^^ Yustia Rahmawati ^^: LESSON PLAN

Major/Faculty : Mathematics Education / Mathematics and Science

School Unit : SMK Muhammadiyah 3 Klaten Tengah

Program / Vocational : Health / Nursery

Subject : Mathematics

Class / Semester : X / 1

Time Allocation : 15 minutes

Standard of Competence : 1. Solving problems related to the concept of real numbers operation.

Basic Competence : 1.2. Applying the operation on exponential

Indicators : 3.1.1. Mention the properties of the exponential of positive integers.

3.1.2. Simplify the forms of numbers in the exponential of positive integers.

I. The Purpose of Learning

a. Students are able to mention the properties of the exponential of positive integers.

b. Students are able to Simplify the forms of numbers in the exponential of positive integers.

II. Topic

Definition of Exponential

Exponential is multiplication repeated with the number itself.

Example :

· 4⁷ = 4 × 4 × 4 × 4 × 4 × 4 × 4

· (-3)⁴ = (-3) × (-3) × (-3) × (-3)

Definition : aⁿ = a × a × a × . . . × a

Its repeated until n factor

with,

a are called as cardinal number

n are called as exsponent

aⁿare called as exponential

Look this example !

^·(-4)³this is an example of positive exponential because the exponent is positive.

^·3^-4 this is not an example of positive exponential because the exponent is negative.

The properties of exponential operations.

1. Integer with positive exponent.

For a

R, m, and n is integer, so we can apply the following properties :

a. Look this example :

1. 3² × 3⁵ = (3 × 3) × (3 × 3 × 3 × 3 × 3)

= 3 × 3 × 3 × 3 × 3 × 3 × 3

= 3⁷

2. 4⁴ × 4² = (4 × 4 × 4 × 4) × (4 × 4)

= 4 × 4 × 4 × 4 × 4 × 4

= 4⁶

From two example above, so :

a^m × aⁿ = (a × a × a × . . . × a) × (a × a × a × a . . . × a)

Its repeated until m factor Its repeated until n factor

= a^m+n

So we can get the properties : a^m × aⁿ = a^m+n

After we konw about the properties of exponential a^m × aⁿ = a^m+n, now try to simplify the following exponential !

1. 6⁵

6³ = . . .

= . . .

2⁸ = . . .

4. 9

27 = . . .

III. Teacing Method

a. Expository

IV. Learning Scenario

Teacher activity

Students activity

Time Allocation

A. Opening

The teacher greet the students (good morning students, assalamualaikum wr.wb) and ask students to pray.

The teacher checking on school attendance with ask to the students “who’s the absent today ?” .

The teacher look into the students, with observe whether the students prepare their school equipment or not.

Students answer the greeting (good morning mom, wassalamualaikum wr.wb) and then praying.

The students answer “none mom”.

The students already prepare their school equipment.

2 minutes

The teacher explain that today we will study about “The properties of Integer with Positive Exponent ” and write that topic on the whiteboard.

The students listened what teacher’s said and they write the topic “The properties of Integer with Positive Exponent ” on their own book.

0,5 minutes

The teacher gives apperception about topic who will learn today.

Remember about real number system (especially integer) and operates two or more integer.

Teacher gives motivation to student about problem related to the properties of integer with positive exponent in daily life .

The student pays attention to what is learning submit.

1,5 minutes

B. Main Activity

Start the lesson, teacher writes down example of integer with positive exponent.

4⁷ = 4 × 4 × 4 × 4 × 4 × 4 × 4

(-3)⁴ = (-3) × (-3) × (-3) × (-3)

Then the teacher writes down 2 example of again and asks 2 student to formulate it and writes down it is whiteboard.

= . . .

Student pays attention to example given by teacher, then student asked by advance to the fore soon writes down its the formulation is whiteboard.

2 minutes

Teacher invites student to define meaning from exponential, that is :

Exponential is multiplication repeated with the number itself.

Or we can write,

Definition : aⁿ = a × a × a × . . . × a

Its repeated until n faktor

with,

a are called as cardinal number

n are called as exsponent

aⁿare called as exponential

Student can define meaning from exponential with their own language.

1 minutes

The teacher gives two examples.

^·(-4)³this is an example of positive exponential because the exponent is positive.

^·3^-4 this is not an example of positive exponential because the exponent is negative.

Then the teacher explain that today we will study about the properties of integer with positive exponent .

Student pays attention to example and explanation from the teacher.

1 minutes

Teacher writes down 2 the problem of multiplication of integer with positive exponent in the whiteboard.

1. 3² × 3⁵ = . . .

2. 4⁴ × 4² = . . .

Teacher invites student to elaborate example of the problem together and explains how to make simplify the problems.

The students make a note what teacher’s write on the whiteboard.

Student elaborates example together with the teacher.

2 minutes

Teacher writes down formula from both examples and challanges student to conclude first at integer with positive exponent .

a^m × aⁿ = (a × a × a × . . . × a) ×

Its repeated until m faktor

(a × a × a × a . . . × a) = . . .

Its repeated until n faktor

Teacher enquired " was properties mentioned by one of the student have been correct or had not ?".

There is student giving conclusion from formulation given teacher that is a^m+n.

The teacher said “correct”.

2 minutes

The teacher gives 4 question and the students must finised that question with properties of exponential a^m × aⁿ = a^m+n .

1. 6⁵

6³ = . . .

= . . .

2⁸ = . . .

4. 9

27 = . . .

Student asked to do 1 problem beforehand and completed does the problem, asked to write down result of their work front of class.

The students make a note and do that exercise in their own book.

There is student is going forward to the fore class to write down result of their work.

1 minutes

C. Closing

Teacher said about the properties of Integer with positive exponent which have been studied today .

Teacher asks student to did 3 problem which had not have time to be done the (as homework) and will be discussed in next meeting .

Teacher also informs that next meeting will study the properties other exponential.

Student pays attention to what is learning submit.

Student pays attention to what is learning instruct.

1 minutes

Teacher closes Iesson by inviting student to pray together. After praying teacher to terminate Iesson by saying greeting at student.

The teacher greet the students : “assalamualaikum wr.wb., good morning students”

Student prays together and answers greeting from teacher.

Students answer the greeting : “wassalamualaikum wr.wb., good morning mom”

1 minutes

V. Medias and Sources

a. Medias : Markres and whiteboard.

b. Sources : Heryadi, Dedi. 2007. Matematika untuk SMK kelas X (Teknologi, Kesehatan, dan Pertanian). Jakarta: Yudistira.

VI. Assessment

A. Assessment Technique : Written test

B. Form Of Instrument : Eassy

C. Instrument of Assessment

a. Cognitve

Simplify the following exponential !

1. 6⁵

6³ = . . .

= . . .

2⁸ = . . .

4. 9

27 = . . .

b. Affektive

No	Student	Aspect assessed
No	Student	participation	appreciate
1.
2.
3.
4.
5.
6.
7.
8.
9.

Explanation :

1. Participation

1 = Less (doesn’t give an idea)

2 = Medium ( sometimes give an idea)

3 = Good (often give an ide)

2. Appreciate

1 = Less (laughs at friend who is replying is wrong)

2 = Medium (just silent when their friend answer some question)

3 = Good (pass an opinion from answer which have been laid open their friend)

D. Key of Answer

No	Key of Answers	Score
No	Key of Answers	Right Answer	Wrong Answer	Didn’t Answer
1	Question : Simplify the exponential 6⁵ 6³ ! Answer : 6⁵ 6³ = 6⁽⁵⁺³⁾ = 6⁸	2,5	0,5	0
2	Question : Simplify the exponential ! Answer : =	2,5	0,5	0
3.	Question : Simplify the exponential 2⁸ ! Answer : 2⁸= 2³ 2⁸ = 2⁽³⁺⁸⁾= 2¹¹	2,5	0,5	0
4.	Question : Simplify the exponential 27 ! Answer : 27 = 3² 3³ = 3⁽²⁺³⁾= 3⁵	2,5	0,5	0