Estimating sums and differences
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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.

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Estimating Sums and Differences

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Estimating sums and differences

Estimating Sums and Differences

Amanda Hobson


Objectives

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

Estimation

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


Estimation1

Estimation

Methods:

  • Rounding

  • Front-End Estimation


Rounding

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.


Rounding1

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

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

Estimate the Sum by Rounding

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

2630

+ 14 + 10

40


Estimate the difference by rounding

Estimate the Difference by Rounding

Example: (round to the nearest thousand) 5,976 - 2,687

5,976 6,000

-2,687 - 3,000

3,000


Front end estimation

Front-End Estimation

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


Front end estimation1

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

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 estimation1

How to estimate the sum using Front-End Estimation

Example: 44,859 + 25,789

44,85940,000

+ 25,789 + 20,000

60,000


How to estimate the difference using front end estimation

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

How estimate the difference using Front-End Estimation

Example: 57,658 - 24,125

57,65850,000

- 24,125 - 20,000

30,000


Estimate differences

Estimate Differences

Rounding

Front-End Estimation

Estimate 4,892-1,431

Subtract the values of the front digits.

4,892 4,000

1,431 - 1,000

3,000

  • Estimate 86,017-35,572

    Round to the nearest ten thousand.

    86,017 90,000

    -35,572 -40,000

    50,000


Estimate sums

EstimateSums

Rounding

Front-End Estimation

Estimate 4,254+2,415

Add the values of the front digits.

4,254 4,000

+ 2,415 + 2,000

6,000

  • Estimate 2,578+1,452

    Round to the nearest thousand.

    2,578 3,000

    + 1,452 + 1,000

    4,000


Review

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


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