# Moving into Motion Graphs

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## Objective

Students will be able to interpret, explain, and draw position, velocity and acceleration graphs.

#### Big Idea

How can students relate kinematics graphs with descriptions? Today, we use a simulation to connect the dots of position, velocity, and time!

## Whole-Class Introductory Activity

10 minutes

I often find that students have trouble understanding kinematics curves, even if they've been exposed to them via our mathematics curriculum. My fabulous AP students have a lot of experience with position v. time and velocity v. time graphs from their algebra courses, but I've still found that they struggle putting the concepts with the graphs. For example, if I ask students to draw the position v. time graph for an object moving with constant, positive velocity they do not have the ability to connect the words with the graphical representation.

So, as an introduction to today's activity I gauge my students' prior knowledge with a Prezi that asks them what they know about kinematics graphs. I choose to read the Prezi and limit the length of pair-sharing to allow students ample time for the main course of today's class:  the moving man simulation. I have the first slide of the presentation already loaded and displayed on a screen at the front of the room when the students walk in. The fact that they are immediately faced with the question of "What do you know about kinematics graphs?" gets them thinking before the bell has even rung.

After everyone is settled, I advance to the second slide and ask students to consider the information presented. I present this information and the students are passive at this point, so that the entire class has a clear understanding of what the moving man in our example is doing. Verbatim from the slide, I read that the man starts at the origin, moves backwards slowly and steadily for 6 seconds, stands still for 6 seconds, and then moves forwards twice as quickly (and still steadily) for 6 seconds. After I'm done reading, I encourage students to write down the times and relative speeds for each segment (on a scrap piece of paper or in a notebook) so they can use the information to choose graphs on the following slides.

After looking around the room and informally assessing that everyone has written down what our moving man is doing, I move on to show them slide 3. I do not say anything immediately after showing the slide and ensure that my students are all quiet and thinking individually. After they've had about 45 second to think on their own, I give them an additional minute to turn to their neighbor and discuss their thoughts. I direct this idea exchange by saying: "Ok, go ahead and talk to someone near you about which graph you think best represents our moving man. Once you've talked it over, go ahead and write down the letter of the graph that you think is the best representation of the man's change in position over time." I say this last part with emphasis so that students realize the type of graph they are looking at.

Again, after looking around the room and informally assessing that everyone is ready, I show the students the final slide. I do not say anything immediately after and have the same quiet expectations (described above) for approximately 45 seconds. Before I direct their second minute-long idea exchange, I say "Now, discuss as you just did and be sure to write down the letter of the graph that you believe best shows the man's change in velocity over time." I'm emphasizing the bold part again to ensure that students recognize the difference.

Finally, I reveal that the answers are graph B for position over time and graph F for velocity over time. I won't elaborate much on why those are the answers since I want students to investigate and explore "the why" during the next activity. I do, however, ask students to raise their hand if they got at least one of the graphs correct. Doing this quick assessment gives me an idea of my students' comfort levels with motion graphs.

## Moving Man Simulation Activity

30 minutes

Today's activity allows students to visualize motion and its correspondence to kinematics graphs while working with someone new. Before we start the activity, I assign partners using the Random Student Generator that already has my students' names loaded. Because this activity does not need to be completed outside of class, I feel comfortable in choosing the pairings for my students. And, if I display the random generator on the front board, there is an element of suspense as the partners are being assigned. Partners work best for this activity so that each student can be actively engaged throughout the work time. We use MacBook Pro's in my district, so my students are familiar with how the computer and cart organization works. After each pair has been assigned, the students move to sit near each other, push their desks together, and grab a computer.

As the computers are booting I pass out the Moving Man Simulation Activity so that each student receives a copy. This document directs them to PhET where they will be using The Moving Man simulation. My activity sheet is also meant to direct the students in their learning so that they are confident in what material needs to be digested. However, the answers to the questions, data tables, and graphs need to all be completed on a separate sheet of paper. At this point in the year students should have acquired all of their own school supplies, which includes notebook and graph paper.

While students are working, I walk around with the Moving Man Simulation Activity Answer Key to ensure they are actively engaged in the learning process. To me, this means that they are on the proper website, reading or discussing some component of the simulation, and writing down appropriate information from the simulation (here's what a student sample should look like). When I walk around, I'm spot checking their written work and engaging students in questions such as "So have you noticed any patterns yet?" or "What do you think will change when you make acceleration a non-zero value?"

The written conclusion is the most important part of this activity, so I ensure my students are thinking through how they will prove any claims they make. For example, if a student claims in the conclusion that a constant velocity results in a linear position vs. time graph, I make sure the student proves this with several additional trial data sets and graphs. I do a lot of walking and questioning throughout their work time.

## Closure & Homework

10 minutes

With about ten minutes left in class, I ask the students to finalize their work, shut down the computers, and return the computers to the cart. My students don't need much guidance with this since they are familiar with the process, so it only takes a minute or two for everyone to clean up. After everyone has returned to their original seat, I tell students to start thinking about a positive change and a negative change that occurred in their thinking today. As I'm talking, I give each student a small, blank notecard.

Once everyone has a notecard, I ask students to divide the notecard in half with a line drawn down the center. On their left side of the card, students should put a plus sign followed by a delta sign.  On the right side of the card students put a minus sign followed by a delta sign. I draw a sample of what their cards should look like on the front of the board so there is no confusion. Once they have their cards organized, students need to write down a positive change in their learning, such as something new they've learned or a part of the activity they really liked. On the other side of the card, students record a negative change in their learning, such as a concept that needs more clarification or a part of the activity that was particularly difficult.

As students finish recording their thoughts on the cards, they bring them forward and put them on my desk. The activity is done in silence so that students can really personalize and consider their responses without inside influences. I save these cards and read them during my next free time so that I can adjust my teaching and the assignment if needed.

When students bring the cards forward they grab a copy of tonight's homework. If there is any time left in class, students should start working on this homework. The assignment is meant to act as a formal assessment for mastery of kinematics curves, so it will be collected and graded for accuracy during the next class period.