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# EDSE 442

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### EDSE 442

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