out on their desks, with the goal being that they compare their individual solutions to my solution. I show students that we are given a radius and angular speed, and our goal is to solve for tangential speed. Students must remember that the angular speed needs to be converted from revolutions per second into radians per second. Because we just went through practice problems that included this conversion, I wait to move on until someone contributes the method for making this type of conversion.
As soon as the class contributes the conversion method, I share the rest of the solution. We don't have much time so I get right to the "meat" of the solution. The point of my direct explanation is to leave time for students to ask questions. Because there is a unit test during the next class meeting, I don't collect the students' work. My hope is that they can use this practice problem as an additional study resource.