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Five-Minute Check (over Lesson 3–3) Main Idea and Vocabulary Example 1: Use Estimation to Solve Problems Example 2: Use Estimation to Solve Problems Example 3: Use Clustering Example 4: Use Front-End Estimation Concept Summary: Estimation Methods Lesson Menu

Estimate sums and differences of decimals. clustering front-end estimation Main Idea/Vocabulary

Use Estimation to Solve Problems POPULATION The table below shows the population of the American colonies in 1770. Estimate the total population of North Carolina and South Carolina. Example 1

Use Estimation to Solve Problems Round each number to the nearest hundred for easier adding. 197.2  200 197.2 rounds to 200. + 124.4  + 100 124.2 rounds to 100. 300 Answer: There were about 300 thousand people in North Carolina and South Carolina. Example 1

300 thousand people 400 thousand people 500 thousand people The table below shows the population of the American colonies in 1770. Estimate the total number of people in Pennsylvania and New Hampshire in 1770. 300 thousand people 400 thousand people 500 thousand people 600 thousand people A B C D Example 1

Use Estimation to Solve Problems 58.2  60 58.2 rounds to 60. – 23.4  – 20 23.4 rounds to 20. 40 Answer: There were about 40 thousand more people in Rhode Island than in Georgia. Example 2

50 thousand people 60 thousand people 70 thousand people The table below shows the population of the American colonies in 1770. Estimate how many more people were in Massachusetts than in Connecticut. 50 thousand people 60 thousand people 70 thousand people 80 thousand people A B C D Example 2

Use Clustering Sid feeds a vitamin-water solution to his guinea pigs. The table shows the amount of solution the guinea pigs drank over a period of four days this week. Which is the closest to the total amount of solution the guinea pigs drank? 40 ounces 60 ounces 80 ounces 100 ounces Example 3

Use Clustering Read the Item The addends are clustered around 20. Round each decimal to 20. 21.8 → 20 19.1 → 20 18.9 → 20 + 22.0 → + 20 80 Example 3

Use Clustering Solve the Item Multiplication is repeated addition. So, a good estimate is 4 × 20, or 80. Answer: C Example 3

During the month of February, Jonathon spent $14 During the month of February, Jonathon spent $14.78 on gasoline the first week, $15.35 on gasoline during the second week, $15.24 on gasoline during the third week, and $14.97 on gasoline during the fourth week. Which is the closest to the total amount Jonathon spent on gasoline during February? $35 $50 $60 $100 A B C D Example 3

Use Front-End Estimation Estimate 14.8 + 55.9 using front-end estimation. 14.8  10.0 + 55.9  + 50.0 Add the front digits. 60.0 Answer: Using front-end estimation, 14.8 + 55.9 is about 60.0. Example 4

Estimate 32.7 + 65.1 using front-end estimation. 90.0 100.0 110.0 120.0 A B C D Example 4

Rounding Clustering Front-End Estimation Estimation Methods Rounding Clustering Front-End Estimation Estimate by rounding each decimal to the nearest whole number that is easy for you to add or subtract mentally. Estimate by rounding a group of close addends to the same number before adding. Estimate by adding or subtracting the values of the digits in the front place. Concept Summary

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Five-Minute Check (over Lesson 3–3) Image Bank Math Tools Modeling Decimals Dividing Decimals Modeling Decimals Resources

Round 8.4302 to the nearest tenth. (over Lesson 3-3) Round 8.4302 to the nearest tenth. 8.4 8.43 8.44 8.5 A B C D Five Minute Check 1

Round 9.6452 to the nearest thousandth. (over Lesson 3-3) Round 9.6452 to the nearest thousandth. 9.65 9.646 9.645 9.64 A B C D Five Minute Check 2

Round 1.257 to the nearest hundredth. (over Lesson 3-3) Round 1.257 to the nearest hundredth. 1.3 1.26 1.25 1.2 A B C D Five Minute Check 3

Round 8.186172 to the nearest ten-thousandth. (over Lesson 3-3) Round 8.186172 to the nearest ten-thousandth. 8.1861 8.18617 8.18618 8.1862 A B C D Five Minute Check 4

Round 8.239 to the nearest hundredth. (over Lesson 3-3) Round 8.239 to the nearest hundredth. 8.2 8.23 8.24 8.3 A B C D Five Minute Check 5

(over Lesson 3-3) The average retail price of gasoline in Texas during the week of March 13, 2006 was $2.283 per gallon. Round this to the nearest cent. $2.30 $2.29 $2.28 $2.27 A B C D Five Minute Check 5

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