Which of the following resources/TLM can be used by the teacher to show that two rectangles of different dimensions can have same area without using formula ?

A. Scale

B. Graph paper

C. Thread

D. Tiles

The correct answer is B & D (Graph paper and Tiles).

Explanation:

To show that two rectangles of different dimensions can have the same area without relying on mathematical formulas (like Area = length × width), a teacher can use concrete Teaching-Learning Materials (TLMs) or visual representations that rely on counting unit squares.

1. Graph paper (B):

Graph paper is divided into equal grid squares. A teacher can draw two different rectangles (for example, a rectangle of 2 units × 6 units and another of 3 units × 4 units) on graph paper. By asking students to count the total number of small grid squares enclosed by each rectangle, students can easily see that both rectangles contain exactly 12 grid squares. Thus, they have the same area without using any formulas.

2. Tiles (D):

Tiles are concrete 2D shapes of equal unit size. Students can arrange a fixed number of unit tiles (e.g., 12 tiles) to form different rectangular shapes (e.g., one row of 12, a 2 × 6 arrangement, or a 3 × 4 arrangement). Since the total number of tiles used remains constant, students visually comprehend that the area is identical despite the differences in length and width.

Why Scale (A) and Thread (C) are not suitable for showing area without formula:

• A Scale (ruler) measures linear dimensions (length and width), which requires using a mathematical formula to calculate area.
• A Thread measures perimeter (boundary length), not the enclosed surface area. Rectangles with different dimensions might have different perimeters even if their areas are equal.

Therefore, Graph paper (B) and Tiles (D) are the appropriate resources/TLMs for this purpose.