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Estimation in numbers and measurement

Form 1 Mathematics Chapter 5. Estimation in numbers and measurement. Lesson requirement Textbook 1A Workbook 1A Notebook (and folder) Before lessons start Desks in good order! No rubbish around!. Reminder. An estimation is a rough guess on the actual values.

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Estimation in numbers and measurement

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  1. Form 1 Mathematics Chapter 5 Estimationin numbers and measurement

  2. Lesson requirement • Textbook 1A • Workbook 1A • Notebook (and folder) • Before lessons start • Desks in good order! • No rubbish around! Reminder

  3. An estimation is a rough guess on the actual values. It does not represent the real answer. In real life, we seldom bring a calculator with us. So, we can use estimation to make some decisions. To get a better estimation, we need some techniques to round off a number. Estimation (p.189)

  4. Consider the “unwanted” leftmost digit. • If greater or equal to 5, add 1 to left digit next to it. • Otherwise, leave left digit next to it unchanged. • E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86 • Rounding off to nearest tenth digit (十分位) • Rounding off to nearest unit(個位) • Rounding off to nearest ten digit(十位) Rounding off a number (四捨五入)

  5. Rounding off to nearest tenth digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 21.3 + 15.8 + 31.0 + 3.2 + 5.9 = 77.2 • Rounding off to nearest unit (or one) • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 21 + 16 + 31 + 3 + 6 = 77 • Rounding off to nearest ten digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 20 + 20 + 30 + 0 + 10 = 80 • The actual answer is 77.14 Rounding off (四捨五入)

  6. Consider the leftmost digit. • Leave the first leftmost digit • Other change to 0! • E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86 • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 20.00 + 10.00 + 30.00 + 3.00 + 5.00= 20 + 10 + 30 + 3 + 5= 68 (Actual answer is 77.14) Front-end method (最左數字)

  7. Consider the “unwanted” digits. • All change to 0 • Add 1 to left digit next to them • E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86 • Rounding up to nearest tenth digit • Rounding up to nearest unit • Rounding up to nearest ten digit Rounding up (上捨入)

  8. Rounding up to nearest tenth digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 21.3 + 15.8 + 31.0 + 3.3 + 5.9 = 77.3 • Rounding up to nearest unit (or one) • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 22 + 16 + 31 + 4 + 6 = 79 • Rounding up to nearest ten digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 30 + 20 + 40 + 10 + 10 = 110 • Actual answer =77.14. All are over-estimated. Rounding up (上捨入)

  9. Consider the “unwanted” digits. • All change to 0 • Leave all left digits next to them unchanged • E.g. 21.29 + 15.78 + 30.97 + 3.24 + 5.86 • Rounding down to nearest tenth digit • Rounding down to nearest unit • Rounding down to nearest ten digit Rounding DOWN (下捨入)

  10. Rounding down to nearest tenth digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 21.2 + 15.7 + 30.9 + 3.2 + 5.8 = 76.8 • Rounding down to nearest unit (or one) • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 21 + 15 + 30 + 3 + 5 = 74 • Rounding down to nearest ten digit • 21.29 + 15.78 + 30.97 + 3.24 + 5.86 20 + 10 + 30 + 0 + 0 = 60 • Actual answer =77.14. All are under-estimated. Rounding down (下捨入)

  11. Page 195 of Textbook 1A • Class Practice • Page 200 of Textbook 1A • Questions 3 – 6 • Pages 93 - 94 of WB 1A • Questions 1 - 4 • SHW (I) • Questions 1 - 8 Time for Practice

  12. Choose one approximate value which is close in value to all (or most) numbers E.g. 21356 + 19587 + 22098 + 18657 + 20485 + 19444  20000 x 6 = 120000 Clustering method (集中數字)

  13. Choose a pair of numbers which makes the calculation easier • E.g. 345678  9  360000  9 = 40000 • E.g. 0.2468 x 163  0.25 x 160 = 40 Compatible numbers (相容數字)

  14. To change the order of the arithmetic operations for easy calculation • Only for first x then  • E.g. Translation (轉移數字)

  15. Make some adjustments during or after arithmetic operations • E.g. 6432x 7 • Consider 6432 x 7 = (6000 +432) x 7 • First, 6000 x 7 = 42000 • Then, 432 x 7  3000 (400 x 7 = 2800  432 x 7 is close to 3000) • So, the answer is about 45000 Compensation (補償數字)

  16. Page 200 of Textbook 1A • Questions 7 – 12 • Page 94 of WB 1A • Questions 5 - 6 • SHW (I) • Questions 9 - 14 Time for Practice

  17. Lesson • Get ready all the time! • Desk • Be order all the time! • Extra Tutorial • Final examination less than 50 • SHW (I) • 11 Jan (Fri) • OBQ & CBQ • Next week Reminder

  18. Enjoy the world of Mathematics! Ronald HUI

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