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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Page 1: 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

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

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.

Page 3: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

Estimation

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

Page 4: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

Estimation

Methods:1.Rounding2.Front-End Estimation

Page 5: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in 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.

Page 6: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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.

Page 7: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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)

Page 8: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

Estimate the Sum by Rounding

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

26 30 + 14 + 10

40

Page 9: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

Estimate the Difference by

RoundingExample: (round to the nearest

thousand) 5,976 - 2,687

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

3,000

Page 10: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

Front-End Estimation

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

Page 11: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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.

Page 12: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

How to estimate the sum using Front-End

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

Page 13: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

How to estimate the sum using Front-End

EstimationExample: 44,859 + 25,789

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

60,000

Page 14: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

How to estimate the difference using Front-End Estimation

• Subtract the digits of the highest place values

• Insert zeros for the other place values

Page 15: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

How estimate the difference using Front-End Estimation

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

- 24,125 - 20,000 30,000

Page 16: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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

Page 17: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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

Page 18: Estimating Sums and Differences Amanda Hobson. Objectives: The students will: 1. Give the definition of Estimation. 2. Explain the differences in rounding

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