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This lesson is all about
"estimation." An estimate tells
you "about how much." The idea
behind estimation is to use numbers "close to"
the actual numbers in the problem so that you can do the
calculations "mentally." Knowing
how to estimate is an extremely important skill.
You should estimate when:
an exact answer is not needed
all you need to know is "about how much"
paper and pencil or a calculator are not available
you want to check and see if your answer makes sense
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After
you have decided to use an estimate it is also important for you
to know whether it is better to
"underestimate" or "overestimate"
your answer. For example, if you are going to estimate the
amount your groceries are going to cost, it would be better to
"overestimate" the cost to make
sure that you have enough money. On the other hand if you
are going to estimate how much gas is left in your tank you
should "underestimate" so that you
don't run out. |
Let's see how it
works!
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On a
recent weekend the number of tickets sold to 4 showings of a
movie were 534, 687. 503 and 615. The manager needed to sell at
least 2000 tickets to earn her bonus.
Did she get it?? |
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Since
you only need to know if the sum is more or less than 2000, we
can estimate the answer. The
sum of 500 + 600 + 500 + 600 = 2200. Since the estimation
we used for each number is less than the
actual number, and since the sum of those estimates is
greater than the target number of
2000, the actual sum must be greater than 2000.
She got her bonus! |
Let's look at
another...
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The
maximum load weight of an elevator is 1000 lbs. There are
5 people in the elevator so far. Their weights are 187
lbs., 92 lbs., 223 lbs., 125 lbs., and 167 lbs.. Can one
more person who weighs 173 lbs. safely ride in this elevator? |
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In this
problem we need to know if the total weights of these 6 people is
more, or less than 1000 lbs.. And because the safety of these
riders is at stake we need to be very careful when estimating.
To make sure that we don't make a mistake we will
overestimate the weight of each of the
5 people, already in the elevator.
Overestimating we get the following 5
weights:
200 + 100 + 250 + 150 + 200 = 900
If we also overestimate the weight of the sixth person and add it to
our earlier estimate:
900 + 200 = 1100
With a maximum load limit of 1000 lbs., putting the additional
passenger into the elevator we are certainly taking a very dangerous
risk.
The answer is NO...the sixth passenger can not
ride safely! |
And one more...
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Gino and
Joe are going on a trip with their parents. The trip will cover a
distance of 686 miles. If they travel at about 50 mph,
estimate how long it will take the family to travel this distance. |
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This is an
easy one...
First round 686 to 700 miles...
Using the Distance formula; D = (r)(t)
We can solve for (t) "time",
t = D/r
Because we have rounded...the estimating is easy...
t = 700/50
t = 14
It will take the family approximately 14
hours! |
For these next 2
should we
underestimate
or
overestimate??
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You are
having a party and you need to know how many pounds of hamburger to
buy.
You know how many guests will be coming, so you will estimate how
much will be needed for one guest and then multiply by the total
number. |
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If you
underestimate the amount of food each guest will consume you might
not have enough food. So for this problem it is best to
overestimate. |
Try this one!
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You are
going to paint a wall in your bedroom with some paint that is left
over from another project. The directions on the paint can
tell you how many square feet of wall area a full can will cover.
The can is not full, do you have enough paint left to paint the
room, or should you go and get some more paint just to be safe? |
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This is a
tricky one. Let's say you measure the walls and determine that
the area you need to cover is 120 square feet. You look at the
can and it says that each 1 gallon of paint will cover 240 square
feet. You look into the can, and it looks to be
about half full. If you estimate
that you have 1/2 a gallon (overestimate)
you will be cutting it very, very close. It would be better in
this case to underestimate and purchase
additional paint...just to be safe. |
Now let's try some
on your own...
Click here!
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