# Multiple Representations of Motion, Day 2

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## Objective

When given one of the three representations of motion, students will be able to create quantitative position vs. time graphs, velocity vs. time graphs and motion maps.

#### Big Idea

Students focus on quantitative instead of qualitative representations of motion.

## Self-Assess Learning Targets

5 minutes

To begin class, I pass out the Unit 1 Learning Target sheet and Constant Velocity Calendar for the unit to students. I give students the learning targets so they can see exactly what we are going to cover over the course of the unit. I give them the calendar so students can see what the homework assignments will be and when the major assessments will be so they can plan their study and work time accordingly. I wait to give them the learning targets until after the dune buggy lab because I want the lab to be true inquiry. I have found in the past that giving students learning targets or other resources prior to a pre-lab discussion or other lab activity makes them say what they think I want to hear instead of exploring any new ideas they would have.

At the beginning of every unit we do a first look at the targets as a preview to the unit. I ask students to read through all of the targets and rate on a scale of 1-4 how they feel about their knowledge and ability to complete that learning target. We use the Assess Yourself labels of (1) Novice, (2) Apprentice, (3) Practitioner, and (4) Expert. I ask students to silently read through the targets and rate themselves on the targets using a symbol the class chooses (ex. circle, square, star, smiley face). When all students have read through all of the targets and rated themselves on the learning targets, I tell them that we will do a couple of checks along the way to see how they are doing with each target throughout the unit.

## Whiteboard Problems

40 minutes

For homework the previous night, student finished the remaining problems on a Multiple Representations of Motion worksheet. I have students share out by putting the answers on large whiteboards and presenting them. I use this whiteboarding strategy because I want students to have a chance to verbalize their thinking throughout the problem and be able to answer questions about how they got to their answer. I believe that by presenting in front of class, students gain a better understanding of their individual 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.

Since there are 8 problems, I tell students that I will do problem #8 and each table group will present the number of their tables. Each table is made up of 3-4 students that will complete the whiteboard and present. They have done whiteboard presentations before so I briefly discuss what they should include on the whiteboard and show them what my #8 looks like as an example. I tell them they should include the original graph they were given as well as the 3 other representations of motion: velocity vs. time graph, motion map and written description. I also tell them that in their work time, they must also decide who is going to say what. Since there are 4 representations of motion, each person should be talking about one of the four representations. After I give them the explanation, I give them about 8-10 minutes to come to a consensus on the answer to the problem, put their whiteboards together and decide who is talking about each representation.

After the time is up and before the presentations start, I ask students what they should be doing when they are in the audience. They should tell me they should be quiet and respectful, looking the the board or their paper and asking questions if their paper does not match the board. When we start presentations, I go first to present my problem so they see exactly how their group should present.

After my presentation, I call groups up in order by their numbers with their whiteboards (Student Whiteboard #1Student Whiteboard #2Student Whiteboard #3). Each group presents and if no one in the audience has a question, I ask them a question. A lot of my questions with this worksheet tend to focus on the mechanical aspects of the graphs and motion maps. If a group has graphs and motion maps that look good, I ask them a more challenging question about their motion, typically a "What if...?" question. For example, "What if the object was moving faster? What would the motion map look like?"

After each group presents and all questions have been answered by the group, we give the group a "one-clap" to thank them for their presentation. The "one-clap" is when I have students clap once all together to prevent loss off time between presentations. I do the "one-clap" because it recognizes students without distracting or taking the class of track.

## Quantitative Representations of Motion Notes

20 minutes

After we have finished the whiteboard presentations on qualitative representations of motion, I take time to do two examples of quantitative representations of motion that students complete as notes. I do this so that students have some examples to reflect on as they work on Worksheet #2 later in the lesson as well as to help them recall important information that we learned during the lab.

In the first example that I do, I provide students with a quantitative position vs. time graph.

From there I want my students to draw a velocity vs. time graph, a motion map and a written description.

I start with the written description because this is similar to what they have seen in Worksheet #1. This example has all 3 types of motion that the students know so far. As we go through the written description, I show them how they can place numbers into the written description as seen in the Motion Maps and Graphs with Numbers Notes. Students recall that the slope on a position vs. time graph represents velocity and I walk them through a few ways that can calculate slope (rise over run or the mathematical equation using 2 points). Students can use the written description to fill out the velocity time graph, using the slopes of each section of the position vs. time graph. We examine how the slope of the position vs. time at a certain point (the tangent, although I avoid that term) corresponds to the data point on the velocity vs. time graph and then complete the motion map based on the given position vs. time graph. I emphasize that in a quantitative motion map each dot or arrow represents 1 second of time.

In the second example that I do, I provide students with a quantitative motion map.

Students create a position vs. time graph from the motion map, recalling each arrow represents 1 second. I show them how to number each dot or arrow so they know what is happening each second. After that, I sketch my position vs. time graph on the board so that it has the same number of time marks on the time axis and the same thing on the position axis. Students identify how many different types of motion there are on the motion map by circling them on their papers. After they have identified the different types of motion, I ask them where the object will start on the position vs. time graph and they respond with 10 meters. Then I show them how I would find the velocity of the object in each second by counting the number of meters it travels each second or each arrow. Once they have determined the velocity. they can draw each type of motion on the graph.

After they make the position vs. time graph, I ask them to create the velocity vs. time graph on with their partners based on what they know. When a minute or two has passed, I ask them to volunteer their answers for each section telling me how I would draw the velocity vs. time graph. Eventually the students come to an agreement on the graph and the example is completed and student's notes should look like the  Motion Maps and Graphs with Numbers Notes.

## Checkpoint

5 minutes

After we go through the notes, I give the students this Unit 1 End of Discussion Checkpoint #1 so that I can see what they learned from doing the worksheet, the presentations and the notes in the qualitative representations of motion. Students work individually on this checkpoint and turn it in for a formative grade. I choose this question because it shows me if they understand the relationships between the different representations of motion and if they retained any material from the lesson we just had.

## Multiple Representations of Data Practice

After students finish the checkpoint, I tell them they may continue working on Multiple Representations of Motion problems. This sheet will also be their homework. I want the students to start on practice problems before they come to class the next day so that they are able to ask questions if they attempt the questions and do not understand them.