Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding.

Estimating Sums and Differences

Amanda Hobson

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.

Estimation

Finding the value that is close enough to the right answer, usually with some thought or calculation.

Estimation

Methods:1.Rounding2.Front-End Estimation

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.

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.

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)

Estimate the Sum by Rounding

Example: (round to the nearest ten) 26 + 14

26 30 + 14 + 10

40

Estimate the Difference by

RoundingExample: (round to the nearest

thousand) 5,976 - 2,687

5,976 6,000 -2,687 - 3,000

3,000

Front-End Estimation

A method in which the front digits in the given numbers are added or subtracted

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.

How to estimate the sum using Front-End

Estimation• Add the digits of the highest place values • Insert zeros for the other place values

How to estimate the sum using Front-End

EstimationExample: 44,859 + 25,789

44,859 40,000 + 25,789 + 20,000

60,000

How to estimate the difference using Front-End Estimation

• Subtract the digits of the highest place values

• Insert zeros for the other place values

How estimate the difference using Front-End Estimation

Example: 57,658 - 24,12557,658 50,000

- 24,125 - 20,000 30,000

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

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

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