Micro-Scholarship, What it is, How can it help me.pdf
RPP Matematika IGCSE
1. Name : Ayanah Septianita
Semester/Class : 5/A1
NPM : 11.84.202.007
Tugas UTS : Matematika Level IGCSE
My impressions are:
In the course of the study IGCSE maths using English I get a lot of
knowledge and can understand math words in the English language ,
how someday I can teach mathematics in English , although not all of
them. I understand ...
I do not understand why because this course should be able to use English
.. when persentasi in class debriefing should use English every week .
But I can understand if there are words that I never learned and find
meaning in Indonesian dictionaries translate through .
The hope :
IGCSE maths should be further enhanced UAS learning until later , because
this lesson is very useful for our students in the future in teaching .
In this course I hope during school hours had begun , faculty and students
should be active in the English language instead of using Indonesian ,
because in this case the lecturers and students learn the English
language fluency ,
and I hope also to get the best value in the eyes of this college ..
2. LESSON PLAN
Education Unit: Junior High School (SMP)
Subjects: Mathematics
Class / Semester: VII / 1
Time Allocation: 2 x 40 minutes ( 1 meeting )
Topic: Algebra
Submateri Principal: Algebra Shape
A. Competency Standards
Understanding the algebra
B. Basic Competency
Perform operations on the algebra .
C. Indicator
a. Perform arithmetic operations on the algebra sum .
b. Perform arithmetic operations on the algebra reduction .
c. Perform arithmetic operations on the algebra multiplication .
d. Perform arithmetic operations division in algebraic form .
e. Perform arithmetic operations on the algebra reappointment .
D. Learning Objectives
After learning , expected
a. Students can perform arithmetic operations on the algebra sum .
b. Students can perform arithmetic operations on the algebra reduction .
c. Students can perform arithmetic operations on the algebra multiplication
d. Students can perform arithmetic operations on the algebra division.
e. Students can perform arithmetic operations on the algebra reappointment .
Character of students who are expected to :
1. Discipline
2. Respect and Attention
3. Diligence
4. Responsibility
3. E. Teaching Materials
1. Apperception
Before discussing the arithmetic operation on the algebra should first
understand the multiplication rate constants and a lot of numbers in a variable
substitution from many tribes. For more details see the following example:
a. 2 (𝑎 + 3) = 2𝑎 + 6 → distributive properties
b. − (𝑥 − 3) = −𝑥 + 3
c. 3𝑚(𝑥 + 2 𝑦 + 3) = 3𝑚𝑥 + 6 𝑚𝑦 + 9𝑚
If the algebraic form 3𝑥 + 5 𝑦, the variable 𝑥 is replaced by 2 and the variable
y is replaced by 4 then obtained:
3 𝑥 + 5 𝑦 = 3 (2) + 5 (4)
= 6 + 20
The process of replacing a variable with a number called the substitution
process.
2. The Core Material
Also known in the form of algebraic arithmetic operations such as addition,
subtraction, multiplication, division and reappointment. To more details will be
outlined as follows:
a. Algebra Forms
Forms 5𝑥 + 2𝑦 + 3𝑧, 2𝑥2
, 4𝑥𝑦2
, 5 𝑥2
− 1, and (𝑥 − 1) (𝑥 + 3) is called the
algebra . The terms contained in the algebra is as follows.
1) Variables
A variable is 𝑎 symbol substitutes 𝑎 number of unknown value clearly.
Variables are usually denoted by the letters 𝑎 , 𝑏 , 𝑐 , . . . , 𝑧 .
Example :
Variables of 5𝑥 + 2 𝑦 is 𝑥 and 𝑦
Variables of 2𝑥2
+ 4 𝑥 − 12 is 𝑥
4. 2) Constants
Is the rate constant of a form of algebra in the form of numbers and no load
variable .
Example :
Constants that exist in 2𝑥2
+ 3 𝑥𝑦 − 8 is − 8
Constants that exist in 3 − 4𝑥2
− 𝑥 is 3
3) Coefficient
Coefficients in the algebra is the number of variables inherent with a tribe in
the form of algebra .
Example :
Coefficient of 𝑥 that of the 5𝑥 + 3 𝑦2
𝑥 is 3
Coefficient of 𝑥 that of the 2𝑥2
+ 6 𝑥 − 3 is 6
4) Rate
Rate is variable and its coefficients or constants in the form of algebraic
operations are separated olrh sum or difference signal .
One tribe is a form of algebra that are not connected by the number sign or
difference operations .
Example :
3𝑥 , 4𝑎2
− 2𝑎𝑏
Is the algebra of two parts connected by a token amount or increment
operation.
example :
𝑎2
+ 3 , 𝑥 + 2 𝑦 , 3𝑥2
− 5𝑥
Is the algebra of three parts which are connected by two operations sum or
difference signal .
Example :
3𝑥2
+ 4 𝑥 − 5 , 2𝑥 + 2 𝑦 − 𝑥𝑦 .
Algebraic forms that have more than two tribes called many tribes or polinim.
5. b. Summation Algebra and Reduction
Properties of addition and subtraction on integers also apply to the algebra
but addition and subtraction operations on ajabar form can only be done on similar
tribes alone. Operations of addition and subtraction in the algebra can be solved using
the distributive properties.
Example:
1) 3𝑥 + 5𝑥 = (3 + 5)𝑥 = 8𝑥
2) 5𝑎 − 3𝑎 − 2𝑎 + 4𝑎 = (5 − 3 − 2 + 4)𝑎 = 4𝑎
3) 7𝑎 + 5𝑏 + 𝑎 − 2𝑏 = 7𝑎 + 𝑎 + 5𝑏 − 2𝑏
= (7 + 1)𝑎 + (5 − 2)𝑏
= 8𝑎 + 3𝑏
Addition operation on the algebra above can not be done because the tribes
are not similar, is 5𝑥, 3𝑦, and 6 were not similar.
Subtract the following algebraic form.
a) 8𝑥 − 4𝑦 from 5𝑥 − 7𝑦
b) 6𝑥2
+ 5𝑥 + 2 from 7𝑥2
+ 2𝑥 − 3
Completion:
a) 5𝑥 − 7𝑦 − (8𝑥 − 4𝑦) = 5𝑥 − 7𝑦 − 8𝑥 + 4𝑦
= −3𝑥 − 3𝑦
b) 7𝑥2
+ 2𝑥 − 3 − (6𝑥2
+ 5𝑥 + 2) = 7𝑥2
+ 2𝑥 − 3 − 6𝑥2
− 5𝑥 − 2
= 𝑥2
− 3𝑥 − 5
What if the algebraic sum operation occurs in fractions?
Operating principle is the same as the sum of fractions, followed just a
matter of form variables aljabar.Contoh:
Determine the results in a simple form:
a)
2
𝑥
+
5
𝑥
=
2+5
𝑥
=
7
𝑥
b)
5
2𝑎
+
3
4𝑎
=
10
4𝑎
+
3
4𝑎
=
13
4𝑎
𝑎(𝑏 + 𝑐) = 𝑎𝑏 + 𝑎𝑐
𝑎(𝑏 − 𝑐) = 𝑎𝑏 − 𝑎𝑐
6. c)
8
𝑥
−
5
𝑥
=
8−5
𝑥
=
3
𝑥
d)
4
3𝑥
−
5
7𝑥
=
28
21𝑥
−
15
21𝑥
=
13
21𝑥
Simplify the following form.
a) (𝑥 − 5𝑦 + 2𝑧) + (−10𝑥 + 3𝑦 − 10𝑧)
b) (2𝑥2
+ 5𝑥 + 3) − (𝑥2
+ 𝑥 − 3)
Completion :
c. Similar Multiplication and Division Rate and are Similar
After studying the concept of multiplication and division of whole numbers
also apply this concept to define multiplication and division algebra form tribes.
Example:
1. a. 𝑎 × 𝑎 = 𝑎2
c. 𝑎9
: 𝑎6
= 𝑎9−6
= 𝑎3
b. 𝑎3
× 𝑎5
= 𝑎3+5
= 𝑎8
d. 12𝑎3
𝑏2
: 4𝑎3
𝑏2
= 3
2. a. 4𝑎 × 2𝑏 = (4 × 2) × 𝑎 × 𝑏 = 8𝑎𝑏 c. 18𝑎3
: 6𝑎2
=
18
6
(𝑎3−2) = 3𝑎
b. 3𝑎3
𝑏 × 5𝑎𝑏2
= 15𝑎4
𝑏3
d. 14𝑥2
𝑦5
: 7𝑥2
𝑦4
= 2𝑦
The same thing also berlakuu ntuk perkalianpecahan algebraic operations. Pay
attention to the following example:
a)
2𝑎
5
×
𝑏
3
=
2𝑎×𝑏
5×3
=
2𝑎𝑏
15
b)
3
2𝑎
×
2𝑏
5
=
3×2𝑏
2𝑎×5
=
6𝑏
10𝑎
c)
2𝑝−3
3𝑞
×
𝑝𝑞
4
=
(2𝑝−3)𝑝𝑞
3𝑞×4
=
2𝑝×𝑝×𝑞
(3×4)𝑞
−
3×𝑝×𝑞
12𝑞
𝑎𝑥(𝑥 + 𝑏) = 𝑎𝑥𝑥 + 𝑎𝑥𝑏
= 𝑎𝑥2
+ 𝑎𝑥𝑏
𝑎 𝑥
× 𝑎 𝑦
= 𝑎 𝑥+𝑦
dan 𝑎 𝑥
: 𝑎 𝑦
= 𝑎 𝑥−𝑦
7. =
2𝑝2
𝑞
12𝑞
−
3𝑝𝑞
12𝑞
=
2𝑝2
− 3𝑝
12
For dalampecahan division operation can be solved by multiplying the
fractional inverse. For example, the reverse
3
5𝑎
or
5𝑎
3
. Example question:
a)
2
3𝑎
:
3
4𝑏
=
2
3𝑎
×
4𝑏
3
=
8𝑏
9𝑎
b)
𝑝2
𝑞
:
3𝑝
4𝑞2 =
𝑝2
𝑞
×
4𝑞2
3𝑝
=
4𝑝2 𝑞2
3𝑝𝑞
=
4𝑝𝑞
3
c)
9+6𝑥
5𝑥
:
3𝑥
2
=
9+6𝑥
5𝑥
×
2
5𝑥
=
(9+6𝑥)2
25𝑥2 =
18+12𝑥
25𝑥2
d. Similar Reappointment of Interest
The concept of integer powers have been studied in previous chapters apply
to determine the powers of the tribes of the algebra, namely:
Example question:
The rank of the algebra of the following:
a. (𝑥3)2
c. (𝑥𝑦)5
b. (3𝑝2)3
d. {(3𝑝3
𝑞2)3}2
Completion:
a. (𝑥3)2
= 𝑥3×2
= 𝑥6
b. (3𝑝2)3
= 33
× 𝑝2×3
= 27𝑝6
c. (𝑥𝑦)5
= 𝑥5
× 𝑦5
d. {(3𝑝3
𝑞2)3}2
= (33
× 𝑝3×3
× 𝑞2×3)2
= 33×2
× 𝑝9×2
× 𝑞6×2
= 36
× 𝑝18
× 𝑞12
= 729𝑝18
𝑞12
𝑎3
= 𝑎 × 𝑎 × 𝑎
8. Fractional powers of algebra to the same concept as integer powers. Pay
attention to the following example:
a) (
5
𝑥
)
2
=
52
𝑥2
=
25
𝑥2
b) (
2𝑎
𝑥𝑦
)
3
=
(2𝑎)3
(𝑥𝑦)3 =
23 𝑎3
𝑥3 𝑦3 =
8𝑎3
𝑥3 𝑦3
c) (
3𝑎
4𝑎2 𝑏
)
3
=
(3𝑎)3
(4𝑎2 𝑏)3 =
27𝑎3
64𝑎6 𝑏3
F. Learning Method
1. Expository used when explaining sub subject matter as well as square and cube
roots and cube roots of integers.
2. Debriefing was made during a routine task that is at the beginning of learning
activities, conducting apersepsi and at the end of the learning activity.
3. Work assignments carried out during the exercises and giving chores.
G. Learning Activities
No
Teaching and Learning
Activities
Time
Allocation
Method
Org
Cla Ind
1.
1 meeting
Preliminary
a. Teachers perform routine
activities at the beginning of
the learning greetings,
praying, and attendance
students.
b. Teachers apersepsi activities.
Teacher gives apperception
on the algebra apada
previous material.
(Elaboration)
5 mnt
3 mnt
Org
Le
√
√
9. 2.
3.
Core Activities
a. Teacher explains about
arithmetic operations on the
algebra (Exploration)
b. Teacher gives students a
chance to ask.
(Confirmation)
c. Students are directed to
work on practice exercises in
pairs.(Elaboration)
d. Students gives the
opportunity to present
answers that have been done
in front of the class.
(Confirmation)
Cover
a. Teachers lead students to
conclude that the material
has been given.
(Elaboration)
b. Teachers give homework.
c. Teachers perform routine
tasks at the end of the
lesson.
25 mnt
1 mnt
15 mnt
15 mnt
2 mnt
2 mnt
3 mnt
Le
Le
Org
Cla
Le
Dis
√
√
√
√
√
√
Description:
Le : Lecture Ex: Expository GT: Giving Task
Dis : Discussion Min: Minutes Sec : Seconds
Org: Organizing Cla: Classical Ind: Individual
10. H. Learning Tools and Resources
Sources:
Books, namely books Mathematics Class VIII Smt 1.
Another reference book.
Tools:
o Laptop
I. Appraisal
Technique:
The written test
Forms Instruments: A brief description
Instruments questions
Procedure
Assessment in the learning process.
Assessment at the end of the lesson.
J. Assessment Tool
The form of questions and answers
Written:
1. Complete the following algebraic operations:
a. −10𝑥 − 2𝑥 + 3
b. 7𝑎 − 5𝑏 + 10𝑎 + 15𝑏
c. 16𝑞 − 5𝑡 + 6𝑞 + 8𝑡
2. Describe the following algebraic form of 5 (𝑎 + 2 𝑏) + 3 (3𝑎 − 4𝑏)
11. 3. Simplify:
a. 5 × 3 × 𝑎 × 𝑏
b. 3 × 𝑚 × 4 × 𝑛 × 𝑚
c. 5 × 𝑎2
× (−2𝑏) × (−𝑎)
d. (−3𝑎𝑏3) × (−3𝑎4
𝑏2)
4. Simplify the distribution of
1. Completion and Scoring tables
No Completion Scores
1. a.6 × 𝑎 = 6𝑎
b.𝑎 × 𝑎 × 𝑎 × 𝑎 × 𝑎 × 𝑎 × 𝑎 = 𝑎7
c.5𝑝 = 𝑝 + 𝑝 + 𝑝 + 𝑝 + 𝑝
2
2
2
Subtotal 6
2 Determine the magnitude of the coefficient of 𝑦 with the
following algebraic forms.
a. 5𝑥2
+ 6𝑦 − 7
b. 3𝑥2
− 4𝑝𝑦 + 2𝑦2
Completion:
a. Coefficient 𝑦 from 5𝑥2
+ 6𝑦 − 7 is 6
b. Coefficient 𝑦 from 3𝑥2
− 4𝑝𝑦 + 2𝑦2
is −4𝑝
7
7
Subtotal 14
3. Define similar tribes from the following algebraic forms.
a. 3𝑚 + 2𝑛 − 5𝑚 + 12
b. 4𝑥 − 2𝑥𝑦 + 3𝑦 − 𝑥 + 3𝑥𝑦
Completion :
a. Similar tribes in 3𝑚 + 2𝑛 − 5𝑚 + 12 is 3𝑚 and
−5𝑚.
6
6
12. b. Similar tribes in 4𝑥 − 2𝑥𝑦 + 3𝑦 − 𝑥 + 3𝑥𝑦 adalah:
(1) 4𝑥 dan – 𝑥
(2)−2𝑥𝑦 dan 3𝑥𝑦
Subtotal 12
4. Determine the number of terms in the following algebraic
forms.
a. 3𝑥 − 2
b. 3𝑥2
+ 2𝑥 − 1
c. 𝑦2
− 2𝑦2
+ 3𝑦 − 5
Completion :
a. The number ot terms in 3𝑥 − 2 is 2, from 3𝑥 and −2
b. The number ot terms in 3𝑥2
+ 2𝑥 − 1 is 3, from
3𝑥2
, 2𝑥, and −1.
c. The number ot terms in 𝑦3
− 2𝑦2
+ 3𝑦 − 5 is 4,yaitu
𝑦3
, −2𝑦2
, 3𝑦,and −5
6
6
6
Subtotal score 18
Total Score 50
13. J. Character Assesment
No Name
Character
Curiosity Honest Diligent Discipline Confidence Independent
1.
2.
3.
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Character columns filled with scores corresponding to the level of the
character of the child.
Very Good = 4
Good = 3
Moderate = 2
Less = 1