Perimeter, Area, Volume, and All That: A Study of Measurement

Introduction

Measurement is about the methods we use to determine the size of things. Every object has different attributes that can be measured, such as length, area, volume, or weight.¹ Length, area, and volume refer to the shape and extent of an object and might be called “geometric” attributes. Weight, on the other hand, refers to the physical constitution of the body.

The measurement of area and perimeter are widely used in everyday life and can be exemplified with a variety of practical situations such as measuring the size of a room by talking about its floor area, or how much fence to put around a playground.

Even though examples of area and perimeter are present in many “real life” situations, learning about these concepts as part of the mathematics curriculum in elementary school can be confusing or challenging for some students.

When teaching tends to focus on procedural understanding and the use of formulas rather than on the conceptual and relational knowledge, students learn to memorize formulas to “solve” problems without the proper understanding of the concepts. Some students also confuse the concepts of area and perimeter because they experience difficulty understanding the differences between linear (one-dimensional) units and squared (two-dimensional) units or are unable to connect their everyday experience with area and perimeter to what they learn in the classroom.²

The close relationship between area measurement with other mathematical concepts, such as multiplication, surface area, and volume, makes area a critical component of the K–12 mathematics curriculum, but without a solid understanding of what area means, students face difficulty in understanding related concepts.³

Conceptual understanding is crucial for understanding mathematical ideas instead of just isolated facts and formulas. Through conceptual understanding, students also acquire the bases and ability to transfer their knowledge into new situations, apply it to new contexts, make connections, and reason with supporting arguments about unfamiliar problems.⁴ The goal of this unit is to develop a solid conceptual understanding of perimeter, and especially, area in my students. The activities proposed in this unit allow students to construct their understanding of area and perimeter and to appreciate how they differ, with manipulatives and classes.