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Example 4-4c Objective Estimate sums and differences of decimals

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Example 4-4c Vocabulary Front-end estimation Add or subtract the front digits

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Example 4-4c Vocabulary Clustering A form of estimating when all the addends are close to the same number

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Lesson 4 Contents Example 1Use Estimation to Solve Problems Example 2Use Estimation to Solve Problems Example 3Use Front-End Estimation Example 4Use Clustering

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Example 4-1a POPULATION The table below shows the population of the American colonies in 1770. Estimate the total population of North Carolina and South Carolina. 240.1 447.0 Population (thousands) Colony Population (thousands) Colony Connecticut 183.9 162.9New York Delaware 35.5 197.2 New Hampshire 62.4 Georgia 23.4 Massachusetts 235.3 124.2 Maryland 202.6 58.2 New Jersey 117.4 Virginia North Carolina South Carolina Rhode Island Pennsylvania Write colony then population 1/4 North Carolina 197.2 South Carolina 124.2

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Example 4-1b Round each number to the nearest tens for easier adding North Carolina197.2 South Carolina 124.2 1/4 North Carolina 197.2 South Carolina 124.2 20 Remember: When add 1 to 9 it = 10 so place a 0 in the 9’s place value and carry the 1 1 Annex a zero to hold the one’s place value 200 12 Again, annex a zero to hold the one’s place value 120

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Example 4-1b Add the numbers + 320 1/4 North Carolina 200 South Carolina 120

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Example 4-1b about 320 thousand 240.1 447.0 Population (thousands) Colony Population (thousands) Colony Connecticut 183.9 162.9New York Delaware 35.5 197.2 New Hampshire 62.4 Georgia 23.4 Massachusetts 235.3 124.2 Maryland 202.6 58.2 New Jersey 117.4 Virginia North Carolina South Carolina Rhode Island Pennsylvania 1/4 Answer: 320

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Example 4-1c POPULATION The table below shows the population of the American colonies in 1770. Estimate how many more people were in Massachusetts than in Connecticut. Answer: about 60 thousand more people 240.1 447.0 Population (thousands) Colony Population (thousands) Colony Connecticut 183.9 162.9New York Delaware 35.5 197.2 New Hampshire 62.4 Georgia 23.4 Massachusetts 235.3 124.2 Maryland 202.6 58.2 New Jersey 117.4 Virginia North Carolina South Carolina Rhode Island Pennsylvania 1/4

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Example 4-2a POPULATION The table below shows the population of the American colonies in 1770. Estimate how many more people lived in Rhode Island than in Georgia in 1770. 240.1 447.0 Population (thousands) Colony Population (thousands) Colony Connecticut 183.9 162.9New York Delaware 35.5 197.2 New Hampshire 62.4 Georgia 23.4 Massachusetts 235.3 124.2 Maryland 202.6 58.2 New Jersey 117.4 Virginia North Carolina South Carolina Rhode Island Pennsylvania 2/4 Write colony then population Rhode Island 58.2 Georgia23.4

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Example 4-2b Round each number to the nearest ten for easier adding and subtracting. Rhode Island58.2 Georgia23.4 2/4 Rhode Island58.2 If 5 or greater, add 1 to the rounding place value 6 Annex a zero to hold the one’s place value 60 Georgia23.4 If less than 5, leave the place value as is 2 Annex a zero to hold the one’s place value 20

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Example 4-2b Answer: Rhode Island had 40 thousand more people than Georgia Need to find how many more people lived in Rhode Island than in Georgia 40 Rhode Island60 Georgia20 Numbers are Population (thousands) 2/4 Decide what process? Subtract -

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Example 4-2c POPULATION The table below shows the population of the American colonies in 1770. Estimate the total number of people in Pennsylvania and New Jersey in 1770. Answer: 360 thousand people 240.1 447.0 Population (thousands) Colony Population (thousands) Colony Connecticut 183.9 162.9New York Delaware 35.5 197.2 New Hampshire 62.4 Georgia 23.4 Massachusetts 235.3 124.2 Maryland 202.6 58.2 New Jersey 117.4 Virginia North Carolina South Carolina Rhode Island Pennsylvania 2/4

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Example 4-3a Estimate using front-end estimation. Write the problem vertically 6 + 55.9 14.8 3/4 Add the front digits. Then add the next digits. 9 Do not add the decimals Answer: about 69

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Example 4-3b Answer: about 97 Estimate using front-end estimation. 3/4

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Example 4-4a MULTIPLE-CHOICE TEST ITEM A cage of guinea pigs at the pet store is given a vitamin-water solution each day. Last week the guinea pigs consumed 21.8 ounces, 19.1 ounces, 20.3 ounces, 18.9 ounces, and 22.0 ounces of the solution each day. Use this information to estimate the total amount of vitamin solution consumed in one day. A 70 ozB 90 ozC 100 ozD 120 oz 4/4 Since there are several numbers, use clustering Write the numbers vertically 21.8 19.1 20.3 18.9 22.0

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Example 4-4b 4/4 21.8 19.1 20.3 18.9 22.0 Clustering means to round all numbers to the same number Since all the numbers are close to 20, round all the numbers to 20 20 → → → → → Since all numbers are 20, multiply by how many numbers there are 20 There are 5 numbers 20 5 100

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Example 4-4a A 70 ozB 90 ozC 100 ozD 120 oz 100 is a good estimation Answer: C 4/4 Choose the appropriate multiple choice answer

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Example 4-4c MULTIPLE-CHOICE TEST ITEM During the month of February, Jonathon spends $14.78 on gasoline the first week, $15.35 on gasoline during the second week, $15.94 on gasoline during the third week, and $14.07 on gasoline during the fourth week. Use this information to estimate the total amount Jonathon spent on gasoline during February. Answer: C A $35B $50C $60D $100 * 4/4

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End of Lesson 4 Assignment Lesson 3:4 Estimating Sums and Differences 11 - 33 All

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