Estimating with Whole Numbers 1-2 Estimating with Whole Numbers Course 1 Warm Up Problem of the Day Lesson Presentation

Warm Up Find each sum. 1. 3,214 + 5,490 2. 9,225 + 8,652 3. 3,210 + 1,200 4. 8,774 + 2,156 8,704 17,877 4,410 10,930

Continue the number pattern below. Explain the pattern you found. Problem of the Day Continue the number pattern below. Explain the pattern you found. 3, 6, 10, 15, ___, ___ 21, 28; One possible pattern is to increase the difference between consecutive terms by one more than the difference between preceding consecutive terms.

Learn to estimate with whole numbers.

Vocabulary compatible number underestimate overestimate

Sometimes in math you do not need an exact answer Sometimes in math you do not need an exact answer. Instead, you can use an estimate. Estimates are close to the exact answer but are usually easier and faster to find. When estimating, you can round the numbers in the problem to compatible numbers. Compatible numbers are close to the numbers in the problem, and they can help you do math mentally.

If that digit is 5 or greater, round up. When rounding, look at the digit to the right of the place to which you are rounding. If that digit is 5 or greater, round up. If that digit is less than 5, round down. Remember!

Additional Example 1A: Estimating a Sum or Difference by Rounding Estimate the sum by rounding to the place value indicated. 12,345 + 62,167; ten thousands Round 12,345 down. 10,000 Round 62,167 down. + 60,000 __________ 70,000 The sum is about 70,000.

Additional Example 1B: Estimating a Sum or Difference by Rounding Estimate the difference by rounding to the place value indicated. 4,983 – 2,447; thousands Round 4,983 up. 5,000 Round 2,447 down. – 2,000 __________ 3,000 The difference is about 3,000.

Estimate the sum by rounding to the place value indicated. Check It Out: Example 1A Estimate the sum by rounding to the place value indicated. 13,235 + 41,139; ten thousands 10,000 Round 13,235 down. + 40,000 __________ Round 41,139 down. 50,000 The sum is about 50,000.

Estimate the difference by rounding to the place value indicated. Check It Out: Example 1B Estimate the difference by rounding to the place value indicated. 5,723 – 1,393; thousands 6,000 Round 5,723 up. – 1,000 __________ Round 1,393 down. 5,000 The difference is about 5,000.

An estimate that is less than the exact answer is an underestimate. An estimate that is greater than the exact answer is an overestimate.

Additional Example 2: Estimating a Product by Rounding Chelsea is planning the annual softball banquet for the 8 teams in the region. Each team has 18 members. Estimate how many plates she will need to buy if all the members attend. Find the number of softball members. Overestimate the number of softball members. 8  18 8  20 The actual number of softball members is less than 160. 8  20 = 160 Chelsea should buy about 160 plates.

Additional Example 2 Continued Another method Find the number of softball members. Overestimate the number of teams. 10  18 10  18 The actual number of softball members is less than 180. 10  18 = 180 Chelsea should buy about 180 plates.

Check It Out: Example 2 Ms. Oliver wants to buy the entire seventh-grade new pencils. There are 5 seventh-grade homeroom classes of 28 students. Estimate how many pencils Ms. Oliver needs to buy for all of the students. Find the number of students in the seventh grade. Overestimate the number of students. 5  28 5  30 The actual number of students is less than 150. 5  30 = 150 Ms. Oliver should buy about 150 pencils.

Additional Example 3: Estimating a Quotient Using Compatible Numbers Mr. Dehmel will drive 243 miles to the fair at 65 mi/h. About how long will his trip take? 240 and 60 are compatible numbers. Underestimate the speed. 243 ÷ 65 240 ÷ 60 Because he underestimated the speed, the actual time will be less than 4 hours. 240 ÷ 60 = 4 The trip will take about 4 hours.

Check It Out: Example 3 Mrs. Blair will drive 103 miles to the airport at 55 mi/h. About how long will her trip take? 100 and 50 are compatible numbers. Underestimate the speed. 103 ÷ 55 100 ÷ 50 Because she underestimated the speed, the actual time will be less than 2 hours. 100 ÷ 50 = 2 The trip will take about 2 hours.

Lesson Quiz Estimate each sum or difference by rounding to the place value indicated. 1. 7,420 + 3,527; thousands 2. 47,821 + 19,925; ten thousands 3. 8,254 – 5,703; thousands 4. 66,845 – 24,782; ten thousands 5. One quart of paint covers an area of 100 square feet. How many quarts are needed to paint a wall 8 feet tall and 19 feet wide? 11,000 70,000 2,000 50,000 2