Transcript Directed Numbers

Directed Numbers
Form 1 Mathematics
Chapter 1
Reminder
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Closed Book Quiz
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Correction of Dictation 2 & Folder checking
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28 Sep (Fri)
Extra Tutorial
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26 Sep (Wed)
8 Oct (Mon) – based on Closed Book Quiz result
Sudden Test on Summer Holiday Homework
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8 – 12 Oct (the week after Athletics Meet)
Mathematics nearby
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Restaurant problem:
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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?
Why we have negative numbers?
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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)
Introduction to Directed Numbers
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Numbers have two parts:
1.
2.
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Example:
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Size or Magnitude
Sign or Direction
What is the Magnitude?
What is the Sign?
Example:
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–6
– 103
What are the sign and magnitude?
Introduction to Directed Numbers
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The sign of a number
has two possibilities
(they are always
opposites):
–
Minus
Negative
Left
Backward
________
South
Right
________
+
Plus
Positive
________
________
West
________
________
Up
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
Directed numbers on a number line
Where does the ZERO go?
Which side is positive & negative?
–
+
0
0
0
0
0
Directed numbers on a number line
How do we write & say this?
–
+
-6
-2
0
4
-6 < 4 say “minus six is less than four”
-2 < 0 say “minus two is less than zero”
7
Directed numbers on a number line
How do we write & say this?
–
+
-6
-2
0
4
7
7
> -2 say “seven is greater than minus two”
4
> 0 say “four is greater than zero”
Directed numbers on a number line
How do we write & say this?
–
+
-6
7
-2
> 0 > -2 > -6
-2 <
0 < 4 < 7
0
4
7
This called “Descending Order”
This called “Ascending Order”
Time for Practice
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Page 37 of Textbook 1A
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Class Practice
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Page 38 of Textbook 1A
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Ascending (遞升)  increasing
Descending (遞降)  decreasing
Questions 3 – 5
Page 18 of Workbook 1A
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Questions 2, 4, 7
Enjoy the world of Mathematics!
Ronald HUI