Dimensional Analysis is one of the most common stumbling blocks for high school students in physics science. In this lesson I give students an opportunity to interact with a tutorial that demonstrates two methods to address metric conversions: the metric ladder and the general formula for conversions. I also explain that scientists use multiple methods to address the same problem based on the constraints of a specific task.
At the beginning of each lesson, I have a quick Bell ringer Activity to get students focused on the tasks for today's lesson. There is a slide with the date, the objective and an additional prompt projected on the interactive whiteboard with a red label that says "COPY THIS" in the top left hand corner. Sometimes the additional prompt is a BIG IDEA for the lesson, or the Quote of the Day or a Quick Fact from current events that is related to the lesson. The red label helps my students easily interact with the information as soon as they enter the room and avoids losing transition time as students enter the classroom.
The BIG IDEA for today is that metric conversions are convenient because they use powers of ten. I choose this type of starter activity because it is aligned to positive habits of work and mind. The BIG IDEA helps students to make connections between the properties of powers of ten they have learned in mathematics and the metric conversions they leverage in physics class. I am concerned with the level of ownership that students take over their learning outcomes, and believe that students should have access to the enduring understandings within a unit of lessons.
Within this lesson, I introduce two methods for metric conversions. I have included a set of notes that I lead at the interactive whiteboard in the front of the room for this section below. This part of the lesson focuses on using powers of ten to convert from one unit to another. For the first ten minutes, I play the notes at the front of the room on the interactive whiteboard for the entire class and pause at the pause points described here.
During the first ten minutes students take notes in their notebooks. I ask students if they have any questions or concerns about the methods discussed in the video and have a whole class discussion for 2-4 minutes. During the last minute of this section of the lesson, I email these notes to the entire class so that students can watch, pause and replay these notes at their desired speed outside of class. During the next section, students will be given a set of practice problems to complete in pairs.
For the first five minutes of this section, I lead an Example Problem related to metric conversions on the interactive whiteboard. I illicit student responses for each step in the problem then add annotations to explain each step in the solution. I then circulate the room while students copy the steps and the annotations into their notebooks. While I do so, I ask students to make connections between the annotations of the solution steps and the method of their choice for completing the additional practice problems.
After 10 minutes have elapsed or I have circulated my entire classroom, whichever comes first, I ask the class if they can identify other units for physical quantities. For example, I ask them to describe distances; many students respond by saying that city blocks serve as a unit of measurement. We then talk about the limitations of the metric ladder for converting between city blocks and meters, which circles back to why scientists develop multiple ways to solve problems. In the case of converting between city blocks and meters, the general formula for conversions can be used for converting between metric units and non-metric units.
Making sure to tease out the idea that while metric units are more convenient because of how easy it is to manipulate powers of ten, many professional fields within the United States use English units that have to be converted when communicating to other scientists around the world.
In this section, I give students 25 minutes to complete the Station Work Practice Activity that gives them the opportunity to make connections to metric conversions and the English units from their everyday lives (MP4). I circulate and provide additional problems from the Metric Conversions Packet to give students at different levels of understanding the opportunity to practice both methods of metric conversions. I also have Quick Checks available in the extras bin at the front of my room for students who complete all of the problems provided during this activity before the 25 minutes have elapsed. I have shared two examples of student work here and here that show two of the ways that students are assessed during this lesson. To ensure that students have a basic structure for this activity, I ask that groups of students be no larger than four and that students remain on task during this activity because the choice of location and team make-up is entirely up to the students.
I want students to consider multiple viewpoints on topics within physics and to use the information they gather from their peers to broaden their understanding of a topic. I focus on collaboration and include a peer editing process within this unit to encourage students to use mathematical thinking and logic to make decisive claims. I want students to learn to ask themselves questions like, "Can I prove it?", "Who cares?" or "Who says so?" to extend their current understanding beyond standard questions.
While students are not necessarily asking these particular questions here in this lesson, I do ask them to seek out the significance of metric conversions and look at how we know what we claim to know about them. I do not want students to follow steps, box a solution and stop exploring alternative routes to attaining the same or similar results. Students instead ask their peers to explain how to move from one step in their solution to another, making certain that their logic is aligned to the mathematical reasoning I demoed in the guided video notes.(SP2)(MP3)
Students discuss their practice problems with their station partners and edit their peer's work using a Rubric. I keep these rubrics in an organizer drawer labeled "extras" in the front of the room. I typically distribute them while students are answering their practice problems, but I also allow resource managers to grab them from the front of the room. Students use the communication and representation rows of this rubric. They are quite familiar with this rubric because it spirals out for all of the courses in physical science that they take throughout their four years of high school.
I provide students with an Exit Slip with a set of writing prompts for a routine called compass points, where students are tasked with identifying key ideas, enduring understandings, challenges, puzzles and suggestions associated with today's topic. I chose this routine because it helps me to visualize the underlying challenges behind gaps in student understanding of conversions. I find that while conversions are taught much earlier in students' academic careers, conversions sometimes remain challenging to students regardless of proficiency level.
To wrap up the lesson, I remind students that I will return the exit slips and review the feedback from their exit slips at the beginning of our next class.