Uniform Acceleration Calculations, Day #2
Lesson 6 of 14
Objective: Students will be able to use mathematical models (equations) developed from position vs. time and velocity vs. time graphs to solve problems.
The goal of this lesson is for students to solve problems using the mathematical models for uniform acceleration that they developed from graphical representations of accelerated motion. They also should be able to explain their thought process in solving these types of problems. I want students to have more practice with the models since we just developed them in the previous lesson. Students will be working with the models and completing problems using computational thinking throughout the worksheet and whiteboard discussion.
To start class, since the unit is about halfway complete and students have a quiz tomorrow, I ask students to take out and have a second look at their learning targets. I have them to look at the Unit 2 Learning Targets to prompt them to think about what will be on the quiz. I have students rate themselves on a scale of 1-4. I want students to recognize that the targets that they rate themselves the lowest on are the ones they should focus their study efforts on. In addition, this opportunity provides time for students to check to see what questions they still have before the quiz.
Worksheet #3 Work Time
After students take a second look at the learning targets, I ask them to spend about 15-20 minutes finishing up the problems on Worksheet #3 Uniform Acceleration Calculations that they started in the previous lesson. They should have finished through #3 for homework. I ask students to compare their answers for #1-3 with their group so that they know that they are properly applying and using the formulas. This is important for my students to see some success or to catch mistakes before they finish the worksheet.
When they are done discussing, 4 additional problems remain. As students are working to complete the worksheet, I walk around to make sure students are on track. I also observe any trends in mistakes that students are making. When I walk around, I carry WS #3 KEY to make sure the students are on track. The only questions I do not answer during this time are questions such "Am I right?" or "Does this look right to you?" I want them to ask their group members first and have them determine if they are correct or not during the whiteboard session instead of me telling them they are right or wrong. It is important that students check with each other as they are going along so that they can catch and mistakes that their group members make along the way and have a discussion about which way is correct and why.
Whiteboard Prep Time
After students have completed the worksheet, I ask them to come sign up for the problem they would like to present to the class. To do this, I put a list of problem numbers on the board and allow a table to sign up when all members have the entire worksheet completed. After students have chosen which number they will be whiteboarding, I remind them that they need to show all work. This includes the mathematical model they used and their answer with units. I also tell them that two people from each group need to speak when they present their answer. The other members will write the problem on the whiteboard. I give the groups 7-8 minutes to prepare for their presentations.
After students have prepared their whiteboards, I ask each group to present. One student explains their choice of equation and another to explain the process of solving and how they determined the units. When students are not presenting, they check their work with what is on the board and ask questions if they don't agree. I make sure that every group answers at least one question. About half the time students ask questions if they did not get the same answer. If no students have questions I will ask a question. If there are things that are incorrect on the board, I ask questions about the sections that are wrong. For example, in problem #5, the students made their answer positive because they knew time shouldn't be negative. Their sole mistake was that they subtracted initial minus final instead of the other way around (as seen below).
I do whiteboard session as an interactive way to go over the homework. Furthermore, students are required to explain their thought process in solving the problem so students can see the answers and how to do the problems if they do not understand. I really like that students get to help explain things to other students, instead of me explaining to the class. By this point in the semester, some students are asking questions if they didn't get the right answer. It is amazing to see other students answering those questions instead of students always looking at me for an answer.
End of Discussion Checkpoint
After the whiteboard session, I have students complete the End of Discussion Checkpoint #2 individually as a formative assessment to see how much they learned from doing the worksheet and participating in whiteboard session. I choose these two questions because each problem asks students to solve for a different variable. I want students to be able to solve for any variables and show their work with accurate answers and units. I give students about 5 minutes to answer these questions; I have them turn over the page on their desk when they are finished. We then, as a class, grade the problems so that students can see what they might want to review before the quiz. I ask students to walk me through how to do the problem until it looks like the Unit 2 EOD KEY. I choose to go over it in class so that students can see how they did on this formative assessment to help them decide what areas to look over before the quiz during the next class period. At the end of the grading session I do a Thumbs Up, Thumbs Down to see where students are at with these types of problems before the quiz.