Contoh RPP bilingual Kelas 7 semester 1 tentang bilangan bulat
LESSON PLAN
School
: …………….
Subject
: Mathematics
Main Topic
: Number
Grade/Semester
: VII/I
Meeting
: 9 meetings
A. Standard Competence
1. Understanding the properties of arithmetic operations and use it in solving
problem.
B. Basic Competence
1.1 Doing arithmetic operations on integers and fractions.
C. Indicators
1. Doing arithmetic operations (addition, subtraction, multiplication and division)
of integers and also mixed operations.
2. Determining the properties of arithmetic
operations (addition, subtraction,
multiplication and division) of integers.
3. Doing arithmetic operation (multiplication, division and exponential) on
exponential integers and also determine the properties.
4. Calculating squared and cubed then the root of square and the root of cubed in
integers.
5. Changing fractions into another form.
6. Determining equivalent fractions.
7. Comparing and ordering the fractions.
8. Explaining decimals, percent and per mill.
9. Doing arithmetic operations (addition, subtraction, multiplication, division and
exponential) of fractions.
10. Determining scientific notation.
11. Determining the rounded of decimals fractions.
12. Give example of very large and very small numbers such as mega/million (106),
giga/billion (109), tera/trillion (1012), micro (10-6), nano (10-9) and pico (10-12)
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D. Learning Objectives
After following this learning activities, Studentss can:
First Meeting :
1. Give example about integers.
2. Determine the position of integers in number line
3. Do arithmetic operations (addition and subtraction) of integers.
4. Determine the properties of arithmetic operations (addition and subtraction)of
integers.
Second Meeting :
1. Do arithmetic operations (multiplication and division) of integers and also mixed
operation.
2. Determine the properties of arithmetic operations (multiplication and division)
of integers.
Third Meeting :
Do arithmetic operation (multiplication, division and exponential) on exponential
integers and also determine the properties.
Fourth meeting :
Calculate squared and cubed then the root of square and the root of cubed in
integers.
Fifth Meeting :
1. Give example about fractions
2. Explaine the definition of fractions and types of fraction.
3. Change fractions to another form.
Sixth Meeting :
1. Determine the position of fractions in number line.
2. Determine equivalent fractions.
3. Compare and order the fractions.
Seventh Meeting :
Explain decimals, percent and per mill.
Eigth Meeting :
Do arithmetic operations (addition, subtraction, multiplication, division and
exponential) of fractions.
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Ninth Meeting :
1. Determine scientific notation.
2. Determine the rounded of decimals fractions.
3. Give example of very large and very small numbers such as mega/million (106),
giga/billion (109), tera/trillion (1012), micro (10-6), nano (10-9) and pico (10-12)
E. Learning Material : Integers and fractions
F. Time Allocation
: 23 x 40 minutes
G. Method of Lesson
Inquiry, expository, discussion and giving task.
H. Learning Resources :
1. “Mathematics Students Book Year VII” Published by Ministry of National
Education
2. Bilingual Book “Mathematics for Junior High School Year VII” written by
Marsigit, Published by Yudhistira
3. “Matematika untuk SMP Kelas VII” written by M. Cholik Adinawan, Published
by Erlangga
Topic integers in The Al-Qur’an
: Q.S At-Taubah:36, Q.S Al-Fajr:1-3.
Topic fractions in The Al-Qur’an
:Q.S An-Nisaa:11-12
I. Learning Activities
First Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
b. Teacher gives some rules while studying mathematics.
c. Teacher tells the learning objectives of this lesson.
Motivation
: Explaining the function of integers in daily life. For
example to read the temperature and etc.
Prerequisite Topic : Whole number
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Time
10’
2.
Core Activities
Time
Exploration
a. Students mention the appliances in our daily life that use integers.
5’
b. Students do pre test about arithmetic operations of integers. This pre 15’
test to check the competence of Studentss about integers.
Elaboration
c. Students write vocabularies about this topic.
10’
d. Students explain the meaning of integers.
10’
e. Students demonstrate how to put integers in number line.
10’
f. Teacher gives
illustration in power point to do addition and 15’
subtraction of integers. This illustration from a media with the name
“MOLAT or Ruler of Integers”
g. Students determine the properties of addition and subtraction of 10’
integers.
h. Students do exercise about addition and subtraction of integers.
15’
Confirmation
i. Students give exercise to the teacher.
5’
j. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
The Problem for Pre Test
1) 8 + 12 − 36 = −16
2) 24 + ( 12 − 4 ) = 32
3) 11 + 6 × 8 = 59
4) 12 × ( 4 + 2 ) − 12 = 60
5) 3 + 4 × ( 9 − 3 ) = 27
6) 3 × ( 10 − 2 ) : 4 + 4 = 10
7) ( 18 − 3 ) × 3: 5 = 9
8) −2 + 6 × 3 − 10 = 6
9) 17 − 8 × 2 + 6 × ( 11 − 5 ) = 37
10) 10: ( 5 + 5 ) × 9 × 9 = 81
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The Problem for Exercise
1)
2)
3)
4)
5)
6)
45 + 56 × 48 − 216 ∶ 9 = 2709
15762 ∶ 37 − 512 + 96 × 72 = 6826
19 × 27 + 5.205 ∶ 15 − 269 = 591
( −9 ) − 6 × ( −72 ) : 16 − 20 = -2
( 8.742 − 9.756) × 36 ∶ ( 4.356 − 4.360 ) = 9126
168 ∶ ( 17 − 24 ) × ( −19 + 15 ) = 6
7) 24 × 240 ∶ ( −36 + 40 ) × ( −23 + 17 )
8) 360 ∶ 15 + ( 27 − 32 ) × ( −9 + 16 )
= -18
9) 420 ∶ ( −7 ) + 70 − 30 × ( −8 ) + 15 = 265
10) 13 × 140 ∶ ( −7 ) + ( −2 ) × 19 = -298
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= −240
“Molat”
Ruler of Integer
Using “Molat” show by line number
Addition and Subtraction
Prerequisite:
For addition, the movement is forward
For subtraction, the movement is backward
Row direction based on integer’s kind. Positive integer, “Molat” go to the
right. Negative integer, “Molat” go to the left.
Example:
4+3=7
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
4 + (-3) = 1
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) + 3 = (-1)
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) + (-3) = (-7)
-8 -7
4–3=1
-8 -7
4 – (-3) = 7
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) – 3 = (-7)
-8 -7
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-6 -5 -4
(-4) – (-3) = (-1)
-8 -7
-6 -5 -4
-3 -2 -1
Notes:
= movement backward
= movement forward
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0
1
2
3
4
5
6
7
Second Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about addition and
subtraction of integers.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations are important while studying
mathematics and another subject. For the next topic
will use this operation
Prerequisite Topic : Addition and subtraction of Integers
2
Core Activities
Time
Exploration
a. Students explain how to do multiplication and division of integers. 5’
Because of the students ever studied before in elementary school.
Elaboration
b. Students tell the rule of multiplication and division of integers
10’
c. Students discuss the properties of multiplication and division of 10’
integers.
d. Students remind about the rule of mixed operation and give example 10’
about mixed operation.
e. Students do exercise about multiplication, division and mixed 15’
operation of integers.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
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Third Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations on exponential integers are
important for studying mathematics and another
subject.
Prerequisite Topic : Arithmetic operations of Integers
2.
Core Activities
Time
Exploration
a. Students remind again about positive and negative integers exponent.
10’
Elaboration
b. Students do worksheet to find the properties of arithmetic operations 25’
(multiplication, division and exponential) on exponential integers.
c. Discuss student’s worksheet.
25’
d. Students do exercise about arithmetic operations (multiplication, 30’
division and exponential) on exponential integers.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
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NAME:
1.
TITLE:
Exponential Integers
2.
1. Multiplication on Exponential Integers
2 4 × 25 = (2 × 2 ×……….) × (2 ×……………………………..)
= 2 × 2 × 2 ……………………..
=2…
= 2 … + ….
So, 24 × 25 = ………
Conclusion :
am × a n = …………..; For a is an integers, the exponents are m and n
2. Division on Exponential Integers
5
5
=
=
5 × 5 × 5 ……………………. .
5 × 5 × ……….
5 × 5 × 5 × 5
5 × 5 ………….
× 5 × …
= 5 ×
= 5 …..
= 5 ….
So,
⋯..
= ………
Conclusion :
= …………..; For a is an integers, the exponents are m and n, m > n
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1
5
=
So,
5 ….
5 ….
⋯
= 5 ….
= 5 …..
= 5 …..
Conclusion
( )
=
( )
=
……
……
3. Exponential on Exponential Integers
(
)× (
) = (
= (
So, (
×
=
….
=
…..× …..
) × ………. . ……
)× (
×
×
……. ) × ………………. . …………
) = ………..
Conclusion :
(
) = …………..; For a is an integers, the exponents are m and n
Exercise:
1. Simplify the following problems
a. 3 × 3 =
− ) ×( +
b. ( +
c. 7 : 7 × 7 =
d.
×
=
e. ( 5 : 5 ) =
f.
(
)
×
(
)
=
2. Determine the value of n:
a. 9 = 3
b. 5 × 25 = 5
c. 16: 2 = 2
d. 81 ∶ 3 = 3
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− ) =
Rubric for Problem Sheet
Problem
1.
Indicators
Can fill the blank with right answer
Can make the conclusion
2.
Can fill the blank with right answer
Can make the conclusion
3.
Can fill the blank with right answer
Can make the conclusion
4.
Can fill the blank with right answer
Can make the conclusion
1= achieve the indicator less than 25%
2= achieve indicator between 25%-50%
3=achieve indicator indicators between 50%-75%
4= achieve indicator more than 75%
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1
2
3
4
Fourth Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations on exponential integers.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic we can apply to another subject, for
example in physics and chemistry.
Prerequisite Topic : Arithmetic operations of exponential integers.
2.
Core Activities
Time
Exploration
a. Students remind again about squared and cubed then the root of 5’
square and the root of cubed in integers.
Elaboration
b. Students discuss to calculate square and the root of square in integers 5’
without and with calculator.
c. Students discuss to calculate the root of square in decimal numbers.
5’
d. Students discuss to calculate cubed and the root of cubed of integers 5’
with calculator.
e. Students do exercise about calculate squared and cubed then the root 20’
of square and the root of cubed in integers.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz
10’
c. Students are given homework
5’
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Problems for quiz:
Calculate:
1) (-2)3
132496
2)
3) Given : √7 04 = 2 ,65
,
Determine: a. √
Key of problems:
0 ,000704
√70 ,4 = 8 ,39
and
b. √
70400000
1) (-2)3 = -8
2)
132496
364
3) a.
√0 ,000704 = √7 ,04: √10000 = 2 ,65 ∶ 100 = 0 ,0265
b.
√70400000 = √70 ,4 × √1000000 = 8 ,39 × 1000 = 8390
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Fifth Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students ask the teacher about homework that difficult for them.
c. Teacher tells the learning objectives of this lesson.
Apperception
: Students remind about fractions that already studied
in elementary school.
Motivation
: We can apply this topic in our daily life. For
example we want to divide something.
Prerequisite Topic : Integers.
2.
Core Activities
Time
Exploration
a. Teacher guides students to mention the problems in our daily life that 10’
use fractions.
b. Give pre test about arithmetic operations on fractions to check 15’
student’s competence about fractions.
Elaboration
c. Students explain the meaning of fractions.
10’
d. Students discuss about the type of fractions.
15’
e. Students change form of fractions to another form.
15’
f. Students do the exercise about changing form of fractions to another 25’
form.
Confirmation
5’
h. Students give exercise to the teacher.
5’
i. Students give questions related to this topic
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
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Problem for Quiz
1. Write down the following fractions in the form of mixed fractions.
b.
a.
2. Write down the following fractions in the form of improper fractions.
b. 12
a. 8
3. Determine two equivalent fractions of:
b.
a.
4. Write in the simplest form:
a.
b.
5. Use the sign > or < for the relation of these fractions.
a.
b. ……
……
6. Arrange these fractions from the smallest to the biggest :
7. Simplify these fractions:
a.
+ (−
)=
b. −1 − −4
=
8. Simplify these fractions:
a. − × 2 =
b. 1 : 2 =
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,
Sixth Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about type of fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic will help us to do arithmetic operations
of fractions.
Prerequisite Topic : Integers.
2.
Core Activities
Time
Exploration
a. Students try to put fractions in number line. Because it is similar with 5’
to put integers in number line.
Elaboration
b. Students discuss about equivalent fractions.
10’
c. Students discuss to compare and order fractions.
10’
d. Students do exercise about equivalent, comparing and ordering 15’
fractions.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
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Problems for Quiz :
1) Determine two equivalent fractions of
2) Which fractions is greater
and ?
3) Arrange the following fractions in order, with the smallest on the left
,
, and .
,
Key of problems:
1)
=
=
2) LCM of 3 and 7 is 21
and
=
=
So, <
3) LCM of 15, 10, 20 and 4 is 60
13
15
So,
=
52
60
,
, ,
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9
10
,
=
54
60
,
11
20
=
33
3
60
4
=
45
60
Seventh Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about equivalent,
comparing and ordering fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: We can apply this topic in our daily life. For
example in economic activities.
Prerequisite Topic : Fractions
2
Core Activities
Time
Exploration
a. Students tell their experience about decimals, percent and per mill in 10’
daily life.
Elaboration
b. Students discuss about decimals, percent and per mill.
15’
c. Students do exercise about decimals, percent and per mill.
15’
Confirmation
d. Students give exercise to the teacher.
5’
e. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
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Problems for Quiz :
1) Write as decimal.
2) Write 32% as simple fractions.
3) Write in per mill.
Key of problems:
1)
= 0,25
2) 32% =
3)
=
=
× 1.000 %0 =500 %0
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Eighth Meeting (3 x 40 Minutes)
1.
Opening Activities
Time
10’
a. Teacher prepares the students for learning mathematics.
b. Students remind the topic in the last meeting about decimals, percent
and per mill.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations of fraction are important.
Because we usually use it while studying
mathematics.
Prerequisite Topic : Fractions
2.
Core Activities
Time
Exploration
a. Students remind again about arithmetic operations (addition, 10’
subtraction, multiplication and division) of fractions. Because the
Students already studied before in elementary school.
Elaboration
b. Students discuss about arithmetic operations (addition, subtraction, 20’
multiplication,
division, exponential and mixed operation) of
fractions.
20’
c. Students determine the properties of exponential fractions.
d. Students
do
exercise
about
subtraction, multiplication,
arithmetic
division,
operations
(addition, 30’
exponential and mixed
operations) of fractions.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
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Problems for Quiz:
1)
+ (− )
2) 5,8 – 4,37
1
3
3) 1 2 4
6 1
:
4) 5 2
5)
( , )
( , )
Key of problems:
1)
+
−
= − =
2) 5,8 – 4,37 =
3) 1 ×
4)
5)
=
: =
( , )
( , )
×
×
=
= ( 0,3)
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−
=
=
−
=
−
=
= 3
= ( 0,3) = 0,09
= 1,43
Ninth Meeting (3 x 40 Minutes)
1
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations of fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic will help us to simplify the result of
arithmetic operations and another subjects.
Prerequisite Topic : whole number
2.
Core Activities
Time
Exploration
a. Students discuss in pairs about the rule of scientific notation and the 15’
rounded of decimals fractions.
Elaboration
b. Students explain in front of the class rule of scientific notation and the 15’
rounded of decimals fractions.
c. Teacher gives more explanation about scientific notation and rounded 10’
decimals fractions.
d. Students discuss about very large and very small numbers such as 15’
mega/million (106), giga/billion (10 9), tera/trillion (1012), micro (10-6),
nano (10 -9) and pico (10-12)
e. Students do exercise about scientific notation and the rounded of 25’
decimals fractions.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for Quiz :
1) Write these number in scientific form:
a. 2.732
b. 0,00000007051
2) Round this following numbers off up to two decimal places.
a. 6,321
b. 78,4934
Key of problems:
1) a. 2.732 = 2,732 x 10 3
b. 0,00000007051= 7,051 x 10 -8
2) a. 6,321 = 6,32
b. 78,4934 = 78,49
J. Assessment :
1. Technical assessment
: observation and written test.
2. Procedure of assessment
: process assessment and last result.
3. Instrument of assessment
: Exercise, quiz and daily test.
Padang,
June 2011
Known By:
Headmaster of SMPN
………………………….
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Mathematics Teacher
Nikmatul Husna, S.pd
School
: …………….
Subject
: Mathematics
Main Topic
: Number
Grade/Semester
: VII/I
Meeting
: 9 meetings
A. Standard Competence
1. Understanding the properties of arithmetic operations and use it in solving
problem.
B. Basic Competence
1.1 Doing arithmetic operations on integers and fractions.
C. Indicators
1. Doing arithmetic operations (addition, subtraction, multiplication and division)
of integers and also mixed operations.
2. Determining the properties of arithmetic
operations (addition, subtraction,
multiplication and division) of integers.
3. Doing arithmetic operation (multiplication, division and exponential) on
exponential integers and also determine the properties.
4. Calculating squared and cubed then the root of square and the root of cubed in
integers.
5. Changing fractions into another form.
6. Determining equivalent fractions.
7. Comparing and ordering the fractions.
8. Explaining decimals, percent and per mill.
9. Doing arithmetic operations (addition, subtraction, multiplication, division and
exponential) of fractions.
10. Determining scientific notation.
11. Determining the rounded of decimals fractions.
12. Give example of very large and very small numbers such as mega/million (106),
giga/billion (109), tera/trillion (1012), micro (10-6), nano (10-9) and pico (10-12)
Document of Nikmatul Husna
D. Learning Objectives
After following this learning activities, Studentss can:
First Meeting :
1. Give example about integers.
2. Determine the position of integers in number line
3. Do arithmetic operations (addition and subtraction) of integers.
4. Determine the properties of arithmetic operations (addition and subtraction)of
integers.
Second Meeting :
1. Do arithmetic operations (multiplication and division) of integers and also mixed
operation.
2. Determine the properties of arithmetic operations (multiplication and division)
of integers.
Third Meeting :
Do arithmetic operation (multiplication, division and exponential) on exponential
integers and also determine the properties.
Fourth meeting :
Calculate squared and cubed then the root of square and the root of cubed in
integers.
Fifth Meeting :
1. Give example about fractions
2. Explaine the definition of fractions and types of fraction.
3. Change fractions to another form.
Sixth Meeting :
1. Determine the position of fractions in number line.
2. Determine equivalent fractions.
3. Compare and order the fractions.
Seventh Meeting :
Explain decimals, percent and per mill.
Eigth Meeting :
Do arithmetic operations (addition, subtraction, multiplication, division and
exponential) of fractions.
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Ninth Meeting :
1. Determine scientific notation.
2. Determine the rounded of decimals fractions.
3. Give example of very large and very small numbers such as mega/million (106),
giga/billion (109), tera/trillion (1012), micro (10-6), nano (10-9) and pico (10-12)
E. Learning Material : Integers and fractions
F. Time Allocation
: 23 x 40 minutes
G. Method of Lesson
Inquiry, expository, discussion and giving task.
H. Learning Resources :
1. “Mathematics Students Book Year VII” Published by Ministry of National
Education
2. Bilingual Book “Mathematics for Junior High School Year VII” written by
Marsigit, Published by Yudhistira
3. “Matematika untuk SMP Kelas VII” written by M. Cholik Adinawan, Published
by Erlangga
Topic integers in The Al-Qur’an
: Q.S At-Taubah:36, Q.S Al-Fajr:1-3.
Topic fractions in The Al-Qur’an
:Q.S An-Nisaa:11-12
I. Learning Activities
First Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
b. Teacher gives some rules while studying mathematics.
c. Teacher tells the learning objectives of this lesson.
Motivation
: Explaining the function of integers in daily life. For
example to read the temperature and etc.
Prerequisite Topic : Whole number
Document of Nikmatul Husna
Time
10’
2.
Core Activities
Time
Exploration
a. Students mention the appliances in our daily life that use integers.
5’
b. Students do pre test about arithmetic operations of integers. This pre 15’
test to check the competence of Studentss about integers.
Elaboration
c. Students write vocabularies about this topic.
10’
d. Students explain the meaning of integers.
10’
e. Students demonstrate how to put integers in number line.
10’
f. Teacher gives
illustration in power point to do addition and 15’
subtraction of integers. This illustration from a media with the name
“MOLAT or Ruler of Integers”
g. Students determine the properties of addition and subtraction of 10’
integers.
h. Students do exercise about addition and subtraction of integers.
15’
Confirmation
i. Students give exercise to the teacher.
5’
j. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
The Problem for Pre Test
1) 8 + 12 − 36 = −16
2) 24 + ( 12 − 4 ) = 32
3) 11 + 6 × 8 = 59
4) 12 × ( 4 + 2 ) − 12 = 60
5) 3 + 4 × ( 9 − 3 ) = 27
6) 3 × ( 10 − 2 ) : 4 + 4 = 10
7) ( 18 − 3 ) × 3: 5 = 9
8) −2 + 6 × 3 − 10 = 6
9) 17 − 8 × 2 + 6 × ( 11 − 5 ) = 37
10) 10: ( 5 + 5 ) × 9 × 9 = 81
Document of Nikmatul Husna
The Problem for Exercise
1)
2)
3)
4)
5)
6)
45 + 56 × 48 − 216 ∶ 9 = 2709
15762 ∶ 37 − 512 + 96 × 72 = 6826
19 × 27 + 5.205 ∶ 15 − 269 = 591
( −9 ) − 6 × ( −72 ) : 16 − 20 = -2
( 8.742 − 9.756) × 36 ∶ ( 4.356 − 4.360 ) = 9126
168 ∶ ( 17 − 24 ) × ( −19 + 15 ) = 6
7) 24 × 240 ∶ ( −36 + 40 ) × ( −23 + 17 )
8) 360 ∶ 15 + ( 27 − 32 ) × ( −9 + 16 )
= -18
9) 420 ∶ ( −7 ) + 70 − 30 × ( −8 ) + 15 = 265
10) 13 × 140 ∶ ( −7 ) + ( −2 ) × 19 = -298
Document of Nikmatul Husna
= −240
“Molat”
Ruler of Integer
Using “Molat” show by line number
Addition and Subtraction
Prerequisite:
For addition, the movement is forward
For subtraction, the movement is backward
Row direction based on integer’s kind. Positive integer, “Molat” go to the
right. Negative integer, “Molat” go to the left.
Example:
4+3=7
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
4 + (-3) = 1
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) + 3 = (-1)
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) + (-3) = (-7)
-8 -7
4–3=1
-8 -7
4 – (-3) = 7
-8 -7
-6 -5 -4
-3 -2 -1
0
1
2
3
4
5
6
7
-3 -2 -1
0
1
2
3
4
5
6
7
(-4) – 3 = (-7)
-8 -7
Document of Nikmatul Husna
-6 -5 -4
(-4) – (-3) = (-1)
-8 -7
-6 -5 -4
-3 -2 -1
Notes:
= movement backward
= movement forward
Document of Nikmatul Husna
0
1
2
3
4
5
6
7
Second Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about addition and
subtraction of integers.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations are important while studying
mathematics and another subject. For the next topic
will use this operation
Prerequisite Topic : Addition and subtraction of Integers
2
Core Activities
Time
Exploration
a. Students explain how to do multiplication and division of integers. 5’
Because of the students ever studied before in elementary school.
Elaboration
b. Students tell the rule of multiplication and division of integers
10’
c. Students discuss the properties of multiplication and division of 10’
integers.
d. Students remind about the rule of mixed operation and give example 10’
about mixed operation.
e. Students do exercise about multiplication, division and mixed 15’
operation of integers.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
Document of Nikmatul Husna
Third Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations on exponential integers are
important for studying mathematics and another
subject.
Prerequisite Topic : Arithmetic operations of Integers
2.
Core Activities
Time
Exploration
a. Students remind again about positive and negative integers exponent.
10’
Elaboration
b. Students do worksheet to find the properties of arithmetic operations 25’
(multiplication, division and exponential) on exponential integers.
c. Discuss student’s worksheet.
25’
d. Students do exercise about arithmetic operations (multiplication, 30’
division and exponential) on exponential integers.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
Document of Nikmatul Husna
NAME:
1.
TITLE:
Exponential Integers
2.
1. Multiplication on Exponential Integers
2 4 × 25 = (2 × 2 ×……….) × (2 ×……………………………..)
= 2 × 2 × 2 ……………………..
=2…
= 2 … + ….
So, 24 × 25 = ………
Conclusion :
am × a n = …………..; For a is an integers, the exponents are m and n
2. Division on Exponential Integers
5
5
=
=
5 × 5 × 5 ……………………. .
5 × 5 × ……….
5 × 5 × 5 × 5
5 × 5 ………….
× 5 × …
= 5 ×
= 5 …..
= 5 ….
So,
⋯..
= ………
Conclusion :
= …………..; For a is an integers, the exponents are m and n, m > n
Document of Nikmatul Husna
1
5
=
So,
5 ….
5 ….
⋯
= 5 ….
= 5 …..
= 5 …..
Conclusion
( )
=
( )
=
……
……
3. Exponential on Exponential Integers
(
)× (
) = (
= (
So, (
×
=
….
=
…..× …..
) × ………. . ……
)× (
×
×
……. ) × ………………. . …………
) = ………..
Conclusion :
(
) = …………..; For a is an integers, the exponents are m and n
Exercise:
1. Simplify the following problems
a. 3 × 3 =
− ) ×( +
b. ( +
c. 7 : 7 × 7 =
d.
×
=
e. ( 5 : 5 ) =
f.
(
)
×
(
)
=
2. Determine the value of n:
a. 9 = 3
b. 5 × 25 = 5
c. 16: 2 = 2
d. 81 ∶ 3 = 3
Document of Nikmatul Husna
− ) =
Rubric for Problem Sheet
Problem
1.
Indicators
Can fill the blank with right answer
Can make the conclusion
2.
Can fill the blank with right answer
Can make the conclusion
3.
Can fill the blank with right answer
Can make the conclusion
4.
Can fill the blank with right answer
Can make the conclusion
1= achieve the indicator less than 25%
2= achieve indicator between 25%-50%
3=achieve indicator indicators between 50%-75%
4= achieve indicator more than 75%
Document of Nikmatul Husna
1
2
3
4
Fourth Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations on exponential integers.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic we can apply to another subject, for
example in physics and chemistry.
Prerequisite Topic : Arithmetic operations of exponential integers.
2.
Core Activities
Time
Exploration
a. Students remind again about squared and cubed then the root of 5’
square and the root of cubed in integers.
Elaboration
b. Students discuss to calculate square and the root of square in integers 5’
without and with calculator.
c. Students discuss to calculate the root of square in decimal numbers.
5’
d. Students discuss to calculate cubed and the root of cubed of integers 5’
with calculator.
e. Students do exercise about calculate squared and cubed then the root 20’
of square and the root of cubed in integers.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for quiz:
Calculate:
1) (-2)3
132496
2)
3) Given : √7 04 = 2 ,65
,
Determine: a. √
Key of problems:
0 ,000704
√70 ,4 = 8 ,39
and
b. √
70400000
1) (-2)3 = -8
2)
132496
364
3) a.
√0 ,000704 = √7 ,04: √10000 = 2 ,65 ∶ 100 = 0 ,0265
b.
√70400000 = √70 ,4 × √1000000 = 8 ,39 × 1000 = 8390
Document of Nikmatul Husna
Fifth Meeting (3 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students ask the teacher about homework that difficult for them.
c. Teacher tells the learning objectives of this lesson.
Apperception
: Students remind about fractions that already studied
in elementary school.
Motivation
: We can apply this topic in our daily life. For
example we want to divide something.
Prerequisite Topic : Integers.
2.
Core Activities
Time
Exploration
a. Teacher guides students to mention the problems in our daily life that 10’
use fractions.
b. Give pre test about arithmetic operations on fractions to check 15’
student’s competence about fractions.
Elaboration
c. Students explain the meaning of fractions.
10’
d. Students discuss about the type of fractions.
15’
e. Students change form of fractions to another form.
15’
f. Students do the exercise about changing form of fractions to another 25’
form.
Confirmation
5’
h. Students give exercise to the teacher.
5’
i. Students give questions related to this topic
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Students are given homework
5’
Document of Nikmatul Husna
Problem for Quiz
1. Write down the following fractions in the form of mixed fractions.
b.
a.
2. Write down the following fractions in the form of improper fractions.
b. 12
a. 8
3. Determine two equivalent fractions of:
b.
a.
4. Write in the simplest form:
a.
b.
5. Use the sign > or < for the relation of these fractions.
a.
b. ……
……
6. Arrange these fractions from the smallest to the biggest :
7. Simplify these fractions:
a.
+ (−
)=
b. −1 − −4
=
8. Simplify these fractions:
a. − × 2 =
b. 1 : 2 =
Document of Nikmatul Husna
,
Sixth Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about type of fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic will help us to do arithmetic operations
of fractions.
Prerequisite Topic : Integers.
2.
Core Activities
Time
Exploration
a. Students try to put fractions in number line. Because it is similar with 5’
to put integers in number line.
Elaboration
b. Students discuss about equivalent fractions.
10’
c. Students discuss to compare and order fractions.
10’
d. Students do exercise about equivalent, comparing and ordering 15’
fractions.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for Quiz :
1) Determine two equivalent fractions of
2) Which fractions is greater
and ?
3) Arrange the following fractions in order, with the smallest on the left
,
, and .
,
Key of problems:
1)
=
=
2) LCM of 3 and 7 is 21
and
=
=
So, <
3) LCM of 15, 10, 20 and 4 is 60
13
15
So,
=
52
60
,
, ,
Document of Nikmatul Husna
9
10
,
=
54
60
,
11
20
=
33
3
60
4
=
45
60
Seventh Meeting (2 x 40 Minutes)
1.
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about equivalent,
comparing and ordering fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: We can apply this topic in our daily life. For
example in economic activities.
Prerequisite Topic : Fractions
2
Core Activities
Time
Exploration
a. Students tell their experience about decimals, percent and per mill in 10’
daily life.
Elaboration
b. Students discuss about decimals, percent and per mill.
15’
c. Students do exercise about decimals, percent and per mill.
15’
Confirmation
d. Students give exercise to the teacher.
5’
e. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for Quiz :
1) Write as decimal.
2) Write 32% as simple fractions.
3) Write in per mill.
Key of problems:
1)
= 0,25
2) 32% =
3)
=
=
× 1.000 %0 =500 %0
Document of Nikmatul Husna
Eighth Meeting (3 x 40 Minutes)
1.
Opening Activities
Time
10’
a. Teacher prepares the students for learning mathematics.
b. Students remind the topic in the last meeting about decimals, percent
and per mill.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: Arithmetic operations of fraction are important.
Because we usually use it while studying
mathematics.
Prerequisite Topic : Fractions
2.
Core Activities
Time
Exploration
a. Students remind again about arithmetic operations (addition, 10’
subtraction, multiplication and division) of fractions. Because the
Students already studied before in elementary school.
Elaboration
b. Students discuss about arithmetic operations (addition, subtraction, 20’
multiplication,
division, exponential and mixed operation) of
fractions.
20’
c. Students determine the properties of exponential fractions.
d. Students
do
exercise
about
subtraction, multiplication,
arithmetic
division,
operations
(addition, 30’
exponential and mixed
operations) of fractions.
Confirmation
e. Students give exercise to the teacher.
5’
f. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for Quiz:
1)
+ (− )
2) 5,8 – 4,37
1
3
3) 1 2 4
6 1
:
4) 5 2
5)
( , )
( , )
Key of problems:
1)
+
−
= − =
2) 5,8 – 4,37 =
3) 1 ×
4)
5)
=
: =
( , )
( , )
×
×
=
= ( 0,3)
Document of Nikmatul Husna
−
=
=
−
=
−
=
= 3
= ( 0,3) = 0,09
= 1,43
Ninth Meeting (3 x 40 Minutes)
1
Opening Activities
a. Teacher prepares the students for learning mathematics.
Time
10’
b. Students remind the topic in the last meeting about arithmetic
operations of fractions.
c. Students ask the teacher about homework that difficult for them.
d. Teacher tells the learning objectives of this lesson.
Motivation
: This topic will help us to simplify the result of
arithmetic operations and another subjects.
Prerequisite Topic : whole number
2.
Core Activities
Time
Exploration
a. Students discuss in pairs about the rule of scientific notation and the 15’
rounded of decimals fractions.
Elaboration
b. Students explain in front of the class rule of scientific notation and the 15’
rounded of decimals fractions.
c. Teacher gives more explanation about scientific notation and rounded 10’
decimals fractions.
d. Students discuss about very large and very small numbers such as 15’
mega/million (106), giga/billion (10 9), tera/trillion (1012), micro (10-6),
nano (10 -9) and pico (10-12)
e. Students do exercise about scientific notation and the rounded of 25’
decimals fractions.
Confirmation
f. Students give exercise to the teacher.
5’
g. Students give questions related to this topic.
5’
3.
Closing Activities
Time
a. Make the conclusion from today’s lesson.
5’
b. Evaluate the lesson by giving quiz.
10’
c. Students are given homework
5’
Document of Nikmatul Husna
Problems for Quiz :
1) Write these number in scientific form:
a. 2.732
b. 0,00000007051
2) Round this following numbers off up to two decimal places.
a. 6,321
b. 78,4934
Key of problems:
1) a. 2.732 = 2,732 x 10 3
b. 0,00000007051= 7,051 x 10 -8
2) a. 6,321 = 6,32
b. 78,4934 = 78,49
J. Assessment :
1. Technical assessment
: observation and written test.
2. Procedure of assessment
: process assessment and last result.
3. Instrument of assessment
: Exercise, quiz and daily test.
Padang,
June 2011
Known By:
Headmaster of SMPN
………………………….
Document of Nikmatul Husna
Mathematics Teacher
Nikmatul Husna, S.pd