The Shrinking Mississippi River
Setting the Stage
Classroom setup: One computer with a projection device in the classroom.
Objectives: The goal of the lesson is to get students to understand and appreciate how graphs can tell meaningful stories. They will practice describing real world phenomena with line graphs which can then be used to note trends and to predict events through interpolation and extrapolation.
Opening - the launch: The teacher begins with a story about a story that Mark Twain once wrote about in reference to the Mississippi River.
T (Teacher): Do you know who Mark Twain was?
S (Student): Yes, he wrote "Huckleberry Finn."
T: That's right. He also wrote a lot of other books about a variety of topics. One of his stories was about the Mississippi River. He said that the river meanders with curves, and from time to time cut-offs take place. This in a sense "straightens out" the river somewhat by cutting off the meanders. As a result Mr. Twain believes the river is becoming shorter. (Here Ms. Ridley shows a picture of a cut-off.)
Here is Twain's supporting data:
The Mississippi between Cairo and New Orleans
T: If we plot these as points on a
year/mile axis we would see this graph.
T: If we extend the line until it
intersects with the year axis it would look like this.
T: Twain made this prediction: "Any calm
person, who is not blind or idiotic, can see that in 742
years from now, the Lower Mississippi will only be a mile
and 3/4ths long!" (1) S what do you think of Twain
S: It seems reasonable to me. If you connect the points with a line the graph will eventually become zero. And graphs don't lie!
T: Well graphs may not lie, but they can be wrong! If you look at the 3 point graph above they appear to show a straight line. Anyone else have any thoughts about the way the graph was extended?
S: The graph can't be a straight line. The river has a limit as to how short it can be.
T: That's right. So what should the graph look like?
S: The graph should be curved.
T: When we draw the "line" past the third point it should start to curve and not go below the length of the Mississippi if it was perfectly straight. When we extend the graph beyond the 3 points we are extrapolating, that is, guessing where the graph would go.
Doing the activity
At this point the teacher introduces the software Relating Graphs to Events. (Available at Greenglobs.net)
The program presents a story and three line graphs marked a, b and c. The goal is to choose the graph that best represents the story. Students work in pairs at a computer that has the software installed.
Here's an example:
Watch the video. Click on image below. (Again, it's 1992. Pretend that the equipment is more up to date. :-))
When the students are finished, give them this challenge problem.
Graph this story
A flight from SeaTac Airport in Washington to LAX Airport in Los Angeles has to circle LAX several times before before being allowed to land. Plot a graph of distance of the plane from Washington against time from the moment of takeoff until landing.
Here's one student's attempt.
Ask your students what they think about this solution. Is it right on? What is your solution? (Student handout)