In grades K-4, the mathematics curriculum should include measurement so that students can-

• understand the attributes of length, capacity, weight, mass, area, volume, time, temperature, and angle;
• develop the process of measuring and concepts related to units of measurement;
• make and use estimates of measurement;
• make and use measurements in problem and everyday situations.

Focus

Measurement is of central importance to the curriculum because of its power to help children see that mathematics is useful in everyday life and to help them develop many mathematical concepts and skills. Measuring is a natural context in which to introduce the need for learning about fractions and decimals, and it encourages children to be actively involved in solving and discussing problems.

Instruction at the K-4 level emphasizes the importance of establishing a firm foundation in the basic underlying concepts and skills of measurement. Children need to understand the attribute to be measured as well as what it means to measure. Before they are capable of such understanding, they must first experience a variety of activities that focus on comparing objects directly, covering them with various units, and counting the units. Premature use of instruments or formulas leaves children without the understanding necessary for solving measurement problems.

Estimation should be emphasized because it helps children understand the attributes and the process of measuring as well as gain an awareness of the sizes of units. Everyday situations in which only an estimate is required should be included. Since measurements are not exact, children should realize that it is often appropriate, for example, to report a measurement as between eight and nine centimeters or about three hours.

As measurement concepts and skills are introduced, they should be integrated throughout mathematics and other curriculum areas. Not only will this enhance other topics but it will also give children opportunities to develop and retain measurement concepts and skills.

Discussion

The approach advocated in this standard will give children a firm foundation that enables them to use any measurement system. The first step in building this foundation is understanding an object's many measurable attributes, such as those illustrated by a cereal box. See figure 10.1.

Fig. 10.1

Children begin to develop an understanding of such attributes through experiences like those in figure 10.2, in which they make decisions about the sizes of objects by looking, feeling, or comparing objects directly. These experiences also provide the opportunity in a natural way to build much of the vocabulary associated with measurement.

Fig. 10.2

The process of measuring is identical for 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 counting, by using an instrument, or by using a formula. In the examples in figure 10.3, the number of area units is determined by counting and the number of length units is determined with a ruler.

Fig. 10.3

Many important understandings are associated with a unit of measure. The choice of a unit is arbitrary, but it must have the same attribute as that which is being measured. That is, a unit of area must be selected to measure area, a unit of weight to measure weight, and so forth. The size of an appropriate unit depends on the size of the object or the desired precision of the measurement. For example, it is appropriate to choose a large container as a unit to measure the capacity of a bathtub and a small container to measure the capacity of a teacup. Children can also explore the relationship between the size of a unit and the number of units it takes to measure an object, as shown in figure 10.4.

Fig. 10.4

If children's initial explorations use nonstandard units, they will develop some understandings about units and come to recognize the necessity of standard units in order to communicate. Children can build an awareness of the approximate size of a standard unit through activities in which they find objects with a length of 1 meter, a mass of 1 gram, or a capacity of 1 liter. Measuring the same object with different standard units provides the background for learning the basic relationships between units and conversions at the middle grades. (For example, children can report the height of a door as 2 meters and 10 centimeters, or as 210 centimeters.) Such work also helps children become aware of the approximate nature of measurement.

Estimation activities should be integrated throughout measurement, including those that ask for an estimate of the measure of an object (About how large is the angle?) and those that ask for an object of a given measure (Find a piece of paper that is five centimeters long). The computer should not be overlooked as a tool that encourages estimation. When drawing figures on a computer, one often finds it necessary to estimate the length of a line or the result of a turn of a given number of degrees. Activities also should be provided that encourage the use of such estimation strategies as chunking (estimating the whole by estimating its parts).

Children can see the usefulness of measurement if classroom experiences focus on measuring real objects, making objects of given sizes, and estimating measurements. Textbook experiences cannot substitute for activities that use measurement to answer questions about real problems.