Estimation and Methods of Estimatation
A close correlate to number sense is estimation. NCTM’s Curriculum Focal Points (NCTM, 2006) state that students in Grade 3 should be able to “develop their understanding of numbers by building their facility with mental computation . . . by using computational estimation, and by performing paper-and-pencil computations.” In Grade 4, students should “extend their understanding of place value and ways of representing numbers to 100,000 in various contexts. They use estimation in determining the relative sizes of amounts or distances.”
Estimation is an extension of the brain’s innate ability to subitize. Estimating how many animals to hunt or how many crops to plant to feed the village was a survival skill. Our ancestors were good at it. Are we? Mathematics educators often comment on the poor estimation skills of students. A frustrated teacher once told me that a middle school student felt very pleased with himself after calculating the size of a molecule to be just over one meter in length. The unreasonableness of this measurement never occurred to him. Yet, ironically, youngsters often successfully use estimation skills outside of school. For example, they can quickly make the computations needed to cross a street with traffic, decide if a sibling is sharing equally, or accurately throw, catch, or hit a ball in sports. Poor estimation skills, it seems, are more likely to appear inside school when dealing with arithmetic estimation, and they can result from at least three factors.
- First, students at an early age are programmed to get the exact answer in a problem, so they have few experiences with estimation. Furthermore, activities that ask students for both an estimated and exact answer undermine the value of estimation. Why should students estimate if they are going to find the exact answer, too?
- Second, when students use a calculator in their work, they assume the calculator’s answer must be right, with no thought that they could have inadvertently entered an incorrect number or a misplaced decimal. Consequently, they rarely reflect on the reasonableness of their answers.
- Third, because students want to get the answer quickly, estimation is avoided because it often takes more time.
Activities involving estimation should begin as early as possible in the primary grades. However, they should not be isolated as a single unit of instruction, but rather should be taught in the context of other mathematics skills throughout all grade levels. If we want to emphasize the value of estimation, then students should be given assignments that require them only to estimate.
Methods of Estimation
The common methods of estimation include (1) rounding, which involves finding a number to the nearest ten, hundred, thousand, or the nearest one, tenth, hundredth, thousandth; (2) front-end estimation, which entails computing the higher place values or leftmost digits, then adjusting the rounded sum using the lower place values or digits to the right; and (3) clustering, which involves grouping numbers, and is useful whenever a group of numbers cluster around a common value. These methods of estimation are most helpful when students are doing computational tasks. They can check whether their answers come close to the estimated answer and to determine if their answer makes sense.
Students need to be aware that methods of estimation may not work in the real world. If you want to buy a shirt for $17.45, rounding down to the nearest dollar will not give you enough money to buy it. This is also true for estimations related to measurement. If you need exactly three and one-quarter yards of fabric to make a dress, you will not succeed if you round down to just three yards. Thus, rounding down of estimations of quantity in real-life situations will not give you enough. So what other types of estimation are available?
National Council of Teachers of Mathematics (NCTM). (2006). Curriculum focal points for mathematics in prekindergarten through grade 8. Reston, VA: Author.