Upload
bathsheba-garrison
View
218
Download
0
Tags:
Embed Size (px)
Citation preview
Directed NumbersForm 1 Mathematics
Chapter 1
Reminder Correction of Dictation 2 & Folder checking
Today!! Correction of Closed Book Quiz (Ch. 0) and
Standard Homework 1 8 Oct (Mon)
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)
Result of Close Book Quiz Result of Open Book Quiz
Highest: 41 (WU SHAN Hao Yi) Lowest: 16 Average: 29.2 Number of students below 30: 17
Result of Close Book Quiz Highest: 48 (LI Sai Kong) Lowest: 18 Average: 31.9 Number of students below 30: 13
Monday Extra Tutorial List Marks in Open Book Quiz < 30
and Marks in Close Book Quiz < 30 9 students Class numbers:
1, 7, 12, 14, 16, 17, 19, 24, 31 If any student wants to join, please talk to me
privately.
Introduction to Directed Numbers Numbers have two parts:
1. Size or Magnitude2. Sign or Direction
The sign of a number has two possibilities (they are always opposites)
Examples of Directed NumbersWhat 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?
-2-6 4 70
+–
-6 4
-2 0
< say “minus six is less than four”
< say “minus two is less than zero”
Directed numbers on a number line
How do we write & say this?
-2-6 4 70
+–
7 -2
4 0
> say “seven is greater than minus two”
> say “four is greater than zero”
Directed numbers on a number line
How do we write & say this?
-2-6 4 70
+–
7 0 -2 -6
-2 0 4 7
> > >
< < <
This called “Descending Order”
This called “Ascending Order”
Why do we learn Directed Numbers? In primary school, you learned: Example 1: 3 + 7 = 10
“3 apples plus 7 apples is 10 apples”
Example 2: 3 – 7 = – 4Are “3 apples minus 7 apples negative 4 apples”?
With Directed Numbers, the “–” now has meaning!
The Four Basic Operations Addition: 3 + 7
Say “3 plus 7” or “The sum of 3 and 7” or “Add 3 to 7”
Subtraction: 3 – 7 Say “3 minus 7” or “The difference of 3 and 7” or “Subtract 7 from 3”
Multiplication: 3 × 7 Say “3 times 7” or “The product of 3 and 7” or “Multiply 3 and 7”
Division: 3 ÷ 7 Say “3 divided by 7” or “The quotient of 3 and 7” or “Divide 3 by 7”
The Four Basic Operations Addition: “+” or “sum” Subtraction: “–” or “difference”
Multiplication: “×” or “product” Division: “÷” or “quotient”
The meaning of “+” and “—” In primary school you learned: Example 1: 3 + 7 = 10
In high school, you learn Directed Numbers: Example 1a: (+3) + (+7) = (+10)
Direction or sign
Magnitude or size
What is this? The OperationWhat sort of operation?
Addition or Sum
The meaning of “+” and “—” “+” has two meanings:
1. Direction of directed number
2. 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? An Operation
What sort of operation? Subtraction or Difference
The meaning of “+” and “—” “–” has two meanings:
1. Direction of directed number
2. Operation between two directed numbers
Rules to Remember (p.50)
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
Rules to Remember (p.50)
( + ) ( + ) = ( + ) ( – ) ( – ) = ( + )
( + ) ( – ) = ( – ) ( – ) ( + ) = ( – )
正正得正 負負得正正負得負 負正得負
Adding directed numbers
+– -2-6 3 70
+–
+–
(+7) + (+3) = (+10)
10
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
Adding directed numbers
+– -3-6 3 70
+–
+–
(+7) – (+3)
= 4
10
(+7) + (–3)7 – 3
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
Examples
( + ) ( + ) = ( + )
( – ) ( – ) = ( + )
( + ) ( – ) = ( – )
( – ) ( + ) = ( – )
+3 + (+9)= +3 + 9= +12
–7 + (+12)= –7 + 12= +5
Time for Practice Page 51 of Textbook 1A
Class Practice Page 52 of Textbook 1A
Questions 7 – 13 Page 20 of Workbook 1A
Questions 2 – 7
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?
Ronald HUI
Good Luck!
Enjoy the world of Mathematics!