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In this lesson we will learn how
to estimate the outcome of a problem, and then compare our estimate
to the actual solution.
Practicing this technique is extremely valuable in
learning how to solve "everyday" problems in a quick and efficient
manner.
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Many
times students will solve a problem either using pencil and
paper methods, or with a calculator, and because they have not
estimated the result before doing
the actual calculation they have no idea as to the
"correctness" of the solution.
If we estimate a result prior to actually doing the work, we can
determine whether the solution we get makes
"sense." |
Let's see how it
works!
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What is the sum of 28 + 71 + 133 + 299?
a. 480 b. 531
c. 570 d. 590
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You can estimate the sum by quickly adding
30 + 70 + 130 + 300, which is 530
Looking at the answer choices we can quickly guess
that choice "b" is probably correct.
Doing the problem with a calculator we arrive at
the sum of 531...it works!
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Let's look at
another...
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Of the 300 students
surveyed, 148 owned a dog, 22 owned both a dog and a cat, and 57
owned neither. How many of the students owned only a cat?
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Again,
quickly we can arrive at an estimated result by
rounding each number to a more
convenient number:
148 becomes 150, 22 becomes 20, and 57 becomes 60
150 + 20 + 60 = 230
Then subtract 230 from 300, and we can estimate that 70 students own
only a cat.
Checking our work with a calculator, we find that
the actual sum is
148 + 22 + 57 = 227
Then 300 - 227 = 73
73 students own only a cat.
A pretty good estimate!
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And one more...
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Mary has a
$10 bill which she is going to use to buy candy necklaces for the
guests at her party. She needs to buy a total of 16 necklaces
and each necklace costs $.39. Does she have enough money? |
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Sometimes
you have to decide what is the best number to round off to.
Sometimes it's to the nearest whole number, or to the nearest tens
or hundreds place. But in this problem it makes sense to
round to the nearest 50 cents.
When we do that this problem turns into a "piece of cake."
(Well Mary is having a party isn't she?)
When we do that, we see that 39 cents rounds easily to 50 cents.
And since there are 2-50 cents in each dollar, she can purchase 2
necklaces per dollar. Since she needs to buy 16 of them, we
can estimate that Mary needs approximately $8 for this purchase.
If she has a $10 bill then she has plenty!
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Let's try one
with fractions!!
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Jake is
building a set of shelves. The shelves are not all the same
length. One shelf is 14 2/3 " long, the next is 35 1/8" long,
the next shelf is 21 9/10" long, and the last shelf
is 23 1/4" long. He would like to buy just one piece of wood,
and then cut each length from that piece. The lumber he is
using comes in 6', 8', 10'. and 12' lengths. Which length
should he buy?
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Now, in
this problem we really have to be careful. Because we want to
be very sure that we have enough wood for all 4 shelves we will
round all of the mixed numbers UP to
the next whole number. That way we can be sure that we won't
be caught short on our last shelf!
13 2/3; will round up to 14
35 1/8; will round up to 36
21 9/10; will round up to 22
22 1/4; will round up to 23
Now we will add the whole numbers (try to do it in your head!)
14 + 36 + 22 + 23 = 95
95 inches divided by 12 ( the number of inches in 1 foot)
95/12 = 7" 11"
Jake needs to buy the 8' piece of lumber.
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Now let's try some
on your own...
Click here!
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