Estimation Strategies
Education's purpose is to replace
an empty mind with an open one.
Malcolm Forbes
Estimation



Estimation is being able to quickly and easily get
a number that is close enough to the exact
answer of a mathematical problem to be useful.
 Usually it involves some simplified mental
calculation.
Every time you use a calculator, for example, it
would be useful to know whether the answer it
gives is sensible.
 This requires making an estimate.
Sometimes a problem does not need an exact
answer because the problem itself is not exact.
Estimation
Estimation is:





using some computation
using easy mental strategies
using number sense
using a variety of strategies
getting close to the exact
answer
Estimation is not:




just a guess
doing hand calculations
using a calculator
exact
Estimation
Students need to know in which situations it is
appropriate to use estimation. These situations
basically fall into three categories:



There is no need to have an exact answer. An estimate
is good enough
 "Do I have enough money?"
There is not enough information to get an exact answer
 "About how many times will my heart beat in an
hour?"
To check if the answer from a calculation is reasonable
When Should You Estimate?
Decide if the situation needs an estimate or an
exact number. Explain your answer.
1.
2.
3.
4.
5.
6.
A headline noting the number of people living in China.
The amount of money a baby sitter charges per hour.
The width of a window screen.
The distance from Earth to the moon.
The hours at soccer practice in one month.
The number of tickets to sell for a play.
Rounding Estimate
•
This is the most familiar form of estimation and
is a way of changing the problem to one that is
easier to work with mentally.
•
•
Good estimators follow their mental computation with
and adjustment to compensate for the rounding.
To round a number simply means to substitute a
“nice” number that is close so that some
computation can be done more easily.
Rounding Estimate

Rounding estimate – choose the digit place
that you will round to, round to that digit
place and then add.
$ 135.95
15.90
+ 24.90
$ 175.75
$ 140
20
+ 20
$ 180
Front-End Estimate
•
This strategy focuses on the leading or leftmost
digits in numbers, ignoring the rest.
•
After an estimate is made on the basis of only
these front-end digits, an adjustment can be
made by noticing how much has been ignored.
Front End Estimate

Front-end estimate – add up the front-end
digits, then round the remaining digits and
add together. This tends to be the more
accurate of estimation.
2.71
1.73
+ 1.10
5.54
2.71
.70
1.73
.70
+ 1.10
+ .10
4
1.50
4 + 1.50 = 5.50
Cluster Estimate

Cluster estimate – Used when several
numbers are all close to the same value.
$ 15.35
16.05
+ 14.90
$ 46.30
$ 15 x 3 = $45
Practice

Using the three methods, estimate the total
cost of the following items:
$4.39, $3.75, $4.96, and $2.40



Which method did you find the simplest?
Which method came the closest to the true
cost?
Why do you think this was the closest?
Practice

Kim ran 2.76 miles on Monday, 2.34 miles on
Tuesday, and 1.97 miles on Wednesday. Use
frontend estimation to estimate the total distance
Kim ran.
7.1 miles

Rico’s dog has a litter of four puppies. The puppies
weigh 2.33 lb, 2.70 lb, 2.27 lb, and 2.64 lb. Use
clustering to estimate the total weight of the
puppies.
9.9 lb
Practice

You have $11.50 to buy two presents. You find one
item that costs $7.43. Another item costs $4.41.
What estimation strategy will help you decide
whether you have enough money to buy both?
Explain.

You used a calculator to find 383.8 – 21.9. Your
estimate was 360, but your display reads 164.8. How
could you have gotten 164.8 on your calculator?
Practice
Use the rounding method to solve the following:
1.
2.
3.
4.
5.
6.
7.
386 + 512
334 + 488 + 574
1,530 – 1,122
41,506 – 28,566
1,788 + 2,308 + 4,952
4.2 + 7.75
17.08 – 15.32
Practice
Now use the front-end method:
1.
2.
3.
4.
5.
6.
7.
386 + 512
334 + 488 + 574
1,530 – 1,122
41,506 – 28,566
1,788 + 2,308 + 4,952
4.2 + 7.75
17.08 – 15.32
Which method
brought you
closer to the
actual answer?
Reasonableness
Explain whether the following are reasonable:
 Fisherman Frank’s fish weighed 2.2 pounds per foot.
The scales showed a weight of 7.3 pounds. Frank
claims his fish was 14.6 feet long. True?
 Trixie the trampolinist bounces at a rate of 2
bounces every 6 seconds. At this rate, how long will
it take her to bounce 3600 times? Trixie says 20
minutes. Accurate?

Pole-vaulter Paula leaps 2.1 times as far as her little
sister Polly. Polly’s highest leap is 5.8 feet. Paula
claims her highest is 28 feet. Can this be?
Estimating Products & Quotients
Use mental math to estimate products &
quotients.
Multiply:
7.65 × 3.2
Round
8 × 3
Estimate
= 24
Estimating Products & Quotients
When dividing, use compatible numbers to
estimate quotients.


Compatible numbers are numbers that are easy
to divide mentally.
Round the divisor first, then round the dividend
to a compatible number.
Divide:
Round the divisor
Round the dividend
to a multiple of 2
38.9 ÷ 1.79
38.9 ÷ 2
40 ÷ 2
= 20
Estimate
Estimate the following by rounding:

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3.9 × 4.67
4 × 8.512
3.25 × 14.7
460 ÷ 92
31,776 ÷ 39
40,995 ÷ 62
20
36
45
5
800
700
Practice

Arlene bought 6 yards of fabric to make a
quilt. The fabric cost $6.75/yard. The sales
clerk charged Arlene $45.90 before tax. Did
the clerk make a mistake? Explain.

Shari is planning a 450 mile car trip. Her car
can travel about 39 miles on a gallon of
gasoline. Gasoline cost $1.89/gallon. About
how much will the gas cost for her trip?