s1 l01 positive and negative number

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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,

: increasing the stored valueby $150.




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


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




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?


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)




Using Number Line – 1Q

–4 –3 –2 –1 0 1 2 3 4 5 6 7


(a) (+5) + (+2)

(b) (¡

1) + (¡

3)

Reminder: “+” mean “move same direction as”

–4 –3 –2 –1 0 1 2 3 4 5 6 7


Using Number Line – Example2

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3


(a) (¡3)¡ (+4)

(b) (¡2)¡ (¡4)

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3





–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3


(a) (¡2)¡ (+5)

(b) (+4)¡ (¡4)

Reminder: “ – ” mean “move OPPOSITE direction as”

–2 –1 0 1 2 3 4 5 6 7 8 9


Using Number Line – Example3

–8 –7 –6 –5 –4 –3 –2 –1 0 1 2 3

(¡4) + (+3) + (¡6)





–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.



–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.




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.


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.




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?


Combining Sign – Concept

+, +

You are good.

+, –You are bad.

–, +You are not good.

–, –

You are not bad.




Combining Sign – Example

(¡14) + (+4)¡ (+11) + (¡13)¡ (¡4)

Helper:

“+” = “same”, “ – ” = “OPPOSITE” Challenger: Don’t use number line first.


Combining Sign – 1Q

(¡13)¡ (¡2) + (¡6) + (+9)¡ (+14)

Helper: Replace “+”,” –” by “good”, “bad”,…Challenger:

Find the answer.





(¡13)¡ (¡15) + (¡8) + (¡13)¡ (¡13)

Helper: Replace “+”,” –” by “good”, “bad”,…Challenger: Find the answer.



(¡10)¡ (+14)¡ (¡3) + (¡7) + (¡11)

Helper: Replace “+”,” –” by “good”, “bad”,…Challenger:

Find the answer.




Without Number Line – Example

(a) ¡23¡ 14 =

(b) ¡1000 + 7 =

(c) ¡500 + 724 =


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




Without Number Line – 2Q

(a) ¡12 + 36

(b) 17¡ 21

(c) ¡13¡ 25


With Bracket – Example1

[(¡14)¡ (¡8)]¡ [¡7¡ 12 + (¡1)]




With Bracket – Concept

+(+ =

+(¡ =

¡(+ =

¡(¡ =


With Bracket – 1Q

[(¡12)¡ (¡6)]¡ [(¡5)¡ (¡9)]¡ (¡15)

Helper: Removing “()”, then “[]” Challenger:

Do it mentally.




With Bracket – 2Q

(¡14)¡ [(¡5)¡ (¡10)¡ (¡13)] + (¡2)

Helper: Removing “()”, then “[]” Challenger: Do it mentally.


Computer Challenge

Click Here

http://nlvm.usu.edu/en/nav/frames_asid_122_g_4_t_1.html?op

en=instructionsFirefoxHTML\Shell\Open\Command

or




Multiplication – Concept 1

Rewrite the following as addition

and evalute:(a) 3£ 2

(b) 3£ (¡4)


Multiplication – 1Q

Rewrite 4 £ (¡25) as addition andevalute.




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



(¡4)£ (3)=

(¡4)£ (2)=(¡4)£ (1)=(¡4)£ (0)=(¡4)£ (¡1)=

(¡

4)£

(¡

2)=





(+)£ (+)=

(+)£ (¡)=

(¡)£ (+)=

(¡)£ (¡)=


Multiplication – 3QEvaluate:

(a) (+5)£ (+6) =

(b) (+12)£ (¡3) =

(c) (¡9)£ (+7) =

(d) (¡15)£ (¡4) =

Helper: + , + = + + , – = –

– , + = –

– , – = +

Challenger: Find mentally within 3seconds




Division – Concept 1

Evalute:

(a) (¡11)£ = (+44)

(b) (+44)¥ (¡11) =


Division – 1Q

Evalute:

(a) (¡9)£ = (+117)

(b) (+117)¥ (¡9) =




Division – 2Q

Evalute:

(a) (+3)£ = (¡21)

(b) (¡21)¥ (+3) =


Division – 3Q

Evalute:

(a) (¡5)£ = (¡45)

(b) (¡45)¥ (¡5) =





(+)¥ (+)=

(+)¥ (¡)=

(¡)¥ (+)=

(¡)¥ (¡)=



(a)¥ (b) =a

b

(¡12)¥ (3) =¡12

3=




Division – 4Q

Evalute:

(a)(¡24)

(¡3)=

(b)(¡196)

(+14)=


s1 l01 positive and negative number

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