estimating sums and differences amanda hobson. objectives: the students will: 1. give the definition...
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Estimating Sums and Differences
Amanda Hobson
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Objectives:
The students will:1. Give the definition of Estimation.2. Explain the differences in rounding and front-end estimation.3. Estimate the sums or differences using the two methods.
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Estimation
Finding the value that is close enough to the right answer, usually with some thought or calculation.
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Estimation
Methods:1.Rounding2.Front-End Estimation
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Rounding
Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use.
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Rounding
Example: 73 rounded to the nearest ten is 70
because the 3 is less than 5; therefore the number 73 will be rounded down.
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How to Round Numbers
• Decide which is the last digit to keep • Leave it the same if the next digit is less
than 5 (this is called rounding down) • Increase it by 1 if the next digit is 5 or
more (this is called rounding up)
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Estimate the Sum by Rounding
Example: (round to the nearest ten) 26 + 14
26 30 + 14 + 10
40
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Estimate the Difference by
RoundingExample: (round to the nearest
thousand) 5,976 - 2,687
5,976 6,000 -2,687 - 3,000
3,000
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Front-End Estimation
A method in which the front digits in the given numbers are added or subtracted
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Front-End Estimation
Front end estimation mostly produces a closer estimate of sums or differences than the answer produced by adding or subtracting rounded numbers.
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How to estimate the sum using Front-End
Estimation• Add the digits of the highest place values • Insert zeros for the other place values
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How to estimate the sum using Front-End
EstimationExample: 44,859 + 25,789
44,859 40,000 + 25,789 + 20,000
60,000
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How to estimate the difference using Front-End Estimation
• Subtract the digits of the highest place values
• Insert zeros for the other place values
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How estimate the difference using Front-End Estimation
Example: 57,658 - 24,12557,658 50,000
- 24,125 - 20,000 30,000
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Estimate Differences
Rounding• Estimate 86,017-35,572 Round to the nearest ten
thousand.
86,017 90,000 -35,572 -40,000 50,000
Front-End Estimation• Estimate 4,892-1,431Subtract the values of the
front digits.
4,892 4,000- 1,431 - 1,000 3,000
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Estimate Sums
Rounding• Estimate 2,578+1,452Round to the nearest
thousand. 2,578 3,000+ 1,452 + 1,000 4,000
Front-End Estimation• Estimate 4,254+2,415Add the values of the
front digits. 4,254 4,000+ 2,415 + 2,000 6,000
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Review:
• What is estimation?– Estimation is the value that is close enough to the
right answer. (Guess)
• What is the difference in rounding and front-end estimation?– When you round , the result will be less accurate .
• Will you be able to estimate using the two methods you have learned? http://www.aaamath.com/g4_73ax1.htm