Chapter 8 Standard 12

New Jersey Mathematics Curriculum Framework - Preliminary Version (January 1995)
© Copyright 1995 New Jersey Mathematics Coalition

CHAPTER 8: THE TEN CONTENT STANDARDS

STANDARD 12: MEASUREMENT

All students will develop their understanding of measurement and systems of measurement through experiences which enable them to use a variety of techniques, tools, and units of measurement to describe and analyze quantifiable phenomena.

Meaning and Importance

Measurement is important because it helps us to quantify the world around us. Although it is perfectly natural to think about length, area, volume, temperature, and weight as attributes of objects that we measure, a little reflection will produce many other measurable quantities: speed, loudness, pressure, and brightness, to name just a few. An understanding of the processes of measurement, the concept of a unit, and a familiarity with the tools and common units of measurement, are critical for children's developing understanding of the world around them.

This standard is also, in many ways, the prototypical "integrated" standard because of its strong and essential ties to almost every one of the other content standards. Measurement is an ideal context for dealing with numbers and numerical operations of all sorts and at all levels. Fractions and decimals especially appear very naturally in real-world measurement settings. In fact, metric measures provide perhaps the most useful real-world model of a base-ten numeration system we can offer to children. Geometry and measurement are similarly almost impossible to think about separately. Very similar treatments of area and perimeter, for instance, are called "measurement" topics in some curricula and "geometry" topics in others because they are, quite simply, measurements of geometric figures. Yet another of the content standards which is inextricably linked to measurement is estimation. Estimation of measures should be one of the focuses of any work that children do with measurement. Indeed, the very concept that any measurement is inexact -- is at best an "estimate" -- is a concept that must be developed throughout the grades.

Think about how many different content standards are incorporated into one simple measurement experience for middle grades students: the measurement of a variety of circular objects in an attempt to explore the relationship between the diameter and circumference of a circle. Clearly involved are the measurement and geometry of the situation itself, but also evident are opportunities to deal with patterns in the search for regularity of the relationship, estimation in the context of error in the measurements, and number sense and operations in the meaning of the ratio that ultimately presents itself.

K-12 Development and Emphases

Throughout their study and use of measurement, students should be confronted explicitly with the important concept of a measurement unit. Its understanding demands the active involvement of the learner; it is simply not possible to learn about measurement units without measuring things. The process of measurement can frequently be thought of as matching or lining up a given unit, as many times as possible, with the object being measured. For instance, in its easiest form, think about lining up a series of popsicle sticks, end to end, to see how many it takes to cover the width of the teacher's desk. Or, on a pan balance, how many pennies does it take to balance the weight of a small box of crayons? At a slightly more sophisticated level, multiple units and more standard units might be used to add precision to the answers. The desk might be measured with as many decimeter sticks as will fit and then with as many centimeter cubes as will fit in the space remaining; the crayons with as many ten-gram weights as can be used and then one-gram weights to get even closer to the weight. These types of activities, this active iteration of units, make the act of measurement and the relative sizes of units significantly more meaningful to children than simply reading a number from a measurement instrument like a yardstick or a postal scale. Of course, as the measures themselves become the focus of study, rather than the act of measurement or the use of units, students should be knowledgeable in the use of a variety of instruments and processes to quickly and accurately determine them.

Much research has been done into the development of children's understanding of measurement concepts and the general agreement in the findings leads to a coherent sequence in curriculum. Young children start by learning to identify the attributes of objects that are measurable and then progress to direct comparisons of those attributes among a collection of objects. They would suggest, for instance, that this stick is longer than that one or that the apple is heavier than the orange. Once direct comparisons can consistently be made, informal, non-standard units like pennies or "my foot" can be used to quantify how heavy or how long an object is. Following some experiences pointing out the necessity of being able to replicate the measurements, regardless of the measurer or the size of the measurer's foot, these non- standard units quickly give way to standard, well-defined units like grams and inches.

Older students should continue to develop their notions of measurement by delving more deeply into the process itself and by measuring more complex things. Dealing with various measurement instruments, they should be asked to confront questions concerning the inexact nature of their measures, and to adjust for, or account for, the inherent measurement error in their answers. Issues of the degree of precision should become more important in their activities and discussion. They need to appreciate that no matter how accurately they measure, more precision is always possible with smaller units and better instrumentation. Decisions about what level of precision is necessary for a given task should be discussed and made before the task is begun.

Students should also begin to develop procedures and formulas for determining the measures of attributes like area and volume that are not easily directly measured, and also to develop indirect measurement techniques such as the use of similar triangles to determine the height of a flagpole. Their universe of measurable attributes expands to include measures of a whole variety of physical phenomena (sound, light, pressure) and a consideration of rates as measures (pulse, speed, radioactivity).

The growth of technology in the classroom also opens up a wide range of new possibilities for students of all ages. Inexpensive instruments that attach to graphing calculators and computers are capable of making and recording measurements of temperature, distance, sound and light intensity, and many other physical phenomena. The calculators and computers, when programmed with simple software, are then capable of graphing those measurements over time, presenting them in tabular form, or manipulating them in other ways. These opportunities for scientific data collection and analysis are unlike any that have been available to math and science teachers in the past and hold great promise for some true integration of the two disciplines.

IN SUMMARY, measurement offers us the challenge to actively and physically involve children in their learning as well as the opportunity to tie together seemingly diverse components of their mathematics curriculum like fractions and geometry. It also serves as one of the major vehicles by which we can bring the real worlds of the natural and social sciences, health, and physical education into the mathematics classroom.