INNOVATIVE MODEL:FOURTH SEMESTER

 

This innovative model demonstrates the derivation of the area of a circle by rearranging circular sectors into a nearly rectangular shape. It is developed using a black chart or cardboard as a base, with a bold title "AREA OF A CIRCLE" for clear visibility and a picture of Archimedes to highlight his contributions. A circle made from colored foam or paper is divided into equal sectors, alternately colored for distinction, and fixed with a pin for rotation.

The transformation process involves cutting out the wedges and rearranging them alternately to approximate a parallelogram. As the number of wedges increases, the shape becomes more rectangular, with its width labeled as the radius (r) and its length as half the circumference (πr). Mathematically, this results in the area formula πr × r = πr².

Additional information, such as π ≈ 3.141592653589 and Circumference = 2πr, is displayed to reinforce learning. Short explanatory notes clarify how the increasing number of sectors smooths the edges. The teaching procedure begins with an introduction to the importance of circles in geometry, followed by a demonstration using the rotating cutout and rearranging the wedges.

The mathematical connection is established by explaining how the rectangle's dimensions relate to the original circle, deriving the area as πr². Student engagement is encouraged by allowing hands-on interaction and prompting them to explain the concept in their own words. The lesson concludes with a summary emphasizing how breaking and rearranging the circle’s parts visually demonstrates its area formula. This interactive approach enhances understanding, making learning more intuitive and effective.