Homework 5 DUE 09 30 Graphs and Covariation 1 Consider these four situations A car leaves home gradually going faster and faster A car returns home quickly slowing its speed A car slows down as it pulls into the library parking lot A child climbs up a slide at a constant speed he stops at the top and then slides down For each situation you are to do two things i Match the situation with the appropriate graph selected from those below H J I k ii Give a clear and thorough explanation of the meaning of the underlined part of each situation only in terms of the behavior of the quantities displayed in the matching graph Explain how the graph shows this behavior 1 For the last situation also explain how each of the graphs you didn t select right panel fails to model the situation 1 The quality of your responses to part ii will be evaluated largely on the basis of the highlighted requirements Responses that do not address these requirements will be treated as non responses 1 Homework 5 DUE 09 30 Graphs and Covariation 2 Each of the following graphs displays the relationship between the height H and volume V of water in a container as water is poured into it a Sketch the two containers best represented by i and ii respectively if water is poured in at a constant rate b Explain the meaning of the underlined idea in a in terms of the behavior of height and volume of water Explain how this is captured in the graph c Describe two scenarios represented by iii and iv respectively in terms of the behavior of height and volume of water Explain how each scenario is captured in its corresponding graph d Reflect on your own reasoning process in completing a c ii What specific difficulties do you anticipate middle or high school students might experience when engaging with the same tasks ii What specific benefits might students derive from engaging with these tasks iii Suggest ways in which you might refine adapt the tasks to address those difficulties mentioned in ii Provide a clear rationale for your suggestions e g I would ask have students do such and such because this would stand to make them focus on such and such for the following reasons 2
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