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Two Graphing Stories Interpret the meaning of the point of intersection of two graphs and use analytic tools to find its coordinates.

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**Learning Goal 2 (HS.N-Q.A.1, 2, 3): **

The student will be able to use units to solve multi-step contextual problems. 4 3 2 1 In addition to level 3.0 and above and beyond what was taught in class, the student may: · Make connection with other concepts in math · Make connection with other content areas. The student will be able to use units to solve multi-step contextual problems. - choose, convert, interpret and justify appropriate units in the context of a problem -interpret and create graphical representations of scenarios. The student will be able to choose and convert units to solve multi-step contextual problems. -interpret graphical representations of scenarios. With help from the teacher, the student has partial success with using units to solve multi-step contextual situations. Even with help, the student has no success with using units to solve multi-step contextual situations.

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Walking down the hall… Maya and Earl live at opposite ends of the hallway in their apartment building. Their doors are 50 feet apart. They each start at their door and walk at a steady pace towards each other and stop when they meet. Sketch a graph of this story. What would their graphing stories look like if we put them on the same graph? When two people meet in the hallway, what would be happening on the graph? Share graphs.

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**Questions about your graphs…**

Are the two people traveling at the same rate? If they are, how would their slopes compare? Sample Graph: Earl Maya

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Graphing Story #2 Watch the video of a man & girl walking on the same stairway. (https://www.youtube.com/watch?v=X956EvmCevI&feature=youtu.be)

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Group Activity Graph the man’s elevation on the stairway versus time in seconds. There was a total of 35 seconds in the video. Each group will need a poster and markers. Extra info: estimate that the rise of each stair is 8 inches. Add the girl’s elevation to the same graph. How do you account for the fact that the two people do not start at the same time? After a few minutes, have students hold up what they have drawn. Give the class further opportunity to revise their own graphs if they wish. Call out groups that have labeled and scaled their axes. The goal should be that all groups have a roughly accurate sketch with axes labeled. (There are 16 stairs at about 8 inches each for a total height of 10 2/3 feet.)

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Sample Graph: Does it seem reasonable to say that each graph is composed of linear segments? Suppose the two graphs intersect at point P (24, 4). What is the meaning of this point in this situation? We have 2 elevation-versus-time graphs, one for each of the two people. The point P lies on the elevation-versus-time graph for the first person, AND it also lies on the elevation-versus-time graph for the second person.

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Duke & Shirley Duke starts at the base of a ramp and walks up it at a constant rate. His elevation increases by three feet every second. Just as Duke starts walking up the ramp, Shirley starts at the top of the same 25 foot high ramp and begins walking down the ramp at a constant rate. Her elevation decreases two feet every second. With a partner sketch two graphs on the same set of elevation-versus-time axes to represent Duke’s and Shirley’s motions. Use graph paper.

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Duke & Shirley What are the coordinates of the point of intersection of the two graphs? (5, 15) At what time do Duke and Shirley pass each other? 5 seconds Write the equation of the line that represents Dale’s motion as he moves up the ramp. y = 3x (y is distance and x is time) Write the equation of the line that represents Shirley’s motion as she moves down the ramp. y = 25 – 2x Students may need a reminder from Linear Algebra about how to write equations of lines.

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