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Note Packet A Lesson 5: Graphing Stories. Lesson 5: Graphing Stories Exercise 1: Consider this story Maya and Earl live at opposite ends of the hallway.

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Presentation on theme: "Note Packet A Lesson 5: Graphing Stories. Lesson 5: Graphing Stories Exercise 1: Consider this story Maya and Earl live at opposite ends of the hallway."— Presentation transcript:

1 Note Packet A Lesson 5: Graphing Stories

2 Lesson 5: Graphing Stories Exercise 1: Consider this story 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 What would their graphing stories look like if we put them on the same graph? When the two people meet in the hallway, what would be happening on the graph? Sketch a graph that shows their distance from Maya’s door.

3 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 Thoughts before we graph: What should go on the x axis? x-axis = Time What should go on the y axis? y-axis = distance How far apart are they to start? 50 feet

4 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 Thoughts before we graph: x-axis = Time y-axis = distance 50 feet Distance (ft) Time Maya Earl What would their graphing stories look like if we put them on the same graph? When the two people meet in the hallway, what would be happening on the graph? The two lines intersect Point of Intersection

5 Exercise 2: Consider this story 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 1. Sketch two graphs on the same set of elevation- versus-time axes to represent Duke’s and Shirley’s motions 2 4 Elevation (ft) Time Duke Shirley

6 Exercise 2: Consider this story 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 2. What are the coordinates of the point of intersection of the two graphs? At what time do Duke and Shirley pass each other? Point of Intersection (5,15) 5 Seconds

7 Exercise 2: Consider this story 3. Duke’s motion can be modeled by the equation y = 3t and Shirley’s can be modeled by the equation y = 25 – 2t. Show that the coordinates of the point you found in the question above satisfy both equations Duke y = 3t Point of Intersection(5,15) 15= 3(5) 15= Shirley y = 25 – 2t 15= 25 – 2(5) 15= 25 –10 15=

8 Exercise 3: Watch the following videovideo 1. Graph the man's elevation on the stairway versus time in seconds 1 2 Elevation (ft) Time (sec) Man

9 Exercise 3: Watch the following videovideo 2. Add the girl’s elevation to the same graph. 1 2 Elevation (ft) Time (sec) Man Girl How did you account for the fact that the two people did not start at the same time? Started the man at 0 secondsStarted the girl at 21 seconds

10 Exercise 3: Watch the following videovideo 3. Suppose the two graphs intersect at the point P(24,3). What is the meaning of this point in this situation? 1 2 Elevation (ft) Time (sec) Man Girl Point of Intersection.Where the people meet

11 Exercise 3: Watch the following videovideo 4. Is it possible for two people, walking in stairwells, to produce the same graphs you have been using and NOT pass each other at time 24 seconds? Explain your reasoning. 1 2 Elevation (ft) Time (sec) Man Girl Yes.They could be in 2 different stair wells

12 In Closing What is a point of intersection? What does it represent? Where the 2 lines cross It represents the solution to both equations


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