Class: Senior Secondary School 1 (SS1, SS 1, SSS1, SSS 1)
Term: 3rd Term
Week: 8
Age: 15 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: General Mathematics
Previous Lesson: Statistics: Data Collection and Bar Charts.
Topic: STATISTICS (II)
Subject Matter: Calculating sectoral component of pie chart, Drawing pie chart correctly, Interpreting the pie chart and bar chart.

Specific Objectives

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

Cognitive Domain:

Calculate the angular equivalents for sectoral components of a pie chart.
Interpret data presented in pie charts and bar charts.

Affective Domain:

Appreciate the importance of accurately representing and interpreting statistical data.
Develop an interest in using charts to understand real-world information.

Psychomotor Domain:

Draw a pie chart correctly using a compass and protractor.
Construct a bar chart from given data.

Collaborate with peers to solve problems involving chart interpretation.
Communicate findings from statistical charts effectively.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Mathematics (Senior Secondary Education).
State Unified Scheme of Work for Senior Secondary Schools.
New General Mathematics for Senior Secondary Schools 1 by J. O. Ojo, et al.
https://www.mathsisfun.com/data/pie-charts.html
https://www.bbc.co.uk/bitesize/guides/z3x4kqt/revision/1

Instructional Materials

The teacher will teach this lesson with the aid of:

Graph board
Graph papers
A pair of compass
Protractor
Ruler
Prepared examples of data tables
Pre-drawn pie charts and bar charts (on cardboard or projected)

Rationale for the Lesson

This lesson helps pupils understand how to visually represent data using pie charts and bar charts. It enables them to present information clearly and interpret statistical data from various sources, which is important for understanding everyday information like election results or population demographics.

Prerequisite/Previous Knowledge

Pupils should have prior knowledge of basic statistics, including the meaning of data, types of data, and how to represent data using simple tables and tally marks from the previous lesson on Statistics (I).

Lesson Content/Board Summary

STATISTICS (II) – PIE CHARTS AND BAR CHARTS

1. Calculating Sectoral Components of a Pie Chart

A pie chart is a circular statistical graphic divided into sectors, illustrating numerical proportion. In a pie chart, the entire circle represents the total quantity (100% or 360°).

To calculate the angle of each sector (sectoral component), the following formula is used:

Angle of sector = (Value of item / Total value) × 360°

The sum of all angles in a pie chart must be 360°.

2. Steps for Drawing a Pie Chart

The following are the steps to draw a pie chart:

Collect and organize the data into a frequency table.
Calculate the total value of all items.
Calculate the angle for each sector using the formula: (Value of item / Total value) × 360°.
Draw a circle using a compass.
Draw a radius in the circle.
Using a protractor, measure and draw the first angle from the radius.
From the new line, measure and draw the next angle, and continue until all sectors are drawn.
Label each sector clearly with its corresponding item and percentage or value.
Give the pie chart a clear title.

3. Interpreting Pie Charts

Interpreting a pie chart involves understanding the proportion each sector represents of the whole. Key aspects to consider include:

The title of the chart, which indicates what the chart represents.
The labels on each sector, which identify the categories.
The size of each sector, which shows its relative proportion or percentage of the total. A larger sector means a larger share.
The total value, which the entire circle represents.

4. Interpreting Bar Charts

A bar chart uses rectangular bars to represent data, with the length or height of the bars proportional to the values they represent. Key aspects to consider when interpreting a bar chart include:

The title of the chart, which explains the data being displayed.
The labels on the horizontal (x-axis) and vertical (y-axis) axes, which indicate the categories and their values.
The scale on the value axis (usually the y-axis), which shows the measurement unit.
The height or length of each bar, which corresponds to the value of its category.
Comparison between bars to identify trends, highest/lowest values, and differences.

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 basic statistics. The teacher then introduces the topic by asking pupils how they think large amounts of data, like election results or population figures, can be shown in a simple picture.
Pupils’ Activity: Pupils respond to questions and listen attentively to the introduction.
Learning Point: Pupils recall previous knowledge and are prepared for the new topic.

Step 2: Calculating Sectoral Components

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what a pie chart is and its components. The teacher then demonstrates how to calculate the angle for each sector using a sample data set and the formula (Value of item / Total value) × 360°. The teacher ensures pupils understand that the sum of all angles must be 360°.
Pupils’ Activity: Pupils listen, take notes, and ask questions for clarification. They participate in calculating the angles for a given example.
Learning Point: Pupils learn how to calculate the angular components for a pie chart.

Step 3: Drawing a Pie Chart

Time: 10 minutes
Teaching Skill: Demonstration/Practical Application
Teacher’s Activity: The teacher guides pupils through the steps of drawing a pie chart on the board, using the calculated angles from Step 2. The teacher demonstrates the correct use of a compass to draw the circle and a protractor to measure and draw the angles accurately, emphasizing proper labeling.
Pupils’ Activity: Pupils observe the demonstration and follow along by attempting to draw their own pie charts on graph paper using their compass and protractor.
Learning Point: Pupils develop the skill of drawing accurate pie charts.

Step 4: Interpreting Pie Charts

Time: 5 minutes
Teaching Skill: Explanation/Questioning
Teacher’s Activity: The teacher displays a pre-drawn pie chart (e.g., showing how pupils spend their pocket money) and explains how to interpret it. The teacher asks questions like “Which activity takes the largest share?” or “What percentage of money is spent on transport?”
Pupils’ Activity: Pupils observe the pie chart and answer the teacher’s questions, practicing interpretation.
Learning Point: Pupils learn to extract information and draw conclusions from pie charts.

Step 5: Interpreting Bar Charts

Time: 5 minutes
Teaching Skill: Explanation/Questioning
Teacher’s Activity: The teacher displays a pre-drawn bar chart (e.g., showing the number of pupils in different clubs) and explains its features (axes, bars, scale). The teacher then asks questions to guide pupils in interpreting the data presented in the bar chart.
Pupils’ Activity: Pupils observe the bar chart and engage in interpreting the data by answering questions.
Learning Point: Pupils learn to interpret information and make comparisons from bar charts.

Step 6: Evaluation/Review

Time: 5 minutes

Teaching Skill: Questioning/Assessment

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

Define a pie chart.
State the formula for calculating the angle of a sector in a pie chart.
List three steps involved in drawing a pie chart.
Given a total of 200 students, if 50 students chose Mathematics as their favourite subject, calculate the angle for Mathematics in a pie chart.
Mention two things you can learn by interpreting a bar chart.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 7: Conclusion

Time: 5 minutes
Teaching Skill: Summarization/Reinforcement
Teacher’s Activity: The teacher summarizes the key learning points of the lesson, reiterating the importance of accurately calculating, drawing, and interpreting pie charts and bar charts for understanding statistical data. The teacher gives pupils an assignment to practice drawing and interpreting charts.
Pupils’ Activity: Pupils listen to the summary, ask any remaining questions, and copy down the assignment.
Learning Point: Pupils reinforce their understanding of the lesson content.

Lesson Keywords

Pie Chart – A circular statistical graphic divided into sectors to illustrate numerical proportion.
Sector – A part of a circle bounded by two radii and an arc, representing a category in a pie chart.
Bar Chart – A graph that uses rectangular bars to represent data, with the length or height of the bars proportional to the values they represent.
Angular Equivalent – The angle (in degrees) that represents a proportion of the total in a pie chart.
Data – Facts and statistics collected together for reference or analysis.

Differentiation

For pupils who grasp the concepts quickly, the teacher will provide more complex data sets for calculating angles and drawing charts. For pupils who need more support, the teacher will provide simpler data, offer individual guidance during the drawing process, and use pre-calculated angles to focus on the drawing skill.

Note for teachers using this lesson plan

Ensure pupils have their geometry sets (compass and protractor) for the practical drawing session. Emphasize neatness and accuracy in drawing charts. Provide diverse real-world examples to make the interpretation of charts relatable and engaging for pupils.