Download LESSON PLAN School : SMK N 1 Purbalingga Code of Competency

LESSON PLAN
School
: SMK N 1 Purbalingga
Code of Competency
: Accountancy
Subject
: Mathematics
Class/Semester
: XI / 3
Meeting
:1–3
Time allocation
: 6 hours (3 times meeting)
Standard of Competency
: Applying the concept of rows and rows of the problem-solving
Basic Competency
: Identifying patterns, sequences and series of numbers
Indicators
:
1. Identifying number patterns, sequences and series based on the characteristics
2. Simplify a series using sigma notation
A. THE PURPOSE OF LEARNING
Meeting 1
After participating in the learning process students are expected to:
1. Identifying a pattern of numbers based on the characteristics
2. Identifying a sequence based on the characteristics
Meeting 2
After participating in the learning process students are expected to:
1. Identifying a series based on the characteristics
2. Using sigma notation to simplify a series
Meeting 3
After participating in the learning process students are expected to:
1. Write the sequence number of the sigma notation
2. Calculate the result of a sigma notation
B. MATERIALS
1. The pattern of numbers, sequences and series
2. Sigma notation
C. METHODS OF LEARNING
1. Lectures
2. Asking and answer
3. Discussion
4. Tasking
D. STEPS OF LEARNING ACTIVITY
 Meeting 1 (2 x 45 minutes)
1. Beginning activity (10 minutes)
 Teachers prepare students for the physically and mentally ready to learn, provide
motivation about the importance of learning, an explanation of the purpose of
studying the standard of competency is applying the concept of rows and rows in
problem solving
 Teachers assign students to cluster in accordance with their respective groups
 Teachers assign students to listen to all the material (module) ranks and rows on
rows and rows of numbers patterns.
2. Core Activity (70 minutes)
Exploration
In exploration activities:
 Teachers facilitate student interaction that occurs between students, students and
teachers by using existing learning resources and the environment, as well as
assigning students to learn about patterns and sequence numbers
 Teachers supervise and guide
Elaboration
In elaboration activities:
 The teacher facilitates the students with discussion groups to bring new opinions
or ideas relating to the settlement pattern and sequence numbers of both written
and oral
 The teacher provides an opportunity to think, analyze, solve problems and express
their opinions without fear in the activities of the group discussions
Confirmation
In confirmation activities:
 The teacher gives positive feedback and reinforcement in the form of oral, written,
in the form of praise to student success in completing the task by discussing the
 Teachers facilitate student reflection to obtain a learning experience that has been
done
 Teachers as resource persons and facilitators in answering questions students had
difficulty
DESCRIPTION OF LEARNING MATERIALS
PATTERN NUMBER
Paterrn number is the arrangement of numbers or row numbers are sorted according to certain
rules which may be a formula, the algebra and the form of the equation.
Example:
a. 1, 3, 5, 7, . . .
b. 2, 4, 6, 8, . . .
c. 1, 5, 9, 13, . . .
d. 2, 6, 12, 20, . . .
e. 1, 4, 9, 16, 25, . . .
Any numbers that form a line called a tribe.
In general, a line was written: U1, U2, U3, ..., Un
consider the sequences of number: 2, 4, 6, 8, . . .
Formula from the sequences of number is Un = 2n
If the formula (pattern) of-n from the sequences known so the sequences can formed,
otherwise if there are sequences so the formula (pattern) of-n from the sequences can definite.
Examples:
Find the term of-n from sequence 5,7,9, 11, ...
Solution:
U1 = 5 = 2.1 + 3
U2 = 7 = 2.2 + 3
U3 = 9 = 2.3 + 3, etc
Un = 2n + 3
The term of-n is Un = 2n + 3.
3. End Activity (10 minutes)
 Teachers with students to make the lesson summary or conclusion
 Conducting an assessment of the activities that have been implemented
consistently and programmed
 Provide feedback on process and learning outcomes
 Assigning students to study the material further
 Meeting 2 (2 x 45 minutes)
1. Beginning activity (10 minutes)
 Teachers prepare physically and mentally to be ready to follow the lessons.
 Teachers provide motivation and trying to arouse interest in students to learn
 The teacher gives some questions relating to past lessons with material that will be
studied
2. Core Activity (70 minutes)
Exploration
In exploration activities:
 Teachers facilitate student interaction that occurs between students, students and
teachers by using existing learning resources and the environment, as well as
assigning students to learn about the series and the sense of sigma notation and
examples.
 Teachers supervise and guide
Elaboration
In the elaboration activities:
 The teacher facilitates the students with discussion groups to bring new opinions
or ideas relating to understanding the sigma notation sequences and series of both
written and oral
 The teacher provides an opportunity to think, analyze, solve problems and express
their opinions without fear in the activities of the group discussions
Confirmation
In confirmation activities:
 The teacher gives positive feedback and reinforcement in the form of oral, written,
in the form of praise to student success in completing the task by discussing the
 Teachers facilitate student reflection to obtain a learning experience that has been
done
 Teachers as resource persons and facilitators in answering questions students had
difficulty
DESCRIPTION OF LEARNING MATERIALS
SERIES OF NUMBER
Series of number is a sum of sequences of numbers.
If U1, U2, U3, ... , Un are a term of sequences so that the form sum of the sequences of
numbers is U1 + U2 + U3 + ... + Un called series of numbers. Un called term of n.
Examples:
a. 2 + 4 + 6 + 8 + ...
b. 1 + 2 + 4 + 8 + …
c. 12 + 8 + 4 + 0 + ...
d. 8 + 4 + 2 + 1 + ...
3. End Activity (10 minutes)
 Teachers with students to make the lesson summary or conclusion
 Conducting an assessment of the activities that have been implemented
consistently and programmed
 Provide feedback on process and learning outcomes
 Assigning students to study the material further.
 Meeting 3 (2 x 45 minutes)
1. Beginning activity (10 minutes)
 Teachers prepare physically and mentally to be ready to follow the lessons.
 Teachers provide motivation and trying to arouse interest in students to learn
 The teacher gives some questions relating to past lessons with material that will be
studied.
2. Core Activity (70 minutes)
Exploration
In exploration activities:
 Teachers facilitate student interaction that occurs between students, students and
teachers by using existing learning resources and the environment, as well as
assigning students to learn about the changing forms of sigma notation into
ordinary addition form and examples
 Teachers supervise and guide
Elaboration
In the elaboration activities:
 The teacher facilitates the students with discussion groups to bring new opinions
or ideas relating to changing the shape of the sigma notation to the usual form of
addition
 The teacher provides an opportunity to think, analyze, solve problems and express
their opinions without fear in the activities of the group discussions
Confirmation
In confirmation activities:
 The teacher gives positive feedback and reinforcement in the form of oral, written,
in the form of praise to student success in completing the task by discussing the
 Teachers facilitate student reflection to obtain a learning experience that has been
done
 Teachers as resource persons and facilitators in answering questions students had
difficulty
DESCRIPTION OF LEARNING MATERIALS
SIGMA NOTITION
Symbol  called sigma means summation.
n
Generally defined that U 1  U 2  U 3  ...  U n  U k
k 1
For write sigma notation using indeks that show the sequences of natural numbers or integer,
the lower limit written on under the form of sigma symbol and the upper limit written on
upper of sigma symbol. k is called index (some people called it variable) and substitute with
all of the characters alfabet.
Examples:
The properties of sigma notation:
n
1.
 k 1  2  3  ...  n
k 1
n
2.
a
k 1
 a1  a 2  a3  ...  a n
k
n
3.
 k  kn
k 1
n
4.
a
k  n 1
0 (lower lim it more upper lim it )
k
n
5.
 c.a
k 1
n
 c a k
k
 c.a
k 1
n
6.
k 1
k
n
7.

m
 a  a
k 1
k
k 1
n
n p
k 1
k 1 p
8.  a k 
n
n
k 1
k 1
 d .bk c  a k  d  bk
k
a

n
a
k  m 1
k
(k  p)
Examples:
1. Define this addition 3  6  9 12 15 with sigma notation!
Solution:
3  6  9  12  15  3(1)  3(2)  3(3)  3(4)  3(5)
5
  3k
k 1
7
2. Define the form of
 (3m) into the ordinary summation!
m2
Solution:
7
 3m  (3).(2)  (3).(3)  (3).(4)  (3).(5)  (3).(6)  (3).(7)
m2
 (6)  (9)  (12)  (15)  (18)  (21)  81
3. End Activity (10 minutes)
 Teachers with students to make the lesson summary or conclusion
 Conducting an assessment of the activities that have been implemented
consistently and programmed
 Provide feedback on process and learning outcomes
 Assigning students to study the material further
E. RESOURCES OF LEARNING
Module Mathematics SMK of MGMP Team Purbalingga
F. EVALUATION
 Teachers assign all students to take tests formative
 For students who not reach for value 7 given a remidial tests
EXERCISES:
1. Find the four beginning of the sequences that formed by the following formula:
a. Un = 2n + 1
b. Un = n2 + 3
c. Un =
2
n 1
2. Write two of the next term of the following sequences:
a. 1, 4, 9, 27, . . .
b. 2, 4, 8 ,16, . . .
c. 2, 6, 12, 20, . . .
3. Detrmine the formula of teh term of-n from the following sequences:
a. 1, 4, 9, 27, . . .
b. 2, 4, 8 ,16, . . .
c. 2, 6, 12, 20, . . .
4. a. Find the four beginning of the sequences that defined by the formula: Un = 3n + 1
b. Find n if the value of the term of sequence is 196?
5. a. Find the four beginning of the sequences that defined by the formula:Un = 2n2 – 1
b. Un = 161 find n = ?
6. From the following form, define thar series of number:
a. 3  5  7  9  ...
b. 1  4  9  16  ...
c. 1  4  8  16  ...
7. Change the following series to sigma notation!
a. 3 + 6 + 9 + 12 + 15
b. 0 + 3 + 8 + 15 + 24 + 35 + ... + 63
c. a + a2 + a3 + a4 + a5
d. 2 + 6 + 12 + 20 + 30 + ... sampai 8 suku
e. 2  4  8 16  32  64 128
8. Define the following sigma notation to ordinary addition!
5
a.
 (a
2
)
a 1
6
b.
 (2 p
p 3
2
 5)
Knowing,
Principal
Vice principal 1 curricullum
Drs. Sukamto
NIP. 19560515 198203 1020
Drs. Sahir
NIP. 19630114 198910 1001
Purbalingga, July 2011
Subject Teachers
Sudiyarti, S. Pd