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EDSE 442 EDSE 442 Presentation Transcript

  • EDSE 442 July 21, 2008 AC By: Jennifer Baerg
  • Exploring the Graphing Calculator (TI-84 Plus)
    • In BC, we explored the following idea:
        • Exploring big ideas through essential questions
    • In AC, we examined the following:
        • Investigating characteristics
  • Investigating Characteristics
    • Renee handed out the following sheet to each table:
    View slide
    • As a table, we were then to complete the following questions:
        • Choose one of the trigonometric functions (from the centre column on the worksheet) and use the graphing calculator to investigate its properties.
            • a) What are the parameters of the equation?
            • b) How does changing one of the parameters change the
            • graph?
            • c) Can you generalize the effects of the change across different functions?
        • From the remaining two columns, write a description of the attributes of each group or subgroup.
    View slide
  • Parameter vs. Variable
    • As a class, we discussed the difference between a parameter and a variable.
      • We first examined the equation:
          • y = a sin b(x-c) + d
      • Blaine and Lindsay started the debate by stating that a parameter is a constant value, but a variable changes on the graph.
      • Next Jimmy expressed that he views a parameter as direct, and a variable as indirect.
      • Chad then stated that it was a matter of “Changing vs. Changeable.” Changing being the variable, and changeable being the parameters.
      • The debate ended with Mike voicing that variables are the basis of the graph, and the parameters are the way that your graph may be expressed.
  • Presentation by Jimmy
    • On behalf of his group (Mike, Lindsey, and Lindsay), Jimmy presented their thought process for part 1 (occurred in BC) of the graphing calculator lesson.
    • This table examined both squares and triangles to try to reveal whether there is a direct relationship between perimeter and area.
    • Squares:
            • Perimeter = y ₁ = 4x
            • Area = y₂ = x²
    • Triangles:
            • Perimeter = y ₃ = 3x
            • Area = y₄ = ? (Renee let this as an exercise)
            • (Hint: Use Pythagorean theorem)
    • As they graphed these four equations, the following was revealed about f(x):
          • The perimeter equations were linear.
          • The area equations were curves.
      • Here are a few screenshots from Smart View:
      • Jimmy also showed us how to limit the “y=”
        • Within y=, first use the open bracket -> x (as the variable) -> 2 nd MATH -> symbol needed (ex. >) -> number (ex. 0) -> close bracket.
    • Conclusion: As perimeter increases, the area increases.
  • Challenge
    • Challenge #1:
      • Is there an example of a regular polygon where the perimeter is not a straight line?
    • Challenge #2:
      • Two intersections occur between the square’s perimeter and area (One when x=0, and the other at x=4). Where would this be significant in life?
  • The End