CHAPTER 5 – USING NUMBERS IN SENSIBLE WAYS

Often, one can compute an answer in one’s head quicker than one could do it with pencil and paper, and sometimes even quicker than with a calculator. To become skilled at mental computation takes practice. Number properties must be used and understood, although oftentimes people are not aware that they are even using them. A key advantage to developing mental computation skills is that it can greatly develop true number sense.

ACTIVITY Do the following computations in your head. Try re-doing them in as many ways as possible:

Research has shown that good estimators use a variety of strategies and demonstrate a deep understanding of numbers and operations. Perhaps the biggest idea in good estimations are the ability of the person doing the estimating to be flexible and adapt the estimation to the situation. Proficiency in flexible rounding requires that a person have a good intuitive notion of the magnitude of numbers and how that fits relative to the situation in question.

EXAMPLE To estimate 257 + 394 + 2 + 49, a good strategy (although not the only one) would be to round 257 to 250, 394 to 400, 49 to 50, and then drop the 2 as insignificant here. However, school students with inflexible rounding skills may instead insist that 257 be rounded to 260. To estimate the quotient of 6217 ÷ 87, you might find it more convenient to round to 6300 and 90 rather than 6200 and 90 because 70  90 = 6300.

Activity

EXAMPLE

Example: (3.5  108)  (5.2  104) = (3.5  5.2)  (108  104) = 18.2  1012. But this is not scientific notation because 18.2 is larger than 10. So, 18.2  1012 = 1.82  1013. (3.5  108) ÷ (5.2  104) = (3.5 ÷ 5.2)  (108 ÷ 104) .67  104. But this is not scientific notation because .67 is smaller than 1. So, .67  104 = 6.7  103.

ACTIVITY