Lesson 1.1.5: two graphing stories |
For this lesson there are 14 steps for you to take. Scroll down and do each step one-by-one. The instructions under each step will help clarify exactly what you need to do, so please read all the instructions.
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Here is the worksheet for Lesson 1.1.5
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1b.) Warm Up
In order to be successful in this lesson, you will need to be able to graph lines and write the equation for the line. You should have learned how to do this in 8th grade. I want you to review these two skills before moving on. Please follow the links to the right for the two Khan Academy activities that will allow you to practice and review how to graph lines and how to write equations for lines. |
Khan Academy Activities
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2.) Example 1: Graph this story
Read this situation and sketch a graphing story. Visualize both the story and what the graph will look like as you read the situation. When you graph the story, you do not need to use exact data, but you do need to label each axis.
Consider the 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.) Watch the video
Watch how I graph this story. Your graph should look similar, but does not have to be exact. If it is different, please have an explanation for why you graphed it that way. |
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4.) Watch this story
This video shows a man and a girl walking on the same stairway. As you watch it, keep in mind you will be graphing the story soon. |
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6.) Double check your work
Watch me graph the man's story. Our graphs don't need to look the exact same, but they should be similar. |
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7.) Graph the girl's story
Add the girl's elevation to the same graph. Make sure you account for the fact that the two people did not start at the same time.
After both stories are on the same graph, find the point where the graphs intersect and label the point "P". Discuss with your neighbor or write in your notes what the meaning of that point is.
Add the girl's elevation to the same graph. Make sure you account for the fact that the two people did not start at the same time.
After both stories are on the same graph, find the point where the graphs intersect and label the point "P". Discuss with your neighbor or write in your notes what the meaning of that point is.
8.) Double check your work
Watch me graph the girl's story. |
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9.) Example 3: Read and graph
Read the story that follows, and keep in mind that you will represent this story with a graph.
Sketch two graphs on the same set of elevation-versus-time axes to represent Duke's and Shirley's motions.
Read the story that follows, and keep in mind that you will represent this story with a graph.
- 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.
Sketch two graphs on the same set of elevation-versus-time axes to represent Duke's and Shirley's motions.
10.) Double check your graph
Watch me graph their stories to make sure you did it right. |
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11.) Analyze the graph
Answer the following questions about the Duke and Shirley story in your notes. Work with a partner if you would like to.
Answer the following questions about the Duke and Shirley story in your notes. Work with a partner if you would like to.
- What are the coordinates of the point of intersection of the two graphs?
- At what time do Duke and Shirley pass each other?
- Write down the equation of the line that represents Duke's motion as he moves up the ramp.
- Write down the equation of the line that represents Shirley's motion as she moves down the ramp.
- Show that the coordinates of the point you found in the question above satisfy both equations.
12.) Double check your answers
Watch the video to make sure you got the right answers. |
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13.) Read the lesson summary
- The intersection point of the graphs of two equations is an ordered pair that is a solution to BOTH equations. In the context of a distance (or elevation) story, this point represents the fact that both distances (or elevations) are equal at the given time.
- Graphing stories with quantities that change at a constant rate can be represented using piece-wise linear equations.
14.) Exit Ticket
Here is some more specific information about Maya and Earl (from example 1). Read the new information and answer the questions that follow (please write these in your notes).
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.
Suppose that:
1.) Graph both people’s distance from Maya’s door versus time in seconds.
2.) According to your graphs, approximately how far will they be from Maya’s door when they meet?
When you are done with these two tasks, raise your hand and show me your great work. A high five is on its way.
Here is some more specific information about Maya and Earl (from example 1). Read the new information and answer the questions that follow (please write these in your notes).
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.
Suppose that:
- Maya walks at a constant rate of 3 feet every second.
- Earl walks at a constant rate of 4 feet every second.
1.) Graph both people’s distance from Maya’s door versus time in seconds.
2.) According to your graphs, approximately how far will they be from Maya’s door when they meet?
When you are done with these two tasks, raise your hand and show me your great work. A high five is on its way.