Estimation

What is estimation?

The fifth graders that come to my class have difficulty with estimation. There is a mathematical gap that began in third grade when they had difficulty rounding whole numbers to the nearest ten or hundred to approximate reasonable results in problem situations. When the students were in fourth grade they had also missed the rounding of whole numbers to at the nearest ten, hundreds, or thousands to approximate reasonable results in problem situations. These students moved up to fifth grade with a math deficiency in using their estimation strategies. They are challenged with rounding and understanding compatible numbers to estimate solutions in addition, subtraction, multiplication and division problems.

The curriculum unit will enable them to develop the ability to estimate and work out how big or how small numbers are. They will be able to figure out a reasonable approximation of how many objects are there in all without computing for the exact value. For instance, they will improve the ability to estimate the number of jelly beans in a jar. Also, when ask to estimate the volume of water, given glasses with different shapes which glass will hold more, the students will be able to estimate the number of ounces or liters.

There are several definitions of the word estimation. According to the definition of estimation, it involves working out a rough answer to a calculation. The most common way to estimate a solution to a calculation is to round the numbers up or down to numbers which are easier to calculate with (Wikipedia). For example estimate the answer to 47×11. One can easily see that that 47 rounds to 50 and 11 rounds to 10. So when one can replace the calculation as 50×10 it is easier to calculate. When using estimation one wants the answers to be close to the reasonable value. The number has to be close enough in order for it to be useful.

Another definition of estimation is to be able to find the upper or lower bounds of a quantity that cannot be readily computed precisely. A third definition is an educated guess. I have mentioned earlier that "taking a guess" is using reasoning to find a useful approximation. The dictionary furthermore explains the Estimation Theory. It is a branch of statistics and signal processing that deals with estimating the values of parameters based on measured empirical data. An estimator attempts to approximate parameters using the measurements.