COT 1 Math 7 IM.pptxbbbbbbbbbbbbbbbbbbbbbbbbbb

DEMONSTRATION
TEACHING
C0T 1
MATHEMATICS 7
CHONA B. ANTONIO
Teacher II

PERFORMS ADDITION ON
INTEGERS.
M6NS-III-156

•Objectives:
•In this lesson, you are expected to:
•1. Use fundamental operations using different
approaches;
•2. Solve word problems involving fundamental
operations of integers.

• Conduct a speed test in adding whole numbers.
1. 5 + 6
2. 9 + 4
3. 2 + 5 + 4
4. 14 + 28
5. 11 + 10 + 22

•Problem: You want to buy house that costs
Php800,000. You only have Php500,000.
If you buy the house, what will your debt
be?
•If you spend more money than you have,
you go into debt.

Solution:
500,000
- 800,000
-300,000
If you spend more money than you have, you
go into debt. Debt is a good example of
working with negative integers.

Adding Integers
Use a number line to help visualize the addition of
integers.

5
2 7

3
6 9
 


 4
2 6


Adding Integers
Use a number line to help visualize the addition of
integers.


 3
8 5

 

 3
4 1

ADDING INTEGERS
•We can use positive and negative counters to model the addition
of integers.
Positive Integer Negative Integer
A positive integer paired with a negative integer form a
zero pair. The value of a zero pair is 0.

Do you notice a pattern or rule?
Adding Integers with like signs.
- When the signs are the same,
add the numbers together and
keep the sign.

WE NOW HAVE THE FOLLOWING
GENERALIZATION:
ADDING A POSITIVE INTEGER TO MEANS
MOVING ALONG THE REAL LINE A DISTANCE OF
UNITS TO THE RIGHT FROM . ADDING A
NEGATIVE INTEGER – TO MEANS MOVING
ALONG THE REAL LINE A DISTANCE OF UNITS
TO THE LEFT FROM.

Add -5 + 3
Remove all
the zero
pairs.
= -2

Add 4 + (-1) = 3
Remove all
the zero
pairs.

Add 3 + (-7)
Remove all
the zero pairs.
= -4

Add -6 + 5
Remove all
the zero
pairs.
= -1

DID YOU NOTICE A PATTERN OR RULE?
Adding integers with unlike signs.
- When the signs are different, subtract
the integers and keep the sign of the
larger digit.

Adding Integers with like signs.
- When the signs are the same, add the numbers together
and keep the sign.
-9 + -3 = -12
Adding integers with unlike signs.
- When the signs are different, subtract the integers and
keep the sign of the larger integer.
-9 + 3 = -6

ADD THE FF. INTEGERS.
1) -8 + 8 =
2) -9 + -11 =
3) 13 + (-19) =
4) 7 + 5 =
5) -12 + 10 =
6) -22 + (-16) =
7) 18 + (-5) =
0
-20
-6
12
-2
-38
13

PERFORMS SUBTRACTION ON
INTEGERS.
M6NS-III-156
DAY 2

PERFORMS SUBTRACTION ON INTEGERS.
M6NS-III-156
DAY 2
I LOVE NUMBERS!!!

Quick Review of Adding Integers
• Adding Rule #1
–If the signs are the same, add
as you normally do.
–Keep the same sign.
• 5 + 8 =
• -8 + -17 =
• Adding Rule #2
– If the signs are DIFFERENT,
pretend the signs aren’t there.
– Subtract the smaller from the
larger one.
– Keep the sign of the number with
the GREATEST Absolute Value.
• 19 + -11 =
• 24 + -86 =
13
-25
8
-62

THE HIGHEST POINT IN ASIA IS THE TOP OF
MOUNT EVEREST, AT A HEIGHT OF 29,028
FEET ABOVE SEA LEVEL. THE LOWEST
POINT IS THE DEAD SEA, WHICH 1312 FEET
BELOW SEA LEVEL. HOW MUCH HIGHER IS
MOUNT EVEREST THAN THE DEAD SEA?

3 Steps to Subtract
Integers
• Keep
–Keep the 1st
number
• Change
–Subtraction sign to Addition
• Opposite
–Write down the opposite of the 2nd
number
-Then add the way you normally do.

29,028 –(-1,312)
Keep Change Opposite
29,028 - (+1,312) =
Now follow the adding integers rules.
30,340

•Show video clip on
how to add integers.

Subtracting Integers
Use a number line to help visualize the subtraction of
integers.

 4
10 6


 2
8 10


 15
9 6

 

 4
10
 


 2
8
 

 15
9

GROUP ACTIVITY:
MATERIALS: FLASH CARDS/POWER POINT, SHOW-ME-BOARD
MECHANICS:
A.DIVIDE THE CLASS INTO 5 GROUPS.
B.CHOOSE A LEADER
C. TEACHER FLASHES NUMBERS ON THE SLIDES
D.LEADER WILL WRITE THE CORRECT ANSWER ON THE SHOW-ME-BOARD
E.THE FIRST GROUP TO FLASH THE CORRECT ANSWER WILL GET 1 POINT
F.THE TEACHER CHECKS THE ANSWERS.
G.THE GROUP HAVING THE MOST NUMBER OF CORRECT ANSWERS WINS.

-3 - 5 = -8
5 - (-3) = 8
-2 - (-10) = 8
-3 - 8 = -11

-6 - 8 = -14
+12
3 - (-9) =
-7 - (-3) = -4
-9 - 0 = -9

-9 – (-7)=-2
+26
16 - (-10) =
-9 - (-17) = -8
-4 – (-9) = +5

5 – (-1)= -6
+2
-8 - (-10) =
-9 - (+7) = -17
-4 – (9) = -13

PRACTICE… BY PAIR….
1.-7 – 15 =
2. 23 – 98 =
3. -48 - -
13 =
4.5 - -
6 =
5.17 – 8 =

PRACTICE… BY PAIR….
1.-7 – 15 =
2. 23 – 98 =
3. -48 - -
13 =
4.5 - -
6 =
5.17 – 8 =
-22
-75
-35
11
9

(Subtraction of integers means adding the minuend and the
opposite of the subtrahend.) or
Subtract Integers
1.Keep
Keep the 1st
number
2.Change
Subtraction sign to Addition
3.Opposite
Write down the opposite of the 2nd
number
-Then add the way you normally do.

Evaluation:
Subtract the following integers.

 4
13


 4
7
 

 17
12
 


 1
9

 9
6


 5
14
 


 4
3
 




 3
2
5
6

Evaluation:
Subtract the following integers.

 4
13 9


 4
7 11

 

 17
12
29
 


 1
9 8


 9
6 3



 5
14 19

 


 4
3
1
 




 3
2
5
6
 



 3
2
11
 


 3
13


 3
13 10


17
12


 4
3

Subtracting Integers
Evaluate the following expressions and problems.
15
6 
from
Subtract


 6
15 21

   




 7
9
2
8
4



 7
9
2
8


 7
9
6


 7
3

Multiplying Integers Day 3
Objective: To perform multiplication of integers

•What two numbers will give you a
product of 64 and a quotient of 4?

•16 and 4
•16 x 4 = 64
•16 ÷ 4 = 4

Subtract the ff.
18- 7=
-26-12=
35- (-8)=
20- (-20)=
-25-(-25)=

Multiplying Integers
 Rule 1:
Positive x Positive = POSITIVE
1)4(5) = 20
2)9(7) = 63

 Rule 2:
Negative x Negative = POSITIVE
1)-2(-7) = 14
2)-10 • -9 = 90

Rule 3:
Negative x Positive = NEGATIVE
1)-6(5) = -30
2)2 • -8 = -16

Rule 4:
Any Number x 0 = ZERO
1)-4(0) = 0
2)0(7) = 0

Why?
Positive x Positive = POSITIVE
Your bank records 5 deposits of Php300 each.
5(300) = +1500
Positive x Negative = NEGATIVE
Your bank records 5 withdrawals of Php30 each.
5(-300) = -1500
Negative x Positive = NEGATIVE
Your bank loses track of 5 deposits of Php300 each.
-5(300) = -1500
Negative x Negative = POSITIVE
Your bank loses track of 5 withdrawals of Php300 each.
-5(-300) = +1500

Some simple rules will help you when multiplying negative numbers.
The rules are the same for division.
•If there is one negative number, then the answer is negative.
•If two numbers are negative, then the answer is positive.
8 x 5 = 40 -8 x 5 = -40
8 x -5 = -40 -8 x -5 = 40
If the signs are the same = positive answer.
If theMultiplication of integers
++  Answer is +
--  Answer is +
+-  Answer is -
-+  Answer is -

GROUP ACTIVITY
• Materials: flash cards/power point, show-me-board
• Mechanics:
• a.Divide the class into 5 groups.
• b.Choose a leader
• c. Teacher flashes numbers on the slides
• d.Leader will write the correct answer on the show-me-board
• e.The first group to flash the correct answer will get 1 point
• f.The teacher checks the answers.
• g.The group having the most number of correct answers wins.

-15
(-3)( 5)=
(5)( -4)=
(-2)(-10)=
(-3)( 8)=
(-6)( 8)=
-20
20
-24
-48

-27
(3)(-9)=
(-7)( -4)=
(-9)(0)=
(-9)( -7)=
(16)( -10)=
28
0
63
-160

63
(-7)(-9)=
(-10)( 4)=
(-9)(-2)=
(-9)( -6)=
(-1)( -9)=
-40
18
54
-9

HOW DO WE MULTIPLY INTEGERS?
1. IF THE SIGNS ARE THE
SAME THE ANSWER
IS POSITIVE
2. IF THE SIGNS ARE
DIFFERENT
THE ANSWER
IS NEGATIVE

Try it with your seatmate:
6 x 8 = - 6 x 8 = 6 x -8 = -6 x -8 =
7 x 4 = -7 x 4 = 7 x -4 = -7 x -4 =
|-8 x 3| = |5 x (-2) – 1| =
2 x |3 – 9| =
6 x 8 = 48 - 6 x 8 = -48 6 x -8 = -48 -6 x -8 = 48
7 x 4 = 28 -7 x 4 = -28 7 x -4 = -28 -7 x -4 = 28
|-8 x 3| = 24 |5 x (-2) – 1| = 11 2 x |3 – 9| = 12
Pair-share: Multiply the ff.
Click for answers:

Evaluate the following:


 8
3
 

 20
0
 

 2
5
 
 5
10
  

 2
6
8
   


 1
2
9

ANSWERS:
Evaluate the following:


 8
3
 

 20
0
 

 2
5
 
 5
10
24

10
0
50

  

 2
6
8
   


 1
2
9
18

 

 2
48
96
 
 1
18

Multiply.
1. (-10)•3 2. (-4)•(-3)
3. 7•(-2) 4. 5•(-2)
YOU TRY IT!

Dividing
Integers
I positively
have negative
feelings about
this!
Let the
confusion End!
Day 4

DRILL: MULTIPLYING INTEGERS
= -30
= 12
= -14
= -10
1. (-10)•3
2. (-4)•(-3)
3. 7•(-2)
4. 5•(-2)

Review:
Multiply the following integers.
¿−𝟑𝟎
¿−𝟗𝟎
¿𝟑𝟓

Dividing Integers
Whenever we divide two integers
with “like” signs, the answer is
always positive.
¿
𝟏𝟔÷𝟒=𝟒
(−)÷(−)=+¿
−𝟏𝟐÷(−𝟒)=𝟑

Dividing Integers
Whenever we divide two integers
with “unlike” signs, the answer is
always negative.
What did you notice about the rules for
multiplying and dividing integers?
¿
𝟗÷ (−𝟑)=−𝟑
(−) ÷ ¿
If you said they’re exactly the same,
you’re right!
−𝟏𝟓÷𝟑=¿−𝟓

Some simple rules will help you when multiplying negative
numbers. The rules are the same for division.
•If there is one negative number, then the answer is
negative.
•If two numbers are negative, then the answer is positive.
40 ÷ 8 = 5
-40 ÷ -8 = 5
-40 ÷ 8 = -5
40 ÷ -8 = -5
If Division of Integers
++  Answer is +
--  Answer is +
+-  Answer is -
-+  Answer is -

It’s Time to Show Your
Stuff!
¿−𝟖
divide the following integers.
¿−𝟔

Group Activity: Divide the ff.:
1)
4)
5) (
2)
3)
¿ −𝟑 ¿+𝟑
¿ −𝟓
¿+𝟏
4

How do we divide integers?
When we divide two integers, the sign rules are different
than when we add or subtract signed numbers.
When divide two positive integers, the solution is
positive.
12 ÷ 3 = 4
16 ÷ 8 = 2
8 ÷ 8 = 1

When we divide two negative integers, the
solution is also positive.
(-12) ÷ (-3) = 4
(-16) ÷ (-8) = 2
(-8) ÷ (-8) = 1

When we divide one positive & one negative integer,
the solution is always negative, regardless of which is
larger or which is written first.
12 ÷ (-3) = - 4
(-16) ÷ 8 = -2
(-8) ÷ 8 = -1

Summary
Multiplying/Dividing Integers:
Positive + Positive = Positive
Negative + Negative = Positive
Positive + Negative = Negative

Try it with your seatmate:
54  6 =
-54  6 =
54  -6 =
-54  -6 =
|-12  -4| =
54  6 = 9 -54  6 = -9 54  -6 = -9
-54  -6 = 9 |-12  -4| = 3
Divide the ff.
Click for answers:

DIVIDE THE FF.
= 4
= -5
= +15
=-50
= +7
= -40
1. (-28)÷(-7)
2. (45)÷(-9)
3. (-75)÷(-5)
4. (-35)÷(-5)
5. (250)÷(-50)
6. (-80)÷2

Thank
you!
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etc. used belong to the
rightful owner. No
copyright infringement
intended

COT 1 Math 7 IM.pptxbbbbbbbbbbbbbbbbbbbbbbbbbb

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