Transcript Slide 1

CHAPTER 5 – USING NUMBERS IN
SENSIBLE WAYS
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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.
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ACTIVITY
Do the following computations in your head. Try
re-doing them in as many ways as possible:
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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.
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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.
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ACTIVITY
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EXAMPLE
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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.
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ACTIVITY
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