Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 3rd Term
Week: 10
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Statistics.
Topic: STATISTICS (III)
Subject Matter: Construction of frequency polygon of a given distribution.

Specific Objectives

By the end of the lesson, pupils should be able to:

Cognitive Domain:

Define a frequency polygon.
State the steps involved in constructing a frequency polygon.

Affective Domain:

Appreciate the use of frequency polygons in representing statistical data.
Develop a positive attitude towards accurate data representation.

Psychomotor Domain:

Construct a frequency polygon from a given grouped frequency distribution.
Accurately label the axes of a frequency polygon.

Work collaboratively with peers to construct frequency polygons.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Mathematics.
State Unified Scheme of Work for Senior Secondary Schools.
New General Mathematics for Senior Secondary Schools 1.

Instructional Materials

The teacher will teach this lesson with the aid of:

Graph board
Graph papers
Ruler
Pencil
Chalk/Marker

Rationale for the Lesson

This lesson helps pupils understand how to visually represent statistical data using a frequency polygon. This skill is important for interpreting data trends and comparing distributions, which is useful in various real-world situations.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of frequency distribution, class intervals, class boundaries, class marks (midpoints), and plotting points on a graph.

Lesson Content/Board Summary

STATISTICS (III)

Construction of Frequency Polygon

A frequency polygon is a graph that represents the frequency distribution of grouped data. It is formed by joining the midpoints of the tops of the bars of a histogram with straight lines.

The frequency polygon starts and ends on the horizontal axis (x-axis) by extending to the midpoints of the class intervals immediately before and after the given data.

Steps for Constructing a Frequency Polygon

The following are the steps to construct a frequency polygon:

Step 1: Prepare a frequency distribution table with class intervals and their corresponding frequencies.
Step 2: Calculate the class mark (midpoint) for each class interval. The class mark is found by adding the lower and upper class limits and dividing by 2.
Step 3: Draw the horizontal axis (x-axis) to represent the class marks and the vertical axis (y-axis) to represent the frequencies.
Step 4: Choose an appropriate scale for both axes.
Step 5: Plot points corresponding to each class mark and its frequency.
Step 6: Join the plotted points with straight lines.
Step 7: Extend the polygon to the x-axis by adding one class mark before the first class and one after the last class, both with zero frequency.

Example:

Construct a frequency polygon for the data below:

Class Interval	Frequency
1-10	5
11-20	10
21-30	15
31-40	8
41-50	2

Solution Steps:

1. Calculate class marks:

1-10: (1+10)/2 = 5.5
11-20: (11+20)/2 = 15.5
21-30: (21+30)/2 = 25.5
31-40: (31+40)/2 = 35.5
41-50: (41+50)/2 = 45.5

2. Add extra class marks with zero frequency:

Before 1-10 (class mark -4.5, freq 0)
After 41-50 (class mark 55.5, freq 0)

3. Plot points (class mark, frequency): (-4.5,0), (5.5,5), (15.5,10), (25.5,15), (35.5,8), (45.5,2), (55.5,0).

4. Join the points with straight lines to form the frequency polygon.

Teaching Methods/Instructional Techniques

Discussion, Lecture, Demonstration, Question and Answer, Visual Aids

Instructional Procedures

Step 1: Introduction

Time: 5 minutes
Teaching Skill: Set Induction
Teacher’s Activity: The teacher greets the pupils and reviews the previous lesson on frequency distribution tables. The teacher then introduces the new topic, “Construction of Frequency Polygon,” and explains that it is another way to visually represent data.
Pupils’ Activity: Pupils respond to greetings, recall previous knowledge, and listen attentively to the introduction.
Learning Point: Pupils are reminded of previous learning and introduced to the new lesson.

Step 2: Explanation of Frequency Polygon

Time: 7 minutes
Teaching Skill: Explanation/Definition
Teacher’s Activity: The teacher defines a frequency polygon as a graph formed by joining the midpoints of the tops of the bars of a histogram (or plotting class marks against frequencies) with straight lines. The teacher emphasizes its use in showing the shape of a distribution.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification.
Learning Point: Pupils understand the definition and purpose of a frequency polygon.

Step 3: Steps for Construction

Time: 8 minutes
Teaching Skill: Explanation/Instruction
Teacher’s Activity: The teacher writes and explains the steps for constructing a frequency polygon on the board, ensuring pupils understand each step, particularly calculating class marks and extending the polygon to the x-axis.
Pupils’ Activity: Pupils copy the steps into their notebooks and ask questions where necessary.
Learning Point: Pupils learn the systematic procedure for constructing a frequency polygon.

Step 4: Practical Demonstration (Example)

Time: 10 minutes
Teaching Skill: Demonstration/Modelling
Teacher’s Activity: The teacher uses the example from the board summary, calculating the class marks and plotting the points on a graph board or a large graph paper, carefully joining them with a ruler. The teacher ensures proper labeling of axes and title.
Pupils’ Activity: Pupils observe the demonstration carefully, noting the teacher’s actions and asking questions.
Learning Point: Pupils see a practical application of the steps and understand the visual representation.

Step 5: Guided Practice

Time: 8 minutes
Teaching Skill: Guided Practice/Collaboration
Teacher’s Activity: The teacher provides another simple frequency distribution table and guides the pupils, either individually or in small groups, to calculate class marks and plot points on their graph papers. The teacher moves around to offer assistance.
Pupils’ Activity: Pupils work on the given problem, calculate class marks, plot points, and draw the frequency polygon under the teacher’s guidance.
Learning Point: Pupils practice the construction process with support.

Step 6: Class Activity

Time: 7 minutes
Teaching Skill: Independent Practice
Teacher’s Activity: The teacher gives a different frequency distribution table for pupils to construct a frequency polygon independently. The teacher collects some of the constructed graphs for quick review.
Pupils’ Activity: Pupils construct the frequency polygon on their own, applying the learned steps.
Learning Point: Pupils consolidate their understanding through independent work.

Step 7: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

Define a frequency polygon.
List any three steps involved in constructing a frequency polygon.
What is the purpose of extending the frequency polygon to the x-axis at both ends?
What is a class mark, and how is it calculated?

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Assignment
Teacher’s Activity: The teacher summarizes the main points of the lesson, reiterating the importance of frequency polygons in data representation. The teacher then gives an assignment for pupils to practice at home.
Pupils’ Activity: Pupils listen to the summary and copy the assignment.
Learning Point: Pupils consolidate the lesson and are given tasks for further practice.

Lesson Keywords

Frequency Polygon – A graph showing frequency distribution by connecting class midpoints.
Class Mark (Midpoint) – The middle value of a class interval.
Class Interval – The range of values in a frequency distribution.
Frequency – The number of times a particular value or class interval occurs.

Differentiation

For pupils who grasp the concept quickly, the teacher can provide more complex data sets or ask them to compare frequency polygons of different data sets. For pupils needing more support, the teacher can provide partially completed tables or step-by-step guides, offering one-on-one assistance during practical sessions.

Note for teachers using this lesson plan

Ensure that pupils have a good understanding of class intervals, class boundaries, and class marks from previous lessons. Emphasize the importance of accurate plotting and clear labeling of axes for effective communication of data. Encourage pupils to use rulers and pencils for neat and precise graphs.