"In the Dark with an Elephant" Teacher Support

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In the Dark with an Elephant Archived PoW || Student Version

In the Dark with an Elephant is no longer the current ESCOT Problem of the Week. The student version allows teachers to use the problem with their students without giving the students access to the archived answers. Teachers can use the link to the archived problem to get ideas about student thinking.

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In the Dark with an Elephant asks students to explore how the look of a graph of a function can vary, depending on how the domain and range of the graph window are set. The students will investigate why the same function can sometimes look straight, while at other times it looks curved.

This ESCOT PoW could be used as an introductory exploration on domain or range, or as a part of larger units on graphing and the effects of scale.

If you have something to share with us as you use any of the links or suggestions on this page (something you tried and changed or a new idea), we would love to hear from you. Please email us.

Alignment to the NCTM Standards - Grades 6-8

    Algebra
    - understand patterns, relations, and functions

    Geometry
    - analyze characteristics and properties of two-dimensional geometric shapes - use visualization, spatial reasoning, and geometric modeling to solve problems

    Problem Solving
    - solve problems that arise in mathematics and in other contexts

    Communication
    - communicate mathematical thinking coherently and clearly to peers, teachers, and others
    - use the language of mathematics to express mathematical ideas precisely

    Connections
    - recognize and apply mathematics in contexts outside of mathematics
Possible Activities:
    Pre-Activity
    - Introduce the idea of the elephant by having the students imagine that they are looking through a rectangular periscope (like the spectator periscopes used at golf matches to see over people). They should think about pointing the periscope at a certain part of the elephant, and then giving the coordinates that would tell someone else how to aim it.

    - Find an appropriate viewing rectangle in order to get a complete graph. For example:

    1. Which of the following points lie in the viewing rectangle [-3,5] by [1,8]?
      1. (0,0)
      2. (0,4)
      3. (4,0)
      4. (3,1)
      5. (1,4)
      6. (2,-2)
    2. Choose a viewing rectangle that includes all of the indicated points:
      1. (-8,9), (1,7) and (4,11)
      2. (19, -2), (12, 48) and (-9,3)

    Post-Activity
    - Quadratics: polynomial form by ExploreMath.com. If you use the magnifying glasses at the bottom of the screen, the graph will zoom in and out, helping to illustrate how the change in scale affects the graph. This can drive home the point of scale change in a very visual way.


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