MTE 494 09 21 10 The 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 1 MTE 494 09 21 10 Horizontal Distance from Start 5 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 Elapsed time seconds 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 2 MTE 494 09 21 10 Diagnosing 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 3 MTE 494 09 21 10 Here 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 particular ways during different segments of the journey 4 MTE 494 09 21 10 Walking 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 keep track of both 5
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