1. Estimation Clothing Groceries Travel Costs Construction

2. Computation Estimation 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 Simplified mental calculation

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. Introduce students to estimation Discuss why estimation is important Value the role of estimation Find out where students use estimation and what they know about it Use real examples Use situations where an estimate is acceptable or essential Use the language of estimationlanguage of estimation Accept a range of estimates Discuss a range of strategies Share each others' strategies Expand the students’ repertoire of estimation strategies through discussion and teaching Expand the students’ repertoire of estimation strategies Do examples that aren’t too hard or too easy Do a little of it often Emphasize mental strategies Sometimes limit the time students have to solve a problem to encourage estimation Link estimation with the reasonableness of exact calculations

5. Estimation Vocabulary Front-end: take only the first number, cut-off (truncate) the other numbers Front-end  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 Rounding Compatible numbers: numbers grouped together to make computation easy Compatible numbers

6. 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.

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

8. Estimation Strategies

9. Front-End Estimation

10. 8857 4758 7045 +2110 8857 4758 7045 + 2110 8000 4000 7000 + 2000 Draw the line after the first number In each addend. Front-End Estimation

11. A.Between 11,000 and 15,000 B.Between 16,000 and 20,000 C.Between 20,000 and 25,000 D.Between 28,000 and 33,000 8000 4000 7000 +2000 21,000

12. 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. Front-end Estimation

13. A.Between 150,000 and 159,000 B.Between 160,000 and 169,000 C.Between 170,000 and 179,000 D.Between 180,000 and 189,000 60,000 70,000 10,000 + 30,000 170,000

14. Use Front-end Estimation Estimate the sum: 357,289 + 238,499 = _________ A. 500,000 B. 580,000 C. 595,000 D. 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? 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. 500,000

15. Front-end with Compensation Front-end estimation with compensation gives a check and an easy way to get a "ballpark" answer. Previous Example: 357,289 + 238,499 = _____  "3 hundred thousand plus 2 hundred thousand is 5 hundred thousand.  There is about another hundred thousand looking at the remainder of the two numbers, since 57 thousand is almost 60 thousand, and 38 thousand is almost 40 thousand.  The answer is about 600,000. Compensation is a great way to develop place value number sense and a very quick way to find an estimate.

16. Front-End is Precursor to Rounding In real life people estimate in a variety of ways, and the accuracy needed is determined by the reason for the estimate. It is important that children learn that they must consider the context in which they are working plays a part in the strategies they choose to solve a problem. Front-end estimation can be considered a precursor to rounding, since it uses the leading digits and doesn't involve any changing of amounts. It is a great way to introduce estimation, and as students become more proficient with using just the leading digits, the skill of making adjustments should be introduced. It is just one way to find a reasonable answer.

17. 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? Learn multiple estimation strategies. Always ask the question: Is the answer reasonable? 4,000,000 No, 2,000,000 is too low.

18. Rounding

19. 8857 4758 7045 +2110 8857 4758 7045 + 2110 9000 5000 7000 + 2000

20. A.Between 11,000 and 15,000 B.Between 16,000 and 20,000 C.Between 20,000 and 25,000 D.Between 28,000 and 33,000 9000 5000 7000 + 2000 23,000 Exact: 22,770

21. 247 6542 489 + 92 247 6542 489 + 92 200 6500 500 + 100

22. 200 6500 500 + 100 A. A little less than 7,000 B. A little more than 7,000 C. A little less than 8,000 D. A little more than 8,000 7300 Exact: 7,370

23. 5028 6732 1285 + 835 5000 7000 1000 + 1000 5028 6732 1285 + 835 14,000 Exact: 13,880

24. 5028 6732 1285 + 835 5000 6700 1300 + 800 5028 6732 1285 + 835 13,800 Exact: 13,880

25. Identify the estimation strategy Front-EndRounding

26. 3,876 5,814 3,176 + 7,895 4,000 6,000 3,000 + 8,000 3,000 5,000 3,000 + 7,000 Closer estimate 20,761 18,00021,000

27. 9,876 8,514 6,092 + 3,895 9,000 8,000 6,000 + 3,000 10,000 9,000 6,000 + 4,000 Closer estimate 28,37726,00029,000

28. Estimate Front-EndRounding vs.

29. A. Between 13,000 and 14,000 B. Between 12,000 and 13,000 C. Between 11,000 and 12,000 D. Between 10,000 and 11,000 5000 6700 1200 + 800 Exact:13700

30. 290 6840 481 + 94 Exact: 7705 A.Between 6,500 and 7,000 B.Between 7,000 and 7,500 C.Between 7,500 and 8,000 D.Between 8,000 and 8,500

31. Real World Problems

32. 23 Can I buy four for $100? Yes a)4 x $25 = $100 and $23 is less than $25 b)$23 rounds to $20 and 4 x $20 = $80 c)$23 rounds to $25 and 4 x $25 = $100 (high estimate) Explain

33. $37 Can I buy three for $100? No a)3 x $33 is $99, so 3 x $37 would be more than $100. b)3 x $40 is $120 Explain

34. The soccer ball would have to cost ______ or less for me to purchase five of them for $60. Can I buy five for $60? No a)5 x $15 = $75 which is more than $60. b)5 x $14 = $70 which is more than $60. c)$60 divided by 5 = $12, and $13.87 is more than $12.00. $12.00 Explain

35. $ 4.95 Can I buy three for $20? Yes a)3 x $5 = $15 Explain

36. 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, $4 + $7 + $8 = $19 No, 2 x $6 + 1 x $4 = $16

38. 0.1 or 10 0.0 1 or 100 0.00 1 or 1000 0.0001 or 10,000 1 digit2 digits