Transcript Directed Numbers

Form 1 Mathematics
Chapter 2 and Chapter 4
Correction of Open Book Quiz (Chapter 1)
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Today!!!
Correction and Parent Signature of
Close Book Quiz (Chapter 1)
24 Oct (Wed)
Standard Homework (I) – Orange
24 Oct (Wed)
You must hand in on time!
Result of Close Book Quiz
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Full mark: 36 (not 40!) and 10 bonus
Highest: 44
Lowest: 11
Average: 24.7
Number of students below 20: 11
Major Problems
Careless Mistakes!
Wrong calculations!
No English answers
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Result of Close Book Quiz
5th place:
LAW Cheuk Hang Ellis
WONG Pui Yin, Paul
4th place:
WU SHAN Hao Yi
3rd place:
FU Ling Yin
2nd place:
LI Ming Chun Edward
1st place:
LI Sai Kong
Congratulations!!!!!! Well done!!!!!!
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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.
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Now, $90 x 3 + $20 = $290!
Where is the last $10?
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Money is there!
Only the calculation is wrong!
The money given by the students (-)
◦ $90 x 3 = $270
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The money goes to (+)
◦ $250 (to meal) + $20 (to waiter) = $270!
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So, the information is correct.
The only problem is we have mixed up the
calculation!
If we can understand better Directed Number,
we will not have this problem!
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Arithmetic Operations
“+” – Addition
◦ Add… to…
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Difference
Times
Product
Over
Quotient
“” – Division
◦ Divide… by…
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Minus
“x” – Multiplication
◦ Multiply… by…
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Sum
“–” – Subtraction
◦ Subtract… from…
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Plus
“=“ – Equals/ is equal to
Ronald HUI
(+)(+)=(+)
(+)(–)=(–)
正正得正
正負得負
(–)(–)=(+)
(–)(+)=(–)
負負得正
負正得負
(+ A) + (+ B) = A + B
(+ A) + (– B) = A – B
(– A) + (+ B) = – A + B
(– A) + (– B) = – A – B
(+)(+)=(+)
(–)(–)=(+)
(+)(–)=(–)
(–)(+)=(–)
(+ A) – (+ B) = A – B
(+ A) – (– B) = A + B
(– A) – (+ B) = – A – B
(– A) – (– B) = – A + B
(+ A)  (+ B) = A  B
(+ A)  (– B) = – (A  B)
(– A)  (+ B) = – (A  B)
(– A)  (– B) = A  B
(+ A)  (+ B) = A  B
(+ A)  (– B) = – (A  B)
(– A)  (+ B) = – (A  B)
(– A)  (– B) = A  B
(+)(+)=(+)
(–)(–)=(+)
(+)(–)=(–)
(–)(+)=(–)
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Consider A as a variable (變數)
We know 3A = A + A + A or 3A = 3  A
So, can we write:
A  7 = A7
or
A  7 = 7A ?
Which is correct:
B  A = BA
or
B  A = AB ?
How about:
3A  4B? 3A4B / 12AB / 12BA / AB12
What if -3A  -4B?
Ronald HUI
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Pay attention to the followings:
Consider A as a variable (變數)
1A=A
A + A + A = 3A
A  A  A = A3
3A  4A = 12A2
Ronald HUI
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When we work on the followings, we should
put together the like terms and then simplify!
For examples:
1. A +2B +3A +4B = A +3A +2B +4B
= 4A + 6B
2. A -2B –3A +4B = A -3A -2B +4B
= (A-3A) + (-2B+4B)
= (-2A) + (2B)
= -2A +2B
Ronald HUI
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Page 77 of Textbook 1A
◦ Class Practice
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Addition of equality (等量相加)
X–7=2
X -7 +7 = 2 +7
X=9
X–7=2
X = 2 +7
X=9
Ronald HUI
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Subtraction of equality (等量相減)
X + 7 = 12
X +7 - 7 = 12 -7
X=5
X + 7 = 12
X = 12 -7
X=5
Ronald HUI
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Multiplication of equality (等量相乘)
X5=4
X 5  5 = 4  5
X = 20
X5=4
X=45
X = 20
Ronald HUI
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Division of equality (等量相除)
5X = 20
5X  5 = 20  5
X=4
5X = 20
X = 20  5
X=4
Ronald HUI
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Page 91 of Textbook 1A
◦ Class Practice
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Use a letter x to represent unknown number
設 x 為變數 (即想求的答案)
Follow the question and form an equation
根據問題，製造算式
Solve for x
算出 x 的值
Write answer in words (with units!)
寫出答案 (包括單位)
Ronald HUI
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If the sum of 3 consecutive (連續) numbers
are 69, find these numbers.
Let x be the smallest number.
Then, x+1 and x+2 are the next 2 numbers
Then,
x + (x+1) + (x+2) = 69
x + x +1 + x + 2 = 69
x + x + x + 1 + 2 = 69
3x
= 66 => x = 22.
So, the numbers are 22, 23 and 24.
Ronald HUI
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Page 99 of Textbook 1A
◦ Questions 3 – 9
Correction of Open Book Quiz (Chapter 1)
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Today!!!
Correction and Parent Signature of
Close Book Quiz (Chapter 1)
24 Oct (Wed)
Standard Homework (I) – Orange
24 Oct (Wed)
You must hand in on time!
Good Luck!
Enjoy the world of Mathematics!
Ronald HUI