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F1 Mathematics
Positive and Negative Number
Lesson 1
By Isaac Yu
1S1 L01 Positive and Negative Number
Directed Number – Concept 1
−$28 : paying $30 by Octopus card,
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2S1 L01 Positive and Negative Number
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Number Line – Example
0
12
3
4−
3−
2−
1−
For 2, ¡3 and ¡3
2
(a) Represent above numberson the number line.
(b) Arrange them in ascending
order
3S1 L01 Positive and Negative Number
Number Line – 1Q
0
1
2
3
4−3−
2−
1−
For ¡1, ¡4 and ¡6
5
(a) Represent above numberson the number line.
(b) Arrange them in ascendingorder
4S1 L01 Positive and Negative Number
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Directed Number – Concept 2
0
12
3
4−
3−
2−
1−
If m > n and m and n are posi-
tive, then ¡m ¡ n
Helper: Make an example of m and n if necessary.
Challenger: What if m and n are not positive?
5S1 L01 Positive and Negative Number
Using Number Line – Example
–4 –3 –2 –1 0 1 2 3 4 5 6 7
Use number line to ¯nd
(a) (¡3) + (+4)
(b) (¡2) + (¡4)
6S1 L01 Positive and Negative Number
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Using Number Line – 1Q
–4 –3 –2 –1 0 1 2 3 4 5 6 7
Use number line to ¯nd
(a) (+5) + (+2)
(b) (¡
1) + (¡
3)
Reminder: “+” mean “move same direction as”
–4 –3 –2 –1 0 1 2 3 4 5 6 7
7S1 L01 Positive and Negative Number
Using Number Line – Example2
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3
Use number line to ¯nd
(a) (¡3)¡ (+4)
(b) (¡2)¡ (¡4)
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3
8S1 L01 Positive and Negative Number
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Using Number Line – 2Q
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3
Use number line to ¯nd
(a) (¡2)¡ (+5)
(b) (+4)¡ (¡4)
Reminder: “ – ” mean “move OPPOSITE direction as”
–2 –1 0 1 2 3 4 5 6 7 8 9
9S1 L01 Positive and Negative Number
Using Number Line – Example3
–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3
(¡4) + (+3) + (¡6)
10S1 L01 Positive and Negative Number
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Using Number Line – 3Q
–5 –4 –3 –2 –1 0 1 2 3 4 5 6
Use number line to ¯nd(+6)¡ (+7) + (¡4)
Helper:
“+” = “same”, “ – ” = “OPPOSITE” Challenger: Don’t use number line first.
11S1 L01 Positive and Negative Number
Using Number Line – 4Q
–8 –6 –4 –2 0 2 4 6 8 10 12 14
Use number line to ¯nd(¡7)¡ (¡5) + (+5)
Helper:
“+” = “same”, “ – ” = “OPPOSITE” Challenger:
Don’t use number line first.
12S1 L01 Positive and Negative Number
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Word Problem – Concept
Adam is originally at the west of the
bus stop. He walks 110 m to the eastand stops at a location which is 15m to the west of the bus stop. Findhis original location.
13S1 L01 Positive and Negative Number
Word Problem – 1Q
Betty is originally at the south of the her
school. She walks 200 m to the north and
stops at a location which is 12 m to the northof the school. Find her original location.
14S1 L01 Positive and Negative Number
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Word Problem – 2Q
Calvin takes a lift at the ground floor. He
goes 5 floors up, and goes 2 floor down. Hegoes 3 floors up again and goes 9 floors up
finally. What is his final location?
15S1 L01 Positive and Negative Number
Combining Sign – Concept
+, +
You are good.
+, –You are bad.
–, +You are not good.
–, –
You are not bad.
16S1 L01 Positive and Negative Number
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Combining Sign – Example
(¡14) + (+4)¡ (+11) + (¡13)¡ (¡4)
Helper:
“+” = “same”, “ – ” = “OPPOSITE” Challenger: Don’t use number line first.
17S1 L01 Positive and Negative Number
Combining Sign – 1Q
(¡13)¡ (¡2) + (¡6) + (+9)¡ (+14)
Helper: Replace “+”,” –” by “good”, “bad”,…Challenger:
Find the answer.
18S1 L01 Positive and Negative Number
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Combining Sign – 2Q
(¡13)¡ (¡15) + (¡8) + (¡13)¡ (¡13)
Helper: Replace “+”,” –” by “good”, “bad”,…Challenger: Find the answer.
19S1 L01 Positive and Negative Number
Combining Sign – 3Q
(¡10)¡ (+14)¡ (¡3) + (¡7) + (¡11)
Helper: Replace “+”,” –” by “good”, “bad”,…Challenger:
Find the answer.
20S1 L01 Positive and Negative Number
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Without Number Line – Example
(a) ¡23¡ 14 =
(b) ¡1000 + 7 =
(c) ¡500 + 724 =
21S1 L01 Positive and Negative Number
Without Number Line – 1Q
(a) 200¡ 215
(b) ¡300 + 36
(c) ¡250¡ 350
Helper: Translate it as “gain” and “loss” Challenger:
Find mentally within 3 seconds
22S1 L01 Positive and Negative Number
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Without Number Line – 2Q
(a) ¡12 + 36
(b) 17¡ 21
(c) ¡13¡ 25
23S1 L01 Positive and Negative Number
With Bracket – Example1
[(¡14)¡ (¡8)]¡ [¡7¡ 12 + (¡1)]
24S1 L01 Positive and Negative Number
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With Bracket – Concept
+(+ =
+(¡ =
¡(+ =
¡(¡ =
25S1 L01 Positive and Negative Number
With Bracket – 1Q
[(¡12)¡ (¡6)]¡ [(¡5)¡ (¡9)]¡ (¡15)
Helper: Removing “()”, then “[]” Challenger:
Do it mentally.
26S1 L01 Positive and Negative Number
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With Bracket – 2Q
(¡14)¡ [(¡5)¡ (¡10)¡ (¡13)] + (¡2)
Helper: Removing “()”, then “[]” Challenger: Do it mentally.
27S1 L01 Positive and Negative Number
Computer Challenge
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en=instructionsFirefoxHTML\Shell\Open\Command
or
28S1 L01 Positive and Negative Number
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Multiplication – Concept 1
Rewrite the following as addition
and evalute:(a) 3£ 2
(b) 3£ (¡4)
29S1 L01 Positive and Negative Number
Multiplication – 1Q
Rewrite 4 £ (¡25) as addition andevalute.
30S1 L01 Positive and Negative Number
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Multiplication – 2QEvaluate:
(a) (+2)£ (¡8)
(b) (¡10)£ (+3)
(c) (+5)£ (¡9)
(d) (¡10)£ (+15)
Helper: These answers are always
positive.
After you find the sign, just do it as normal multiplication.
Challenger: Find mentally within 3seconds
31S1 L01 Positive and Negative Number
Multiplication – Concept 2
(¡4)£ (3)=
(¡4)£ (2)=(¡4)£ (1)=(¡4)£ (0)=(¡4)£ (¡1)=
(¡
4)£
(¡
2)=
32S1 L01 Positive and Negative Number
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Multiplication – Concept 3
(+)£ (+)=
(+)£ (¡)=
(¡)£ (+)=
(¡)£ (¡)=
33S1 L01 Positive and Negative Number
Multiplication – 3QEvaluate:
(a) (+5)£ (+6) =
(b) (+12)£ (¡3) =
(c) (¡9)£ (+7) =
(d) (¡15)£ (¡4) =
Helper: + , + = + + , – = –
– , + = –
– , – = +
Challenger: Find mentally within 3seconds
34S1 L01 Positive and Negative Number
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Division – Concept 1
Evalute:
(a) (¡11)£ = (+44)
(b) (+44)¥ (¡11) =
35S1 L01 Positive and Negative Number
Division – 1Q
Evalute:
(a) (¡9)£ = (+117)
(b) (+117)¥ (¡9) =
36S1 L01 Positive and Negative Number
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Division – 2Q
Evalute:
(a) (+3)£ = (¡21)
(b) (¡21)¥ (+3) =
37S1 L01 Positive and Negative Number
Division – 3Q
Evalute:
(a) (¡5)£ = (¡45)
(b) (¡45)¥ (¡5) =
38S1 L01 Positive and Negative Number
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Division – Concept 2
(+)¥ (+)=
(+)¥ (¡)=
(¡)¥ (+)=
(¡)¥ (¡)=
39S1 L01 Positive and Negative Number
Division – Concept 3
(a)¥ (b) =a
b
(¡12)¥ (3) =¡12
3=
40S1 L01 Positive and Negative Number
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Division – 4Q
Evalute:
(a)(¡24)
(¡3)=
(b)(¡196)
(+14)=
41S1 L01 Positive and Negative Number