# Multiple Representations of Motion, Day 1

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## Objective

When given a position vs. time graph, students will be able to create qualitative velocity vs. time graphs and motion maps.

#### Big Idea

The motion of an object can be represented in multiple ways.

## Mini Lesson: Position vs. Time Graphs

20 minutes

The goal of this lesson is for students to have another opportunity to learn about multiple representations of motion and how they are related. Students continue to develop the models for constant velocity motion and use them to create Position vs. Time graphs, Velocity vs. Time graphs, Motion Maps and written descriptions of motion.

I start out class talking about the learning targets addressed in this lesson. The students have watched a video about Position vs. Time graphs, Velocity vs. Time graphs and Motion Maps. This part of the lesson is a mini-lesson so I am giving them information that they can use as a resource. I try to limit my lectures, but every once in a while they are needed.

In this mini-lesson, I start by asking my students what kind of graph they made in the Dune Buggy Lab from the previous day. They tell me a Position vs. Time Graph. I start by drawing a new Position vs. Time graph on the board as shown (Position vs. Time and Motion Map Notes). I go through the important things they should have in their notes like what the slope represents and what the y-intercept represents for a orange line on the graph. When we talk about the slope, I make sure to point out the difference between speed and velocity. Then we talk about the steepness of the slope of a line and I draw a second line in blue on our graph. I ask them which one has a greater velocity and we come to the conclusion that the steep the line, or the more vertical the line, has a greater velocity.

Then I move onto a new type of graph, a Velocity vs. Time graph. I ask them what they think the orange line would look like on this new graph. If they are struggling to see the relationship I ask them what information do we know on the Position vs. Time graph that could help us on the Velocity vs. Time graph. Eventually students realize that the slope of the Position vs. Time graph gives us the y-intercept on the Velocity vs. Time graph for constant velocity. Then I have them try to graph the blue line on their own. When they are done I ask them to check with a partner to see if they agree. When everyone has checked, I ask them to raise their hand if they agree with their partner and I call on a student to answer.

After that, I tell them about a motion map. I allow the dune buggy to go across the floor and I tell them that they need to open and close their eyes each second that I say open. I tell them that this is what we are trying to display on a motion map, a snapshot or "selfie" of the car's motion at each second in time. I show an example of what the orange car's motion map would look like. Then I ask students what they think the blue car's motion would look like. We discuss that because it is moving faster, the dots would be farther apart because it would be covering more distance. By the end of the lesson student's should have notes that look similar to this Student's Notes.

## Discussion Checkpoint

10 minutes

This end of discussion checkpoint is to see what information students pulled out of the whiteboard session after the Dune Buggy Lab  and discussion on graphing. At this point I expect that my students are able to look at a Position vs. Time graph and tell me what the slope and y-intercept mean. To complete this end of discussion checkpoint I project a graph on the front screen for all students to see. I have them take out a notecard from the supply bins at the center of the tables and then have them answer the following questions:

1. What does the slope represent?

2. What does the y-intercept represent?

3. Write the mathematical model for this graph.

After students are done I have them bring their notecards to the front table. After all of my students are finished and have turned in their notecards, I go over the answers with them.

## Constant Velocity Motion Practice Problems

30 minutes

I use this worksheet give students a first look at how to represent motion in different ways. By the end of the unit I want them to be able to look at a Position vs. Time graph, Velocity vs. Time graph, a Motion Map or a written description and be able to give me the other 3. Since we discussed this as a class after the whiteboard session, they have an idea of how to complete these graphs, maps and descriptions. I provide them with additional resources if they want to look at so they can understand the materials. I attach a Motion Map reading to the website as well as a video on how to look at Position and Velocity vs. Time graphs and how to look at graphs and motion maps to determine the correct answers.

Before I let them use the rest of the period to work on a Multiple Representations of Motion worksheet, I do the first problem with them to show them my thinking out loud so that they can see where I am going with each section of the problem. Some resources to locate appropriate worksheets for this activity include those created by the AMTA (easily found in a web search) and resources posted on Ms. Laky's Science site.

After I do the example, I let them work on the remaining problems with their table groups. I tell students to try to use each other as resources as well as the notes to help them to answer the problems. As students work I walk around to try make sure students are on task and that if the entire group is stuck on a problem I can help guide them to the answers.