Transcript Directed Numbers

Directed Numbers
Form 1 Mathematics
Chapter 1
Reminder
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Correction of Dictation 2 & Folder checking
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Correction of Closed Book Quiz (Ch. 0) and
Standard Homework 1
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8 Oct (Mon)
Extra Tutorial
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Today!!
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)
Result of Close Book Quiz
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Result of Open Book Quiz
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Highest: 41 (WU SHAN Hao Yi)
Lowest: 16
Average: 29.2
Number of students below 30: 17
Result of Close Book Quiz
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Highest: 48 (LI Sai Kong)
Lowest: 18
Average: 31.9
Number of students below 30: 13
Monday Extra Tutorial List
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Marks in Open Book Quiz < 30
and Marks in Close Book Quiz < 30
9 students
Class numbers:
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1, 7, 12, 14, 16, 17, 19, 24, 31
If any student wants to join, please talk to me
privately.
Introduction to Directed Numbers
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Numbers have two parts:
1.
2.
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Size or Magnitude
Sign or Direction
The sign of a number has two possibilities
(they are always opposites)
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 “+”):
Go up 3 steps: +3; Go down 4 steps: – 4
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”
Why do we learn Directed Numbers?
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In primary school, you learned:
Example 1: 3 + 7 = 10
“3 apples plus 7 apples is 10 apples”
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Example 2: 3 – 7 = – 4
Are “3 apples minus 7 apples negative 4 apples”?
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With Directed Numbers, the “–” now has meaning!
The Four Basic Operations
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Addition: 3 + 7
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Subtraction: 3 – 7
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Say “3 minus 7” or “The difference of 3 and 7” or “Subtract 7 from 3”
Multiplication: 3 × 7
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Say “3 plus 7” or “The sum of 3 and 7” or “Add 3 to 7”
Say “3 times 7” or “The product of 3 and 7” or “Multiply 3 and 7”
Division: 3 ÷ 7
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Say “3 divided by 7” or “The quotient of 3 and 7” or “Divide 3 by 7”
The Four Basic Operations
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Addition: “+” or “sum”
Subtraction: “–” or “difference”
Multiplication: “×” or “product”
Division: “÷” or “quotient”
The meaning of “+” and “—”
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In primary school you learned:
Example 1: 3 + 7 = 10
Direction or sign
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In high school, you learn Directed Numbers:
Example 1a: (+3) + (+7) = (+10)
Magnitude or size
What is this?
What sort of operation?
The Operation
Addition or Sum
The meaning of “+” and “—”
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“+” has two meanings:
1.
2.
Direction of directed number
Operation between two directed numbers
The meaning of “+” and “—”
Primary school:
 Example 2: 3 – 7 = –4
Directed Numbers:
 Example 2a: (+3) – (+7) = (–4)
Direction or sign
What is this?
What sort of operation?
An Operation
Subtraction or Difference
The meaning of “+” and “—”
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“–” has two meanings:
1.
2.
Direction of directed number
Operation between two directed numbers
Rules to Remember (p.50)
(+)(+)=(+)
(+)(–)=(–)
(–)(–)=(+)
(–)(+)=(–)
Rules to Remember (p.50)
(+)(+)=(+)
(+)(–)=(–)
正正得正
正負得負
(–)(–)=(+)
(–)(+)=(–)
負負得正
負正得負
Adding directed numbers
–
+
–
+
-6
-2
0
3
–
7
10
+
(+)(+)=(+)
(+7) + (+3) = (+10)
(–)(–)=(+)
(+)(–)=(–)
(–)(+)=(–)
Adding directed numbers
–
+
–
+
-6
-3
0
–
3
7
10
+
(+7) – (+3)
(+7) + (–3)
7–3 = 4
(+)(+)=(+)
(–)(–)=(+)
(+)(–)=(–)
(–)(+)=(–)
Examples
+3 + (+9)
= +3 + 9
= +12
–7 + (+12)
= –7 + 12
= +5
(+)(+)=(+)
(–)(–)=(+)
(+)(–)=(–)
(–)(+)=(–)
Time for Practice
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Page 51 of Textbook 1A
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Page 52 of Textbook 1A
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Class Practice
Questions 7 – 13
Page 20 of Workbook 1A
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Questions 2 – 7
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?
Good Luck!
Enjoy the world of Mathematics!
Ronald HUI