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**Estimating Sums and Differences**

Amanda Hobson Go ahead and open up your . We will be using it at the end of the lesson. Minimize your after you have opened it.

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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. By the end of today’s lesson, if I ask, you should be able to give me the definition of estimation, explain the differences in rounding and front-end estimation and you should also be able to estimate the sums and/or differences using the two methods of estimation.

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Estimation Finding the value that is close enough to the right answer, usually with some thought or calculation. Finding a value that is close enough to the right answer, usually with some thought or calculation involved. What does Estimation mean to you?

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**Estimation Methods: Rounding Front-End Estimation**

1.The estimation method chosen is determined by how close to the actual answer you will need the estimate to be. An estimate of a sum by rounding will be closer to the exact sum than a front-end estimate. 2. A front-end estimate of a sum will always give an estimate less than the actual sum. 3. You can adjust an estimate to make it closer to the actual answer by looking at the values of the digits to the right of the of the front-end digits

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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. When you round, you reduce the digits in a number while trying to keep its value similar.

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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. Another way to think of it is, 73 is closer to 70 than 80………..USE HAT WITH NUMBERS….HAVE STUDENTS COME UP TO THE BOARD AND WRITE THE CORRECT ESTIMATE OF THE NUMBER BY ROUNDING TO THE NEAREST TEN (IF TWO NUMBERS), NEAREST HUNDREAD (IF THREE NUMBERS) NEAREST THOUSAND(IF FOUR NUMBERS) AND SO ON>>>

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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) In order to round a number there are 3 steps to follow…1. decide which is the last digit to keep. 2. leave it the same if the next digit is less than 5 (this is called rounding down) 3. 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)

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**Estimate the Difference by Rounding**

Example: (round to the nearest thousand) 5, ,687 5,976 6,000 -2, ,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 Tell them to take out a sheet of paper.

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**How to estimate the sum using Front-End Estimation**

Example: 44, ,789 44,859 40, , ,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, ,125 57,658 50, , ,000 30,000

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**Estimate Differences Rounding Front-End Estimation**

Round to the nearest ten thousand. 86, ,000 -35, ,000 50,000 Estimate 4,892-1,431 Subtract the values of the front digits. 4, ,000 1, ,000 3,000 Rounding- remember that when you round, you have to be given a nearest place value to round to. If the number before the place value you are rounding to is 4 or below then you will keep that number and turn all the numbers behind it to zero. If the number is 5 or larger you will round up one number and turn all other numbers behind it to zero. Then you can add or subtract the facts. In front end estimation…There is no rounding! You simply take the front digits and turn all the other digits to zero then you will add or subtract, which ever the directions ask you to do.

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**Estimate Sums Rounding Front-End Estimation Estimate 2,578+1,452**

Round to the nearest thousand. 2, ,000 + 1, ,000 4,000 Estimate 4,254+2,415 Add the values of the front digits. 4, ,000 + 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?

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