Estimating Differences. Finding Distances on a Map

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1 Estimating Differences Problem Solving: Finding Distances on a Map Estimating Differences How do we use rounding to estimate differences? Sometimes subtraction is like addition. There are times when we do not need to compute the exact number. We can estimate a close answer. To estimate a difference, we subtract numbers that are close to the numbers in the problem but that are easier to work with. One way we estimate is by rounding. In this strategy, we round each number to the nearest ten, hundred, thousand, or greater place value. Let s look at an example of how this strategy is used to estimate the difference between and 41. apple 41 First we round to the nearest ten. The number is between 60 and 70. It is closer to 70 than 60. So rounds up to 70. This is the nearest ten Then we round 41 to the nearest ten. The number 41 is between 40 and 50. It is closer to 40 than 50. So 41 rounds down to 40. This is the nearest ten. Think about where is on the number line. Is it closer to 60 or 70? Finally, we subtract the rounded numbers: 41 rounds to apple apple Think about where 41 is on the number line. Is it closer to 40 or 50? The extended fact is = 30. The estimated difference is 30. Unit 2 Lesson 6 93

2 There is a simple way to decide whether to round a number up or down. When rounding to the nearest ten, if the number is halfway or more to the next ten, round up. If the number is less than halfway to the next ten, round down. When rounding to the nearest hundred, if the number is halfway or more to the next hundred, round up. If the number is less than halfway to the next hundred, round down. Let s use the rounding strategy to estimate a difference by rounding to the nearest hundred. Estimate the difference between and 213. Round each number to the nearest hundred. Round to the nearest hundred The number is between 400 and 500. It is closer to 500 than 400. So rounds up to 500. This is the nearest hundred. Round 213 to the nearest hundred The number 213 is between 200 and 300. It is closer to 200 than 300. So 213 rounds down to 200. This is the nearest hundred. Finally, subtract the rounded numbers. The extended fact is = 300. The estimated difference is 300. apple apple Unit 2 Lesson 6

3 How do we determine which place value to round to? When estimating differences, we follow these steps to round each number: Look at the lesser number. Round that number to its greatest place value. Round the other number to the same place value. Let s look at an example of how this works. Estimate the difference between 12,100 and 8, ,100 8,860 The number 8,860 is the lesser number. Its greatest place value is the thousands. So round both numbers to the nearest thousand. The number 12,100 is between 12,000 and 13,000. It is less than halfway to 12,000, so it rounds down. 8,860 12,100 5,000 6,000 7,000 8,000 9,000 10,000 11,000 12,000 13,000 12,100 8,860 12,000 9,000 3,000 Remember to round to the greatest place value of the lowest number. The estimated difference is 3,000. Apply Skills Turn to Interactive Text, page 65. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. Unit 2 Lesson 6 95

4 Problem Solving: Finding Distances on a Map How do we use estimation to solve problems about distance? We often use estimation when we determine driving distances. Most of the time, we do not need to know the exact distance from one place to another, so we use estimation. The most common data displays for driving distances are maps. The map below shows the driving distances between three U.S. cities. Solve the word problem using estimation. Problem: The distance from Seattle to Phoenix is 1,508 miles. Rounded to the nearest hundred, the estimated distance is 1,500 miles. The distance from Seattle to San Francisco is 810 miles. Rounded to the nearest hundred, the estimated distance is 800 miles. About how much farther is the distance from Seattle to Phoenix than the distance from Seattle to San Francisco? We can create an extended fact and subtract to find the estimated distance: 1, = 700. Estimation is a good skill to use when reading maps because we usually do not need to know the exact distance. SEATTLE 1,508 miles 810 miles SAN FRANCISCO PHOENIX The distance from Seattle to Phoenix is about 700 miles more than the distance from Seattle to San Francisco. Problem-Solving Activity Turn to Interactive Text, page 66. Reinforce Understanding Use the mbook Study Guide to review lesson concepts. 96 Unit 2 Lesson 6

5 Homework Activity 1 Find the difference using expanded form. Then write the answer in standard form. Model 276 apple 157 S S S = apple apple apple apple 59 Activity 2 Find the difference using traditional subtraction apple Activity apple apple Estimate the difference. Then use a calculator to compute the exact answer and compare. Model 91 apple 37 S apple rounds down to rounds up to 40 S apple apple The exact answer (using a calculator) is = 54. Since 50 is close to 54, the answer is reasonable apple 319 Activity 4 Distributed Practice Add , , ,407 Unit 2 Lesson 6 97