Surface area - Circle
At grade 8 Austrians students learn a lot about the measurement of circles. To derive the formula of the area of a circle another applet can be used.
Derivation of the formula
Derivation of the formula
First of all you cut the circle in equal pieces. And the number of pieces can get very high. Than you take one piece after another and lay it in a row. Than you rearrange the pieces. And now you can see that the area of a circle is equal to the area of a rectangle. One side has the length of the radius, the other pi times the radius.
All together shows that the area of the circle is pi times the radius squared.
So with this applet again students can find and understand the formula of the circles area. This applet and this derivation respond to the first three levels.
It enables the disposition to engage in reasoning (Level 1).
It enables the ability to understand, comprehend and explain prescribed reasons (Level 2).
And it also enables the ability to explain and argue the formula of the area of a circle in communication situations (Level 3).
So at grade 8 it’s the first time students see the approximation of an area.