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Directed Numbers

Directed Numbers. Form 1 Mathematics Chapter 1. Reminder. Closed Book Quiz 26 Sep (Wed) Correction of Dictation 2 & Folder checking 28 Sep (Fri) Extra Tutorial 8 Oct (Mon) – based on Closed Book Quiz result Sudden Test on Summer Holiday Homework

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Directed Numbers

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  1. Directed Numbers Form 1 Mathematics Chapter 1

  2. Reminder • Closed Book Quiz • 26 Sep (Wed) • Correction of Dictation 2 & Folder checking • 28 Sep (Fri) • Extra Tutorial • 8 Oct (Mon) – based on Closed Book Quiz result • Sudden Test on Summer Holiday Homework • 8 – 12 Oct (the week after Athletics Meet)

  3. Mathematics nearby • Restaurant problem: • 3 students went to a restaurant for a meal of $250. • Everyone firstly paid $100. So, totally $300 • When the waiter came back with $50, they decided to get $30 back (everyone gets $10 back) and then left $20 for tips. • So, every student paid $90 only. • Now, $90 x 3 + $20 = $290! • Where is the last $10?

  4. Why we have negative numbers? • We know the difference between 3 and 4 is 1 • We also know 4 – 3 = 1 • But what do we have when 3 – 4 ? • If 3 – 4 = 1, then 3 – 4 + 4 = 1 + 4 3 = 5 !!!! • So, 3 – 4  1. Then, 3 – 4 = ??? • Now, we define 3 – 4 = – 1 (minus 1 / negative 1)

  5. Introduction to Directed Numbers • Numbers have two parts: • Size or Magnitude • Sign or Direction • Example: – 6 • What is the Magnitude? • What is the Sign? • Example: – 103 • What are the sign and magnitude?

  6. Introduction to Directed Numbers • The sign of a number has two possibilities (they are always opposites):

  7. Examples of Directed Numbers What does the negative mean? • Money in bank: +$1,100 – $950 • Students in class (36 students in class) Mon: – 2; Tue: – 1; Wed: 0; Thu: – 3; Fri:0 • World time: Sydney: +2; Rome: – 6; London: – 8; New York: – 13 • Stairs in the building (up is “+”): How do I write it? - Go up 3 steps - Go down 4 steps - Go up 15 steps

  8. Directed numbers on a number line Where does the ZERO go? Which side is positive & negative? – + 0 0 0 0 0

  9. Directed numbers on a number line How do we write & say this? – + -6 0 -2 4 7 < say “minus six is less than four” -6 4 < say “minus two is less than zero” -2 0

  10. Directed numbers on a number line How do we write & say this? – + -6 0 -2 4 7 > say “seven is greater than minus two” 7 -2 > say “fouris greater than zero” 4 0

  11. – + Directed numbers on a number line How do we write & say this? -6 0 -2 4 7 > > > 7 0 -2 -6 This called “Descending Order” < < < -2 0 4 7 This called “Ascending Order”

  12. Time for Practice • Page 37 of Textbook 1A • Class Practice • Ascending (遞升)  increasing • Descending (遞降)  decreasing • Page 38 of Textbook 1A • Questions 3 – 5 • Page 18 of Workbook 1A • Questions 2, 4, 7

  13. Enjoy the world of Mathematics! Ronald HUI

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