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## Estimation

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**Clothing**Estimation Groceries Travel Costs Construction**Computation Estimation**Simplified mental calculation • Computation estimation is: • using some computation • using easy mental strategies • using number sense • using a variety of strategies • getting close to the exact answer • It is not: • just a guess • doing hand calculations • using a calculator • exact Quickly and easily get a number that is close enough to the exact answer to be useful**When do we estimate?**• When there is no need to have an exact answer and an estimate is good enough: for example "Do I have enough money?" • When there is not enough information to get an exact answer: for example, "About how many times will my heart beat in an hour?" • To check if the answer from a calculation is reasonable.**Estimation Vocabulary**• Front-end: take only the first number, cut-off (truncate) the other numbers • Adjusting with front-end:compensate for the values that were truncated • Compensation: adjust, amend, improve, revise, modify your estimate, make it bigger, make it smaller • Rounding: round to the nearest to the desired place value • Compatible numbers: numbers grouped together to make computation easy**Use a variety of strategies**• There is not really any such thing as a "wrong" estimate... • some estimates are less useful than others... • any estimate made using the original problem is a valid estimate. • The goal is not to find the one correct "estimate" but to have the skill to reason about the numbers being used, to be able to come up with a range that is suitable for using to predict the answer, and to have a quick and easy-to-do method for checking to see what a reasonable answer would be.**Questions You Should Ask**"How did you get that answer?" "Why do you think it's a reasonable answer?"**Front-End Estimation**8857 4758 7045 + 2110 8857 4758 7045 + 2110 8000 4000 7000 + 2000 Draw the line after the first number In each addend.**Estimate to choose the most reasonable answer.**Between 11,000 and 15,000 Between 16,000 and 20,000 Between 20,000 and 25,000 Between 28,000 and 33,000 8000 4000 7000 +2000 21,000**Front-end Estimation**62,899 10,236 75,000 + 37,596 62899 10236 75000 + 37596 60,000 10,000 70,000 + 30,000 Draw the line after the first number In each addend.**Estimate to choose the most reasonable answer.**Between 150,000 and 159,000 Between 160,000 and 169,000 Between 170,000 and 179,000 Between 180,000 and 189,000 60,000 70,000 10,000 + 30,000 170,000**Use Front-end Estimation**• Estimate the sum: 357,289 + 238,499 = _________ • 500,000 • 580,000 • 595,000 • 600,000 Is the front-end estimation reasonable? What could you do to improve the front-end estimate? What is the best estimate and why? 500,000 No, it is low. Estimate with compensation. 600,000 is a closer. Use compatible numbers since 60,000 + 40,000 would be about 100,000 more.**What error is acceptable?**• The numbers: “59”, “54”, “55” are all “50” using front-end estimation. • 1,999,999 + 1,999,999 = 2,000,000 • What is a better estimate? • Is the error acceptable? 4,000,000 No, 2,000,000 is too low. Learn multiple estimation strategies. Always ask the question: Is the answer reasonable?**Round each number to the thousandsplace to estimate the sum.**8857 4758 7045 + 2110 8857 4758 7045 + 2110 9000 5000 7000 + 2000**Estimate to choose the most reasonable answer.**Between 11,000 and 15,000 Between 16,000 and 20,000 Between 20,000 and 25,000 Between 28,000 and 33,000 9000 5000 7000 + 2000 23,000 Exact: 22,770**Round each number to the hundredsplace to estimate the sum.**247 6542 489 + 92 247 6542 489 + 92 200 6500 500 + 100**Choose the most reasonable answer.**A little less than 7,000 A little more than 7,000 A little less than 8,000 A little more than 8,000 200 6500 500 + 100 7300 Exact: 7,370**Round each number to the thousands to estimate the sum.**5028 6732 1285 + 835 5028 6732 1285 + 835 5000 7000 1000 + 1000 Exact: 13,880 14,000**Round each number to the hundreds to estimate the sum.**5028 6732 1285 + 835 5028 6732 1285 + 835 5000 6700 1300 + 800 Exact: 13,880 13,800**Identify the estimation strategy**Front-End Rounding**Describe the estimation strategy used.**Front-End Rounding 3,876 5,814 3,176 + 7,895 4,000 6,000 3,000 + 8,000 3,000 5,000 3,000 + 7,000 20,761 21,000 18,000 Which method would you use and why? Closer estimate**Describe the estimation strategy used.**Rounding Front-End 9,876 8,514 6,092 + 3,895 9,000 8,000 6,000 + 3,000 10,000 9,000 6,000 + 4,000 28,377 26,000 29,000 Which estimation strategy would you use and why? Closer estimate**Estimate**vs. Front-End Rounding**Estimate to choose the most reasonable answer.**• Between 13,000 and 14,000 • Between 12,000 and 13,000 • Between 11,000 and 12,000 • Between 10,000 and 11,000 5000 6700 1200 + 800 Exact:13700**Estimate to choose the most reasonable answer.**Between 6,500 and 7,000 Between 7,000 and 7,500 Between 7,500 and 8,000 Between 8,000 and 8,500 290 6840 481 + 94 Exact: 7705**Can I buy four for $100?**23 Explain • Yes • 4 x $25 = $100 and $23 is less than $25 • $23 rounds to $20 and 4 x $20 = $80 • $23 rounds to $25 and 4 x $25 = $100 (high estimate)**Can I buy three for $100?**$37 Explain • No • 3 x $33 is $99, so 3 x $37 would be more than $100. • 3 x $40 is $120**Can I buy five for $60?**$13.87 Explain • No • 5 x $15 = $75 which is more than $60. • 5 x $14 = $70 which is more than $60. • $60 divided by 5 = $12, and $13.87 is more than $12.00. The soccer ball would have to cost ______ or less for me to purchase five of them for $60. $12.00**Can I buy three for $20?**CHESS Explain $4.95 • Yes • 3 x $5 = $15**Would you have enough money?Estimate to find your answer.**• If you buy 3 items that cost $4.93 each, will $15.00 be enough to buy all 3 items? Explain. • If you buy 2 items for $6.29 and 1 item for $3.55 will $15.00 be enough? Explain. • If you buy items for $4.32, $6.90, and $7.86, will $18.00 be enough? Explain. Yes, 3 x $5 = $15 (high estimate) No, 2 x $6 + 1 x $4 = $16 No, $4 + $7 + $8 = $19**Round**Exact Estimation Front-End**0.01**or 100 0.001 or 1000 0.0001 or 10,000 0.1 or 10 1 digit 2 digits Round Exact Estimation Front-End