Program
of Study / Faculty :
Mathematics Education / MIPA
Name
of School : SMP N 4 Kalasan
Subject
: Mathematics
Class
/ Semester : VII / 1
Time
Allocation : 20 minutes
Standard
of Competence
Number
1. Understanding the properties
of arithmetic operations of number and use in problem solving
Basic
Competence
1.2 Using the properties of
integer arithmetic operations and fractions in problem solving
Indicator
1.2.1
Find the properties of addition on integers
1.2.2
Resolving problems relating to the properties of addition on integers
I.
Learning
Objectives
After the students work on
worksheets and discussing with the other students are expected to:
1. The
students can find the properties of addition on integers
2. The
students can use the properties of addition on integers in problem solving
II.
Learning
Materials
Addition Properties on Integers
a. Closure Law
Example:
1)
2 + 5 = 7
2
is an integer member
5
is an integer member
7
is an integer member
2)
17 + (-9) = 8
17
is an integer member
-9
is an integer member
8
is an integer member
3)
(-32) + (-11) = -43
-32
is an integer member
-11
is an integer member
-43
is an integer member
From
example 1), 2) and 3), the sum of two integers above is an integer.
Properties
above is Closure Law.
That
is, if a and b are element of integers then a + b also element of integer.
b. Commutative Properties
Example:
1) 7
+ 8 = 15
2) 8
+ 7 = 15
3) 2
+ (-17) = -15
4) (-17)
+ 2 = -15
5)
(-3) + (-5) = -8
6)
(-5) + (-3) = -8
From
example 1) and 2) it can be concluded:
7
+ 8 = 8 + 7
From example 3) and 4) it can be
concluded:
2
+ (-17) = (-17) + 2
From example 5) and 6) it can be
concluded:
(-3)
+ (-5) = (-5) + (-3)
Properties
above is Commutative Properties.
That
is, if a and b are element of integers then:
a + b = b + a
c. Associative Properties
Example:
1) (9
+ 8) + 2 = 19
2) 9
+ (8 + 2) = 19
3) ((-7)
+ 12) + (-13) = -8
4) (-7)
+ (12 + (-13)) = -8
5)
((-3) + (-1)) + (-5) = -9
6)
(-3) + ((-1) + (-5)) = -9
From
example 1) and 2) it can be concluded:
(9
+ 8) + 2 = 9 + (8 + 2)
From
example 3) and 4) it can be concluded:
((-7)
+ 12) + (-13) = (-7) + (12 + (-13))
From
example 5) and 6) it can be concluded:
((-3) + (-1)) + (-5) = (-3) + ((-1) + (-5))
Properties
above is Associative Properties.
That
is, if a, b, and c are element of integers then:
(a + b) + c = a + (b + c)
d. Identity Element
Example:
1) 8
+ 0 = 8
2) 0
+ 8 = 8
3) (-12)
+ 0 = -12
4) 0
+ (-12) = -12
From
example 1) and 2) it can be concluded:
8
+ 0 = 0 + 8 = 8
From
example 3) and 4) it can be concluded:
(-12) + 0 = 0 + (-12) = -12
For
every a is an integer then:
a + 0 = 0 + a = a
So, 0 is Identity Element on addition of integer.
e. Inverse of Addition
Example:
1)
-1 + 1 = 0
2)
-2 + 2 = 0
From example 1) and 2) it can be
concluded that, for every a is an integer then:
a
+ (-a) = (-a) + a = 0
So, -a is Inverse of Addition for every a is integer.
III.
Learning
Methods
Expository method and demonstration method.
IV.
Teaching
and Learning Activity
|
No
|
Teacher
Activity
|
Student
Activity
|
Duration
|
|
A.
Introduction
|
3
minutes
|
||
|
1
|
Teacher says greeting, and with students pray together
|
Students answer greetings and pray
|
30 seconds
|
|
2
|
Teacher reminded the students that have studied the topic
at a previous meeting, about the members of integers and arithmetic
operations on integers
|
Students listen and express the topic has been studied in
a previous meeting
|
1 minutes
|
|
3
|
Teacher tells the students the topic to be studied about addition
properties on integers
|
Students listen
|
30 seconds
|
|
4
|
Teacher motivate the students with give explanations about
the importance of knowing addition properties on integers for example in counting
many oranges
|
Students listen
|
1 minutes
|
|
B.
Main Activity
|
14
minutes
|
||
|
1
|
Teacher gives worksheet for each students
|
Students receive the worksheet
|
30 seconds
|
|
2
|
Teacher asks students to read the instructions on the
worksheet
|
Students read the instructions
|
30 seconds
|
|
3
|
Teacher gives one explanation of addition properties on
integers that is closure law in accordance with examples that have been
available at the worksheet
|
Students observe the examples
|
1 minutes
|
|
4
|
Teacher gives chance to students to solve the next problem
in worksheet so that students will find the commutative properties of
addition on integers
|
Students work on worksheet
|
2 minutes
|
|
5
|
Teacher asked one student to write the answers on the
whiteboard
|
Student working on the whiteboard
|
1 minutes
|
|
6
|
Teacher gives chance to students to solve the next problem
in worksheet so that students will find the associative properties of
addition on integers
|
Students work on worksheet
|
2 minutes
|
|
7
|
Teacher asked one student to write the answers on the whiteboard
|
Student working on the whiteboard
|
1 minutes
|
|
8
|
Teacher gives chance to students to solve the next problem
in worksheet so that students will find the element of identity on addition
of integers
|
Students work on worksheet
|
2 minutes
|
|
9
|
Teacher asked one student to write the answers on the
whiteboard
|
Student working on the whiteboard
|
1 minutes
|
|
10
|
Teacher gives chance to students to solve the next problem
in worksheet so that students will find the inverse of addition on addition
of integers
|
Students work on worksheet
|
2 minutes
|
|
11
|
Teacher asked one student to write the answers on the
whiteboard
|
Student working on the whiteboard
|
1 minutes
|
|
C.
Closing
|
3
minutes
|
||
|
1
|
Teacher gives the task some of the questions that must be
done by students
|
Students write down and solve the problem
|
1 minutes
|
|
2
|
Teacher asks some students to express what they have
learned
|
Students express have just learned
|
1 minutes
|
|
3
|
Teacher asks the students to learn the material for the
next meeting that is the properties of the operation of subtraction,
multiplication, and division of integers
|
Students listen
|
30 seconds
|
|
4
|
Teacher close the lesson with pray and greeting
|
Students pray and answer greeting
|
30 seconds
|
V.
Learning
Resources
Worksheet.
Wagiyo, dkk.
2008. Pegangan Belajar Matematika untuk
SMP/MTs Kelas VII. Jakarta: Galaxy Puspa Mega.
VI.
Assessment
Type :
Individual assignment
Form of Instrument :
Essay
A.
Question
Fill in the blank!
1. 8
+ (-3) = … + 8 = …
2. 7
+ … = 0
3. …
+ 0 = -3
4. 2
+ ((-4) + 6) = (… + …) + … = …
5. 6
+ 25 = 6 + (… + …) = …
B.
Answer
Key
1. 8
+ (-3) = (-3) + 8 = 5
2. 7
+ (-7) = 0
3. (-3)
+ 0 = -3
4. 2
+ ((-4) + 6) = (2 + (-4)) + 6 = 4
5. 6
+ 25 = 6 + (20 + 5) = 31
Yogyakarta,
April 3rd 2012
Fifi Yuniarti
NIM. 09301244030
Student Worksheet
Topic : Identify
the addition properties on integers
Purpose : Encourage
students to discover the addition properties on integers
Objectives : Students can find the addition
properties on integers
Equipment : Stationery
Instructions : Fill in the blank below
to get the addition properties on integers
Addition
Properties on Integers
Activity
1
1)
2 + 5 = ….
2
is an integer member
5
is an integer member
………………………
2)
17 + (-9) = ….
17
is an integer member
-9
is an integer member
………………………
3) (-32) + (-11) = ….
-32
is an integer member
-11
is an integer member
………………………
From
number 1), 2) and 3), the sum of two integers above is an
…………………………………………………………………………………………….
Properties
above is Closure Law.
That
is, if a and b are element of integers then a + b also element of integers.
Activity
2
4) 7
+ 8 = ….
5) 8
+ 7 = ….
6) 2
+ (-17) = ….
7) (-17)
+ 2 = ….
8)
(-3) + (-5) = ….
9)
(-5) + (-3) = ….
From
number 4) and 5) it can be concluded:
………………………………………………………………………………………...
From
number 6) and 7) it can be concluded:
………………………………………………………………………………………...
From
number 8) and 9) it can be concluded:
………………………………………………………………………………………...
Properties
above is Commutative Properties.
That
is, if a and b are element of integers then:
………………………………………………………………………………………...
Activity
3
10) (9
+ 8) + 2 = ….
11) 9
+ (8 + 2) = ….
12) ((-7)
+ 12) + (-13) = ….
13) (-7)
+ (12 + (-13)) = ….
14)
((-3) + (-1)) + (-5) = ….
15)
(-3) + ((-1) + (-5)) = ….
From
number 10) and 11) it can be concluded:
……………………………………………………………………………………………
From
number 12) and 13) it can be concluded:
…………………………………………………………………………………………….
From
number 14) and 15) it can be concluded:
………………………………………………………………………………………...
Properties
above is Associative Properties.
That is, if a, b, and c are element
of integers then:
…………………………………………………………………………………………….
Activity
4
16) 8
+ 0 = …
17) 0
+ 8 = …
18) (-12)
+ 0 = …
19) 0
+ (-12) = …
From
number 16) and 17) it can be concluded:
……………………………………………………………………………………………
From
number 18) and 19) it can be concluded:
…………………………………………………………………………………………….
For
every a is an integer then:
…………………………………………………………………………………………….
So,
…… is Identity Element on addition
integer.
Activity
5
20)
-1 + 1 = …
21)
-2 + 2 = …
From
number 15) and 16), it can be concluded, for every a is an integer then:
…………………………………………………………………………………………….
So,
…… is Inverse from a in the integer
addition operations.
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Name
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Student
ID
|
Signature
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