Using Geogebra To Teach Parametric Problem Solving

Table 1: The Outline of the paper

Preparatory stage
1.	Draw a circle given by the equation ${(x - 1)}^{2} + {(y - 1)}^{2} = 1$ . First, draw the circle in a copybook and then in the GeoGebra graphing calculator.
2.	Draw a circle given by the equation ${(x + 1)}^{2} + {(y - 1)}^{2} = 1$ in the copybook and the GeoGebra graphing calculator.
3.	Compare the two equations and the arrangement of the circles. Present both circles by the same equation.
4.	Draw a circle given by the equation ${(x + 1)}^{2} + {(y - 1)}^{2} = 4$ in GeoGebra graphing calculator
5.	Discuss how the numbers in the equation affect the arrangement and image of the circle in a coordinate system
Progress
1.	Replace one of the numbers in the formula with a letter, try to move the automatically generated slider and re-range the values of the letter: ${(x - a)}^{2} + {(y - 1)}^{2} = 1,$ ${(x - 1)}^{2} + {(y - a)}^{2} = 1,$ ${(x - 1)}^{2} + {(y - 1)}^{2} = a^{2}$
2.	Write the circle equation in general terms ${(x - a)}^{2} + {(y - b)}^{2} = c^{2},$ generate a slider for each parameter. By moving sliders, obtain the circles shown in Figure 1
Main assignment
	1. Follow a link https://www.geogebra.org/graphing/nngpfhms and examine the proposed parameter equations. Select the values of the parameters to obtain a bear cub’s face. (See a sample image in Figure 2.)
	2. Examine the equation separately that gives the bear cub’s smile, which is a semicircle.
	3.*Finish drawing the bear cub’s eyebrows as two semicircles above the eyes

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Using Geogebra To Teach Parametric Problem Solving

Table 1: The Outline of the paper

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