The Skateboarder (Pair Activity)MTE 494 09/21/10The Skateboarder (Pair Activity)Watch the video showing the skateboarder performance on the half-pipe. You will probably need to watch it several times as you work to develop a graph of the skateboarder’s horizontal distance from start (the left edge of the half-pipe) as a function of time elapsed. The following questions are designed to promote your thinking about how these quantities relate to each other in this situation, and how to capture their relationship graphically.1. Use appropriately labeled axes and create a graph of the skateboarder’s horizontal distance from start (the left edge of the half-pipe) as a function of time since the video began. 2. This graph is to appear as part of an article or report and you are given the task of writing the caption for this graph. Write a descriptive caption that communicates the information that the graph provides.3. Choose a particular point on the graph. Describe the meaning of this point.4. What aspect of the graph do you hope your audience envisions as you describe the meaning of the point in #3 by pointing to it?1MTE 494 09/21/105. Students were asked to create the graph as you were asked to do. A student created the graph shown in Figure 1. The student explains that the graph shows how the skateboarder first “goes down”, then travels across the bottom of the half-pipe, then goes “back up”, etc. Figure 1- Discuss how the student might have been thinking as he created such a graph. - What aspects of the situation might the student NOT have been thinking about? - What would you first say to or ask this student? Explain why you would ask him this. 2Elapsed time (seconds)Horizontal Distance from StartMTE 494 09/21/10Diagnosing and Remediating Graphing Misconceptions(a) Write a story problem describing a journey you took that could be described by the graph shown below. Your description should be largely in terms of the quantities elapsed time and distance from home. Avoid using catch phrases like “constant speed” or “increasing speed” without explaining the meaning of the ideas to which they point.3MTE 494 09/21/10Here are two descriptions typical of that given by several students in an Algebra I class:Student 1: “First I walked up a hill, and then I walked on the top of the hill for a while before going down the other side of the hill. When I got to the bottom of the hill, I continued walking until I came to another hill. I walked up the second hill, which was lower but steeper than the first hill. Then I walked on the top of the second hill for a while before stopping.”Student 2: “I rode my bike down our street for a while. Then I turned right and rode for a shorter while. I then I turned right again onto another street and rode for a longer while until I turned left onto a short street on which I kept riding. That short street veered to the left onto a curvy road and I rode on it for a while before turning right onto a straight road. I rode on this straight road for a while.”(b) On the basis of these responses, explain how such students might have been thinking about the graph (i.e., give a diagnosis of their understandings of the graph).(c) Suppose you had the opportunity to interact as a teacher with one such student. Outline features of what you would say and do to help the student understand the given graph as depicting how the two quantities distance from home and elapsed time vary together in particularways during different segments of the journey.4MTE 494 09/21/10Walking on a Circular Track Matt walked around a circular track (see diagram). The black square shows where he began. The arrows show that we are tracking Matt’s (straight-line) distance from his current location to the starting point and the total distance he had walked (along the track) to get to his current location.Imagine Matt walking around the track once. Use covariational reasoning/incremental thinking to sketch a graph of Matt’s walk. Keep mental track of the total distance he walked along the track and his distance from the start (Hint: Think of playing Matt’s walk a frame at a time to keeptrack of
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