Aniekan Ebiefung, Ph.D

Goals

1. To give students the intuitive definition of the area of plane figures.
2. To coach students to discover for themselves the formulas for finding areas of the square, rectangle, parallelogram, trapezoid, rhombus, and triangle.
3. To actively involve students in the learning process.
4. To let the learning of area concepts evolve through a natural situation.
5. To indirectly lay the foundation to the learning of integral calculus.

Rationale

Objectives

1. To compute areas of squares, rectangles, and so on.
2. To summarize the formulas for computing areas and explain how the formulas are derived.

Methodology

1. Review plane figures: square, rectangle, parallelogram, rhombus, triangle, trapezoid, and so on.
2. Explain to the students the meaning of a square unit. (This is very important. Area will be defined in terms of square units and the same area using different units might have different numerical value. Conversion from one square unit to another should also be done.)
3. Define the area of a plane figure as the number of square units contained on its surface. Give examples involving different plane figures: polygonal plane figures and non-polygonal plane figures. The teacher should not give students any formula!
4. Direct students to the appropriate location on the Internet given below. A suggested starting point is with rectangles.
5. On the screen the the student is asked to input the width and the length of a rectangle. The picture of a rectangle appears on the screen with square units indicated. The student is asked to give the area of the rectangle. If the answer given is wrong, hints are provided, and the student is guided until he/she gives the correct answer. When the answer is correct, the student is reminded of the length l and the width w that were input. The program asks the student to compute the product lw and to compare the answer with the area of the associated rectangle. The student is asked to suggest a formula for the area of the rectangle and to show it to the teacher. The teacher should assist the student in any anyway the teacher sees fit.
6. After mastery of the lesson on areas of rectangles, students should proceed to finding areas of other planes figures, depending on the decision of the teacher.
7. For Advanced Students: The definition for area in terms of square units applies to all planes figures. If the figure were not bounded by lines, enclosing the figure in a rectangle, square, and so on can allow us to approximate the area. The areas of the polygonal figures can then be used to approximate the area of the desired figure. The program directs students on what to do. This is exactly how definite integrals are approximated in calculus.

1. The Rectangle
2. The Square
3. The Triangle
4. The Circle