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Estimation Strategies
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Education's purpose is to replace an empty mind with an open one.
Malcolm Forbes
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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.
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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
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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
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When Should You Estimate?
Decide if the situation needs an estimate or an exact number. Explain your answer.
1. A headline noting the number of people living in China.
2. The amount of money a baby sitter charges per hour.
3. The width of a window screen.
4. The distance from Earth to the moon.
5. The hours at soccer practice in one month.
6. The number of tickets to sell for a play.
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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.
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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
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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.
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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
.70 .70+ .10 1.50
2.71 1.73+ 1.10 4
4 + 1.50 = 5.50
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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
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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?
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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.
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.
7.1 miles
9.9 lb
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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?
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PracticeUse the rounding method to solve the following:
1. 386 + 512
2. 334 + 488 + 574
3. 1,530 – 1,122
4. 41,506 – 28,566
5. 1,788 + 2,308 + 4,952
6. 4.2 + 7.75
7. 17.08 – 15.32
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PracticeNow use the front-end method:
1. 386 + 512
2. 334 + 488 + 574
3. 1,530 – 1,122
4. 41,506 – 28,566
5. 1,788 + 2,308 + 4,952
6. 4.2 + 7.75
7. 17.08 – 15.32
Which method brought you closer to the actual answer?
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ReasonablenessExplain 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?
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Estimating Products & Quotients
Use mental math to estimate products & quotients.
Multiply: 7.65 × 3.2
Round 8 × 3
Estimate = 24
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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: 38.9 ÷ 1.79
Round the divisor 38.9 ÷ 2
Round the dividend 40 ÷ 2 to a multiple of 2 = 20
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Estimate
Estimate the following by rounding:
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
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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?