Measurement is one of the most widely used applications of mathematics. It bridges two main areas of school mathematics—geometry and number. Measurement activities can simultaneously teach important everyday skills, strengthen students' knowledge of other important topics in mathematics, and develop measurement concepts and processes that will be formalized and expanded in later years.

Teaching that builds on students' intuitive understandings and informal measurement experiences helps them understand the attributes to be measured as well as what it means to measure. A foundation in measurement concepts that enables students to use measurement systems, tools, and techniques should be established through direct experiences with comparing objects, counting units, and making connections between spatial concepts and number.

Understand measurable attributes of objects and the units, systems, and processes of measurement

Children should begin to develop an understanding of attributes by looking at, touching, or directly comparing objects. They can determine who has more by looking at the size of piles of objects or identify which of two objects is heavier by picking them up. They can compare shoes, placing them side by side, to check which is longer. Adults should help young children recognize attributes through their conversations. "That is a deep hole." "Let's put the toys in the large box." "That is a long piece of rope." In school, students continue to learn about attributes as they describe objects, compare them, and order them by different attributes. Seeing order relationships, such as that the soccer ball is bigger than the baseball but smaller than the beach ball, is important in developing measurement concepts.

Teachers should guide students' experiences by making the resources for measuring available, planning opportunities to measure, and encouraging students to explain the results of their actions. Discourse builds students' conceptual and procedural knowledge of measurement and gives teachers valuable information for reporting progress and planning next steps. The same conversations and questions that help students build vocabulary help teachers learn about students' understandings and misconceptions. For example, when students measure the length of a desk with rods, the teacher might ask what would happen if they used rods that were half as long. Would they need more rods or fewer rods? If students are investigating the height of a table, the teacher might ask what measuring tools would be appropriate and why.

Although a conceptual foundation for measuring many different attributes should be developed during the early years, linear measurements are the main emphasis. Measurement experiences should include direct comparisons as well as the use of nonstandard and standard units. For example, teachers might ask young students to find objects in the room that are about as long as their foot or to measure the length of a table with connecting cubes. Later they can supply standard measurement tools, such as rulers, to measure classroom plants and use those measurements to chart the plants' growth. »

Students need opportunities to expand their beginning understandings of attributes other than those related to linear measures and area. Preschool children learn about volume as they pour sand or water from one container to another. In the classroom, they should continue to explore the capacity of various containers by direct comparisons or by counting the number of scoops or cups required to fill each one. They also should experiment with filling larger containers with the contents of smaller ones and conjecture whether a quantity may be too much for a proposed container.

Young students should also have experiences with weighing objects. Balances help them understand comparative weights and reinforce the concept of equality; for example, they can predict that two cubes will weigh the same as twenty links and then test their prediction. Or they can measure equal weights of clay for an art project or compare the weights of different-sized blocks. Scales permit students to assign numerical values to the weights of objects (as rulers allow them to assign numerical values for linear measures) and allow them to begin using standard measures in meaningful ways. By the end of second grade, students should relate standard measures such as kilograms or pounds to the attribute "how heavy."

Another emphasis at this level should be on developing concepts of time and the ways it is measured. When students use calendars or sequence events in stories, they are using measures of time in a real context. Opportunities arise throughout the school day for teachers to focus on time and its measurement through short conversations with their students. A teacher might say, for example, "Look at the clock. It's one o'clock—time for gym! It is just like the picture of the clock on our schedule." As teachers call attention to the clock, many young students will learn to tell time. However, this is less important than their understanding patterns of minutes, hours, days, weeks, and months. »

The measurement process is identical, in principle, for measuring any attribute: choose a unit, compare that unit to the object, and report the number of units. The number of units can be determined by iterating the unit (repeatedly laying the unit against the object) and counting the iterations or by using a measurement tool. For example, students can tile a space and count the number of tiles to find the area. For linear measurement, they can record their height by using a meterstick.

Teachers should provide many hands-on opportunities for students to choose tools—some with nonstandard and others with standard units—for measuring different attributes. Students should learn that rods and rulers with centimeters and inches may be used to measure length. They should recognize that different units give different levels of precision for their measurements. Although for many measurement tasks students will use nonstandard units, it is appropriate for them to experiment with and use standard measures such as centimeters and meters and inches and feet by the end of grade 2.

Apply appropriate techniques, tools, and formulas to determine measurements

If students initially explore measurement with a variety of units, nonstandard as well as standard, they will develop an understanding of the nature of units. For example, if some students measure the width of a door using pencils and others use large paper clips, the number of paper clips will be different from the number of pencils. If some students use small paper clips, then the width of the door will measure yet a different number of units. Similarly, when students cover an area, some using dominoes and others using square tiles, they will recognize that "domino measurements" have different values from "tile measurements." Such experiences and discussions can create an awareness of the need for standard units and tools and of the fact that different measuring tools will yield different numerical measurements of the same object. »

Measurement concepts and skills can develop together as students position multiple copies of the same units without leaving spaces between them or as they measure by iterating one unit without overlapping or leaving gaps. Both types of experiences are necessary. Similarly, using rulers, students learn concepts and procedures, including accurate alignment (e.g., ignoring the leading edge at the beginning of many rulers), starting at zero, and focusing on the lengths of the units rather than only on the numbers on the ruler. By emphasizing the question "What are you counting?" teachers help students focus on the meaning of the measurements they are making.

Teachers cannot assume that students understand measurement fully even when they are able to tell how long an object is when it is aligned with a ruler. Using tools accurately and questioning when measurements may not be accurate require concepts and skills that develop over extended periods through many varied experiences. Consider the following episode drawn from a classroom experience:

Estimation activities are an early application of number sense; they focus students' attention on the attributes being measured, the process of measuring, the sizes of units, and the value of referents. Thus estimating measurements contributes to students' development of spatial sense, number concepts, and skills. Because precise measurements are not always needed to answer questions, students should realize that it is often appropriate to report a measurement as an estimate.