Chapter 8 Standard 13

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

CHAPTER 8: THE TEN CONTENT STANDARDS

STANDARD 13: ESTIMATION

All students will develop their understanding of estimation through experiences which enable them to recognize many different situations in which estimation is appropriate and to use a variety of effective strategies.

Meaning and Importance

As used in this standard, estimation is the process of determining approximate values in a variety of situations. Estimation strategies are used universally throughout daily life, but an examination of the mathematics curriculum of the past leads to the view that the strength of mathematics lies in its exactness, the ability to determine the right answer. The growing use of calculators in the classroom has placed some greater emphasis on determining the reasonable-ness of answers, a process that requires estimation ability, but efforts in support of this goal have been minimal compared to the time devoted to getting that one right answer. As a result, students have developed the notion that exactness is always preferred to estimation and their potential development of intuition has been hindered with unnecessary calculations and detail.

People who use mathematics in their lives and careers find estimation to be preferable to the use of exact numbers in many circumstances. Frequently, it is either impossible to obtain exact answers or too expensive to do so. An air conditioning salesperson preparing a bid would be wasting time and money by measuring rooms exactly. Astronomers attempting to determine movements of celestial objects cannot obtain precise measurements. Many people use approximations because it is easier than using exact numbers. Shoppers, for example, use approximations to determine whether they have sufficient funds to purchase items. Travelers use rough estimates of time, distance, and cost when planning trips. Commonly reported data often use levels of precision which have been accepted as appropriate, even though they may not be considered "exact". Astronomers always report information to two significant digits, and baseball players always report their batting averages as three place decimals.

K-12 Development and Emphases

Part of being functionally numerate requires expertise in using estimation with computation. Such facility demands a strong sense of number as well as a mastery of the basic facts, an understanding of the properties of the operations as well as their appropriate use, and the ability to compute mentally. As these skills and understandings are developed throughout the mathematics curriculum, students should frequently be presented with problems that allow them to form processes for obtaining estimates, to recognize that estimation is useful, and to appreciate that modifying numbers can change the outcome of a computation. They should be able to determine the correct answer from a set of possible answers in addition to establishing the reasonableness of answers that theyve computed.

Instruction in estimation has traditionally focused on the use of rounding. There are times when rounding is an appropriate process for finding an estimate, but this standard emphasizes that it is only one of a variety of processes. Computational estimation strategies are a new and important component in the curriculum. Clustering, front-end digits, compatible numbers, and other strategies are all helpful to the skillful user of mathematics, and can all be mastered by young students. Selection of the appropriate strategy to use depends on the setting and the numbers and operations involved.

The foregoing discussion describes a new emphasis on the use of estimation in computational settings, but students should also be thoroughly comfortable with the use of estimation in measurement. Students should develop the ability to estimate measures such as length, area, volume, and angle size visually as well as through the use of personal referents such as the width of a finger being about one centimeter. Measurement is also rich with opportunities to develop an understanding that estimates are often used to determine approximate values which are then used in computations and that results so obtained are not exact but fall within a range of tolerance.

Estimation should be an emphasis in many other areas of the mathematics curriculum in addition to the obvious uses in numerical operations and measurement. Within statistics, for example, it is often useful to estimate measures of central tendency for a set of data; estimating probabilities can help a student determine when a particular course of action would be advisable; problem situations related to algebraic concepts provide opportunities to estimate rates such as slopes of lines and average speed; and working with sequences in algebra and increasing the number of sides of a regular polygon in geometry yield opportunities to estimate limits.

In summary, estimation is a combination of content and process. Students ability to use estimation appropriately in their daily lives develops as they have regular opportunities to explore and construct estimation strategies and as they acquire an appreciation of its usefulness through using estimation in the solution of problems.