We are returning from our April break and need to double back and move forward. We had many absences just before the break, so many of the newest ideas need to be re-introduced, and even students who were here benefit from taking a step back for review. My goal for the day is to ensure that all students are introduced to the summaries of motion graphs before introducing our next investigation.
Today is the first day of a multi-day design task: students are challenged to create a situation where a given object accelerates at 1.00 m/sec2. This naturally involves iterations and adjustment made to equipment and measuring strategies and, as such, provides us with opportunities to practice several of the NGSS Science and Engineering Practices. Furthermore, the focus on acceleration as a key parameter of an object's motion moves us closer to achieving the NGSS Performance Expectation HS-PS2-1.
After a brief welcome back from our April break, I review the agenda for the day with students and alert them to the way in which today's work will influence their final exam grade: an investigation that we start later today will culminate in a report that comprises 30% of the final exam grade. My intention is to count scientific process in addition to scientific content knowledge as part of the final exam grade.
I then reveal a warmup problem on the board and have students consult their notes and one another to make traction on it. As we are returning from a break, I give a few extra minutes to this work, allowing students to re-familiarize themselves with our most recent work.
After about 10 minutes, I show a solution on the board and reiterate the primary content lesson: the slope of a position graph is the velocity of an object. Given the two tangent lines that are shown, students can create a simple velocity graph which leads to the determination of the acceleration by, once again, calculating a slope, this time of the velocity graph.
To determine depth of understanding, I ask two "What if ..." questions. First, I change the time to the peak position from 7 to 24 seconds and ask students to raise their hands if they know immediately how this change impacts the entire problem. Once I see 6-7 hands, I select a student to discuss the changes. In a similar fashion, I alter the initial velocity to see if students can articulate the implications for the position, velocity, and acceleration graphs. This gives me a good basis for the next segment of class where we consider the two cases of motion - constant velocity and constant acceleration.
In this segment of class, I want to ensure that all students have a summary of graphs that describe the two cases of motion we will explore in this unit - constant velocity and constant acceleration. I reveal the constant velocity graphs first and review the critical idea of slopes. then I reveal the constant acceleration case and spend a bit more time describing the relationship between the linear velocity graph and the resulting parabolic position graph. To conclude this work at the board, I ask two "What if . . . " questions, altering the velocity graph to check for understanding about he impact on the position graphs.
I thne share a short set of graphical motion practice problems on the SmartBoard. Students may work individually or collbaoratively. I check in with students to gain insight into their understanding and to provide targeted feedback or affirmation. As students begin to finish the problems, i ask some of them to share their work on the board:
Here's a student solution to problem #2:
I use the student solution (in red) as a starting point and add in the green tangent line as a way of reminding students how to indicate the initial velocity on the position graph.
Below is a student solution to problem #3. Again, my contribution is in green.
Before concluding this segment of class, I ask students to participate in a "fist-to-five" formative assessment. First I ask students to indicate how confident they are at establishing an acceleration, given velocity information. Most students show 4 or 5 fingers, an indication of high confidence. I then ask how confident they are at drawing a position graph, given velocity information. There is a greater variation in this response, with some "fists" indicating very little confidence and some "fives." We will, no doubt, return to this kind of activity in coming classes.
Before beginning our next lab challenge, I share a handout with my students that expresses the goals, the available tools, and the assessment of the final report. I spend the bulk of this ten minutes reviewing the goals, assuring students that there will be time for them to look more carefully at the assessment before their reports are due. From the handout, I focus on the following:
- To create an acceleration as close to 1.00 m/sec2 as possible.
- To gather enough data to know that your result is reliable.
- To produce an error bar that will identify the variation within your data.
- To collect and provide visual and mathematical evidence that is compelling
enough to convince others that these goals have been achieved.
In particular, I discuss the kind of evidence that demonstrates an acceleration. Despite the fact that we have just been discussing this, students do need reminding that getting the slope of a velocity graph is critical! Indeed, one major reason for pursuing this work is to provide students a hands-on experience with the ideas of position, velocity, and acceleration. Furthermore, as we near the end of the year, I want students to have a goal that involves multiple iterations - self-evaluating their progress and adjusting their approach to hone in on a desired result.
I alert students to the need for assembling into six groups, the maximum number of stations I can support with materials (a variety of carts, cars, ramps, and so forth). I allow students to organize into groups of their choosing, as long as everyone is in a group and there are no more than six groups. Students use motion detectors, used throughout this unit, that produce position and velocity graphs. These graphs are assessed by students to establish whether they have met the target or not.
Given the remaining time (about 25 minutes or thereabouts), I recognize that student teams will only get so far today. Indeed, I designed the timing of this lesson with the idea that the first 20-30 minutes of an exploration are often given over to figuring out how the equipment works, how to get reasonable data, and other logistics. I know we will return to this work in the next class and am willing to set aside some time today for those early issues to be worked out.
Here a set of four boys are working at one of the ramp stations, getting familiar with the motion detector.
These girls have moved out into the hallway to work out the issues with their ramp station.
These girls have collected some early data that seems promising.
These boys are working at a station with two masses connected via a string and a pulley. They are altering the ratio of the masses to hone in on the correct acceleration.
We continue in this mode until there are just a few minutes left. I ask students to return materials to the back bench for easy retrieval next class.