Reflection: Real World Applications More Graphing Stories - Section 1: Opener: A Tea Cup of Boiling Water


  1. You'll see in the image of student work on the board (Cooling Tea Cup) that one of the graphs starts on the origin before rising and falling again.  Can you figure out what this student was thinking?  Ok here it is: he wanted his graph to show the temperature of the water from the time it was poured into the tea kettle and then heated.  For any student who makes this move, I explain how important it is to read the problem.  It's not wrong to consider that the water had to be heated at some point, but it's never a good idea to read a problem that isn't there.  (Of course, what is wrong about this graph is that it starts at the origin, which would mean that a handful of ice cubes was thrown into the kettle, boiled, and...).
  2. Depending on the class, I pay more or less attention to the idea that the graph should be curved.  If we haven't taken too long to discuss the graph and I have everyone's attention, I'll ask, "When is the water cooling at the fastest rate?"  We discuss that the drop from boiling - and here I use specifics, 212 degrees - to, say 150 degrees happens pretty quickly, but that the drop from warm - say, 100 degrees - to room temperature is more gradual.  With that kind of thinking in mind, the idea of a curve should emerge.  On the other hand, if it feels unnatural to have this conversation now, I move on; we'll return to this graph and to the idea of a curved graph a little later this week.

  Real World Applications: Telling Stories with Graphs
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More Graphing Stories

Unit 8: Linear and Exponential Functions
Lesson 6 of 19

Objective: SWBAT sketch informal graphs that represent different real-world situations. Foundations are laid for students to make sense of how algebraic rules can be used to model these situations.

Big Idea: It's all about the graphs, baby! In this lesson, the task of graphing a real-world situation is presented in three different ways, and each builds toward a deep understanding of how a graph can tell a story.

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3 teachers like this lesson
Math, Algebra, Graphing (Algebra), modeling, Function Operations and Inverses, Linear and Nonlinear Equations, Graphing, graphing functions, Graphing Stories, representations of functions
  43 minutes
four situations i
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