Transcript g6_ch01_01
1-1 Estimating with Whole Numbers Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1-1 Estimating with Whole Numbers Warm Up Find each sum. 1. 3,214 + 5,490 8,704 2. 9,225 + 8,652 17,877 3. 3,210 + 1,200 4,410 4. 8,774 + 2,156 10,930 1-1 Estimating with Whole Numbers 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. 1-1 Estimating with Whole Numbers Learn to estimate with whole numbers. 1-1 Estimating with Whole Numbers Vocabulary estimate compatible number underestimate overestimate 1-1 Estimating with Whole Numbers 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. 1-1 Estimating with Whole Numbers Remember! 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. 1-1 Estimating with Whole Numbers 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 10,000 +__________ 60,000 70,000 Round 12,345 down. Round 62,167 down. The sum is about 70,000. 1-1 Estimating with Whole Numbers 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 5,000 – 2,000 __________ 3,000 Round 4,983 up. Round 2,447 down. The difference is about 3,000. 1-1 Estimating with Whole Numbers 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. 1-1 Estimating with Whole Numbers Check It Out: Example 1B Estimate the difference by rounding to the place value indicated. 5,723 – 1,393; thousands 6,000 – 1,000 __________ 5,000 Round 5,723 up. Round 1,393 down. The difference is about 5,000. 1-1 Estimating with Whole Numbers An estimate that is less than the exact answer is an underestimate. An estimate that is greater than the exact answer is an overestimate. 1-1 Estimating with Whole Numbers 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. 8 18 8 20 Overestimate the number of softball members. 8 20 = 160 The actual number of softball members is less than 160. Chelsea should buy about 160 plates. 1-1 Estimating with Whole Numbers Additional Example 2 Continued Another method Find the number of softball members. 8 18 10 18 Overestimate the number of teams. 10 18 = 180 The actual number of softball members is less than 180. Chelsea should buy about 180 plates. 1-1 Estimating with Whole Numbers Check It Out: Example 2 Ms. Oliver wants to buy the entire seventhgrade 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. 5 28 5 30 5 30 = 150 Overestimate the number of students. The actual number of students is less than 150. Ms. Oliver should buy about 150 pencils. 1-1 Estimating with Whole Numbers 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? 243 ÷ 65 240 and 60 are compatible 240 ÷ 60 numbers. Underestimate the speed. 240 ÷ 60 = 4 Because he underestimated the speed, the actual time will be less than 4 hours. The trip will take about 4 hours. 1-1 Estimating with Whole Numbers 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? 103 ÷ 55 100 and 50 are compatible 100 ÷ 50 numbers. Underestimate the speed. Because she underestimated 100 ÷ 50 = 2 the speed, the actual time will be less than 2 hours. The trip will take about 2 hours. 1-1 Estimating with Whole Numbers Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 1-1 Estimating with Whole Numbers Lesson Quiz Estimate each sum or difference by rounding to the place value indicated. 1. 7,420 + 3,527; thousands 11,000 2. 47,821 + 19,925; ten thousands 70,000 3. 8,254 – 5,703; thousands 2,000 4. 66,845 – 24,782; ten thousands 50,000 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? 2 1-1 Estimating with Whole Numbers Lesson Quiz for Student Response Systems 1. Estimate by rounding to the indicated place value. 8,240 + 3,428; thousands A. 10,000 B. 11,000 C. 12,000 D. 13,000 1-1 Estimating with Whole Numbers Lesson Quiz for Student Response Systems 2. Estimate by rounding to the indicated place value. 52,842 + 18,725; ten thousands A. 60,000 B. 70,000 C. 80,000 D. 90,000 1-1 Estimating with Whole Numbers Lesson Quiz for Student Response Systems 3. Estimate by rounding to the indicated place value. 7820 – 4860; thousands A. 1,000 B. 2,000 C. 3,000 D. 4,000 1-1 Estimating with Whole Numbers Lesson Quiz for Student Response Systems 4. Estimate by rounding to the indicated place value. 55,726 – 25,832; ten thousands A. 50,000 B. 40,000 C. 30,000 D. 20,000 1-1 Estimating with Whole Numbers Lesson Quiz for Student Response Systems 5. One gallon of floor polish is required to polish an area of 50 square feet. How many gallons are required to polish a floor 9 feet long and 11 feet wide? A. 1 gallon B. 2 gallons C. 3 gallons D. 4 gallons