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# Estimation

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1. Clothing Estimation Groceries Travel Costs Construction

2. 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

3. 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.

4. 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

5. 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.

6. Questions You Should Ask "How did you get that answer?" "Why do you think it's a reasonable answer?"

7. Estimation Strategies

8. Front-End Estimation

9. 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.

10. 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

11. 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.

12. 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

13. 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.

14. 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?

15. Rounding

16. Round each number to the thousandsplace to estimate the sum. 8857   4758 7045 + 2110 8857   4758 7045 + 2110 9000 5000 7000 + 2000

17. 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

18. Round each number to the hundredsplace to estimate the sum. 247 6542 489 + 92 247 6542 489 + 92 200 6500 500 + 100

19. 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

20. 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

21. 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

22. Identify the estimation strategy Front-End Rounding

23. 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

24. 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

25. Estimate vs. Front-End Rounding

26. 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

27. 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

28. Real World Problems

29. 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)

30. 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

31. 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

32. Can I buy three for \$20? CHESS Explain \$4.95 • Yes • 3 x \$5 = \$15

33. 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

34. Round Exact Estimation Front-End

35. 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