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, then3 – 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: 1. Size or Magnitude 2. 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): – Minus Negative Left Backward ________ South Right ________ + Plus Positive ________ West ________ Up

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? 0 0 00 0 Which side is positive & negative? +–

9. Directed numbers on a number line How do we write & say this? -2 -6 47 0 +– -6 4 -2 0 < say “minus six is less than four” < say “minus two is less than zero”

10. Directed numbers on a number line How do we write & say this? -2 -6 47 0 +– 7 -2 4 0 > say “seven is greater than minus two” > say “four is greater than zero”

11. Directed numbers on a number line How do we write & say this? -2 -6 47 0 +– 7 0 -2 -6 -2 0 4 7 > > > < < < This called “Descending Order” 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. Ronald HUI Enjoy the world of Mathematics!