MATEMATIKA DLM BHS INGGRIS

 

LESSON PLAN

1.   SUBJECT IDENTITIES

School                            :  Senior High School 2 Prabumulih

Grade                             :  XI

Semester                         :  Even

Program                          :  Science

Subject                           :  Mathematics

Topic                              :  Statistics

Time allotment        :         4 x 45 minutes (two times meetings)

2.      STANDARD OF COMPETENCE

Using the rules of statistics, counting rules, and properties of probability in problem solving

3.      BASIC COMPETENCE

Presentation of data in table, bar chart, line graph, pie chart, and its interpretations.

4.   INDICATORS

       1. Presentation data in bar chart, line diagram, pie chart, and ogive and its interpretations.

       2. Interpretation data in bar chart, and line diagram

5.    OBJECTIVE                       

The student can be presentation the data in diagram:

      - line diagram

      - box and whisker plot

      - stem and leaf diagram

      - pie chart

      - compound diagram

6.   LESSON MATERIALS

      There are the kind of presentation of the data:

      1.  Pictogram

A pictogram is a simple way of representing data. Frequency is indicated by identical pictures (called symbols or motif) arranged in row or columns. Symbols may be divided into halves or other fractions to represent parts of a number.

            Pictograms are mainly used in newspapers, magazines, and reports in order to make a striking display. They are usually aimed at people who are unskilled in statistics or who have limited interest in the information shown, and are more suitable for comparisons than measurements.

2. Bar chart

In bar chart or bar graphs, data are represented in a series of bars that are equally wide. The width itself is not significant, but all the bars should be the same width. Sometimes the bars are just thick lines.

Bars can touch each other or be separated by gaps of equal width. The height of the bars represents the magnitude or frequency of the figures. Bars may be horizontal or vertical.

Bar chart are particularly useful for showing more than one set of facts. This makes them useful for comparing data.

3.   Pie chart

            A pie chart is a circle graph in which the angles of the sectors represent the frequency. When sectors are nearly the same size, it is difficult to compare them. In such cases, the measurements are usually given on the graph.

4.   Broken line graph.

      5. Stem-and-leaf diagrams

The following data, which are the heights of 39 people in cm (correct to the nearest cm), taken from the datafile ‘Brain size’.

         164   184   186   175   165   175   164   168   168   175   164    178     175

         179   168   173   174   187   168   178   194   157   173   160    183     173

         196   160   169   159   170   192   175   169   169   179   164    188     192

         These value are what statisticians call raw data. Raw data are the values collected in a survey or experiment before they are categorized or arranged in any way. Usually raw data appear in the form of a list. It is very difficult to draw any conclusions from these raw data just by looking at the numbers. One way of arranging the values that gives some information about the patterns within the data is a stem-and-leaf diagram.

We can represent these data with the stem-and-leaf diagram shown in Figure, which uses stem from 15 to 19

         15     7   9                                                                                (2)

         16     0   0   4   4   4   4   5   8   8   8   8   9   9   9                    (14)

         17     0   3   3   3   4   5   5   5   5   5   8   8   9   9                    (14)

         18     3   4   6   7   8                                                                 (5)

         19     2   2   4   6                                                                      (4)

Key: 17|3 means 173 cm    

6.  Box-and-whisker plot

You can convert a five-number summary into a useful diagram, called a box-and-whisker plot or a box plot.

Example:

The data below give the number of fish caught each day over period of 11 days by an angler. Give a five-number summary of the data:

   0    2     5     2      0     4     4     8     9      8     8

   Rearranging the data in order gives:

   0     0     2     2     4     4     5     8     8     8     9

The median value is = 4. As the number of data values is odd, deleting the middle one and finding the medians of the lower and upper halves gives

Q1 and Q3

The five-number summary is the minimum value 0, the lower quartile 2, the median 4, the upper quartile 8, and the maximum value 9.

7.   TIME ALLOTMENT

      4 X 45 Minutes

8.   TEACHING AND LEARNING METHOD

1. Lecturing

2. Answer and question

3. Discuss (cooperative)

4. Individual task

9.   LEARNING ACTIVITIES

      9.1. THE FIRST MEETING

Steps	Teaching Learning activity	Time Allotment
Pre-activities	a.   The teacher giving a greeting, inspecting presence of student, inspecting cleanness and neatness of class, then readiness of student for studying. b.   Motivation : If the material well be understood, so the student are hope make the presentation data in bar chart, line diagram, pie chart and ogive and its interpretation. c.   Apperception : Remember agains about presentation of the data set.        Discuss the home work	20 minutes
Main Activities	EXPLORATION a.  The students are given stimulus about the materials by the teacher (suppose in worksheet form,  to find the task from the resourse books or the other required books, from internet / materials which are related to the environment, or give the examples of materials which can be improved by the students from interactive media, and so on b.   The teacher explain the material, and give the examples about one. c.   Using “answer-question” method, the teacher asks students about that. d.    The teacher gives another example to presentation the kind of diagrams. ELABORATION a.     The students do the worksheet. b.  The teacher monitors the students by walking around the classroom and help or guides the students who found the difficulties c.   Asking the students representative to present their work in front of class by writing down at the whiteboard and explaining how to find the answer d.    After the students present their work, the teacher asks to the other students to give some responses, such as a question, suggestion, or an alternative way/step in how to find the answer CONFIRMATION a.   The teacher facilitated students to gain the learning experiences b.   The teacher formulates the right answer c.   Student to gain reflection	20 minutes 20 minutes 15 minutes

LESSON PLAN

Education Level     : Senior High  School

School                    : Senior High School 2 Prabumulih

Subject                    :  Mathematic

Grade/Semester      : XI /1

Main Topic             :  Probability  (Permutations and Combinations)

Time Allocation      : 1 x 45 minutes

I.                   Standard Competency:

To use the rules of statistic, the rules of numbering and the properties of probabily in problem solving

II.                Basic Competence (ies):

To use the multiplications law, permutations and combinations in problem solving

III.             Indicator (s)

Indicator of achieving the learning outcomes

·      To know what a permutation is and calculate with permutations

·      To know what a combination is and calculate with combinations

IV.             Learning Outcomes:

a.          The aim of process

The students are able to:

§  To know what a permutation is and calculate with permutations

§  To know what a combination is and calculate with combinations

b.         The aim of affective

Student are able to:

1.      To tell their opinion about the material.

2.      To work in group

3.      To ask about their problem in learning material

4.      To respect their friend’s opinion

V.                Learning Material

The number of permutations of n  distinct object is P(n,n), where

        P(n,n) = n! = n × (n-1) × (n-2) ×(n-3) ×................... × 2 × 1

The number P(n,r) of different permutations of r objects which can be made from n distinct objects is given by

                    P(n,r) =    , where   n ˃r

The number of distinct permutations of n objects, of which p are identical to each other, and then q of the remainder are identical, and r of the remainder are identical, and so on is

                                     , where                                 p + q + r + ...= n

A combination is a selection in which the order of the objects selected is unimportant

The number of different combinations of r objects selected from n distinct object is

 ,    n ˃r

VI.             Teaching Method

Method: Expository (direct instruction), cooperative learning (Think Pair Share)

VII.          Learning Experience

No	Teacher Experience	Student Experience	Time Allocation	Method
1	Opening -    To greet the students -    To tell the material to the student and the purpose of material -    To review the material about the multiplications law and the factorial notation	-   the students listen to the  teacher’s explanation	10 minutes	Expository
	Whilst activity -    To ilustrate the case related with permutation -    To explain to the students about the formulas and the concept of calculation in permutation -    To give the example about apply permutation to solve the problem -    To ilustrate the case related with combination -    To explain about the formulas and the concept of calculation in combination -    To give the example about applying combination in solving the problem -    To distribute a worksheet -    To ask the students to do the worksheet and discuss it with their tablemate	-     Listens to the teacher’s explanations and asks about unclear material -     Do the worksheet  and discuss it with their tablemate	20 minutes 10 minutes	Expository, direct instructions Think Pair Share