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INNOVATIVE TEACHING MANUAL

NAME OF THE TEACHER : SANDHYA J DATE :

STANDARD : IX – A DURATION : 45 Minutes

SUBJECT : MATHEMATICS PERIOD :

UNIT : STATISTICS

TOPIC : FREQUENCY POLYGON

CURRICULAR STATEMENT:

The pupil understands the statistical idea of frequency and the way to construct a

frequency polygon of a given data.

LEARNING OUTCOMES:

Enable the students in

(i) comprehending about the preparation of a frequency table.

(ii) constructing frequency polygon with the given data.

CONTENT OUTLINE

STATISTICS - FREQUENCY POLYGON

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CONTENT ANALYSIS:

TERMS: FREQUENCY POLYGON

FACTS:

(i) Statistics is the branch of Mathematics which deals with the organized

presentation and indepth analysis of such data and the methods of drawing logical

conclusions from them.

(ii) The presentation of numerical data can be done in the form of pictures and

tables.

(iii) Numbers used in studying some situation are called scores in Statistics.

(iv) Frequency is the number of times a score is repeated.

(v) The table prepared by using frequencies is called a frequency table.

(vi) A histogram is a graphical representation of a frequency distribution in the

form of rectangles with class intervals as bases and heights proportional to

corresponding frequencies such that there is no gap between any two successive

rectangles.

(vii) A frequency polygon is a graphic representation of a given frequency

distribution; obtained by joining the midpoints of the classes of a histogram.

CONCEPT:

FREQUENCY POLYGON

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PRE-REQUISITES:

The pupils have already learned about

(i) Frequency distribution table

(ii) Histogram

TEACHING-LEARNING MATERIALS:

Computers

Smart phones

REFERENCES:

MATHEMATICS - STANDARD IX(PART 1), GOVT OF KERALA

PUPIL ACTIVITY TEACHER RESPONSE

INTRODUCTION

Students are eager to get the topic Teacher suggests the topic “Frequency Polygon” and

advice the students collect information about it.

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PUPIL ACTIVITY TEACHER RESPONSE

Students grouped among themselves into two groups –

A and B.

Students browse about frequency polygons through

smartphones.

Group A collected details about the following:

Teacher checked the response of Group A. FREQUENCY

DISTRIBUTION

HISTOGRAM

FREQUENCY POLYGON

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PUPIL ACTIVITY TEACHER RESPONSE

Group B collected details about the following:

PRESENTATION

Akshay from Group A presented about

frequency distribution table and the

construction of frequency distribution

table with the help of the following

question:

Teacher again checked the response of Group B.

Teacher consolidated and asked students to present the

details collected.

FREQUENCY POLYGON

WITH ILLUSTRATIVE EXAMPLES

6PUPIL ACTIVITY TEACHER RESPONSE

All students started constructing frequency table

Teacher assesses Akshay’s performance and checked

whether the students are performing well.

The marks that 42 students of class 9A got

in the continuous evaluation for I.T are given below.

Make a frequency table taking each marks

separately.

9,8,10,7,6,10,8,7,9,8,5,6,9,4,7,6,9,8,5,4,9,8,7,6,

7,8,5,4,7,6,8,4,7,6,7,5,9,8,5,4,4,8

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Students constructed frequency distribution table

Grade Students 4 6 5 5 6 6 7 8 8 9 9 6 10 2TOTAL 42

Shanitha from group A about histogram to recall it.

The following activity is given.

Shanitha : Friends, now you can see that it is a rainy

season, right?

Students : Yes.

Shanitha : Then, here is an interesting question

regarding rain.

Draw a Histogram of the rainfall during June to

August.

Rain(mm) 10-20 20-30 30-40 40-50 50-60Days 8 10 14 20 15

Teacher appreciated the students for their performance.

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TEACHER RESPONSE

Teacher checked the figure

Teacher appreciated the students

PUPIL ACTIVITY TEACHER RESPONSE 0

FREQUENCY POLYGON

DAYS

Students drawn Histogram correctly

Dhanya from group B explained about frequency polygon

with the help of the above illustrative example:

Dhanya: Mark the midpoints of the top of each rectangle

and connect these points using straight lines. A new class 0-

10 before the first one of the table and another new class

60-70 after the last class of the table are introduced with

frequency 0 in each so that a frequency polygon can be

attained.

Teacher checked all answers.

Teacher called another student for presenting about

frequency polygon

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PUPIL ACTIVITY

Students drawn correctly

0 10 20 30 40 50 60 7005

10152025

FREQUENCY POLYGON

DAYS

Students among themselves prepared an algorithm for

drawing frequency polygon and displayed.

Step I: Take a graph paper and draw x an y axes. mark

them as OX and OY.

step ii: Choose a suitable scale for X and Y axes to

represent class limits and frequencies respectively.

step iii: Mark the midpoints of each class.

step iv: Join these points with a scale and pencil.

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GENERALIZATION

APPLICATION

Students searched and finally they got the answer.

Teacher arised a doubt:

If the data collected is very huge, what will you do for

drawing a frequency polygon?

A frequency polygon is a

graphic

representation obtained by

joining the midpoints of the

class interval.

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PUPIL ACTIVITY

We can use any spreadsheet program to do this. In

GNU/LINUX, some such programs are open office Calc and

Gnumeric.

Students further explained with the help of the projector

TEACHER RESPONSE

Teacher satisfied with the presentation

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One student presented as follows:

Height No.of people140-150 5150-160 7160-170 18170-180 10

RECAPITULATION

(i) What is frequency polygon?

(ii) Write the steps in the construction of frequency polygon.

Conduct a field study to get the data about any phenomena in our

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Teacher advices the students to reflect on the class.

FOLLOW-UP ACTIVITY

Prepare a learning module for the “Frequency polygon”