Class: Junior Secondary School 3 (JSS 3 / JS3)
Term: 3rd Term
Week: 2
Age: 14 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Statistics
Previous Lesson: Statistics: Calculating Mean of a Given Data from Raw Scores.
Topic: STATISTICS (DATA PRESENTATION)
Subject Matter: Frequency table, Pictograms, Ordering or ranking data, Representing and interpreting data on a bar chart: Representing and interpreting data on a pie chart

Specific Objectives

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

Cognitive Domain:

Define frequency table, pictogram, bar chart, and pie chart.
Explain the steps involved in constructing different data presentation methods.
State the importance of presenting data clearly.

Affective Domain:

Appreciate the need for accurate data presentation.
Show interest in analyzing and interpreting statistical data.
Develop a positive attitude towards solving problems involving data representation.

Psychomotor Domain:

Construct frequency tables from raw data.
Draw pictograms, bar charts, and pie charts accurately.
Interpret information presented in various charts and tables.

Collaborate with peers to solve data presentation problems.
Share ideas on the best methods to present different types of data.
Participate actively in group discussions on data interpretation.

Reference Materials

The following resources were used in planning this lesson:

9 Years Basic Education Curriculum for Junior Secondary Schools.
State Unified Scheme of Work for Mathematics JSS 3.
New General Mathematics for Junior Secondary Schools, Book 3.
https://www.youtube.com/watch?v=M9lF2p1b250
https://www.youtube.com/watch?v=S0y1C-q7qjI

Instructional Materials

The teacher will teach this lesson with the aid of:

Charts showing examples of frequency tables, pictograms, bar charts, and pie charts.
Whiteboard/blackboard and markers/chalk.
Rulers, protractors, and compasses.
Worksheet with raw data for practice.

Rationale for the Lesson

This lesson helps pupils organize and understand raw data, making it easier to identify patterns and draw conclusions. Learning data presentation skills enables pupils to interpret information encountered in daily life, such as news reports, economic statistics, and survey results.

Prerequisite/Previous Knowledge

Pupils are expected to have basic knowledge of collecting and counting data, as well as an understanding of fractions and percentages.

Lesson Content/Board Summary

STATISTICS (DATA PRESENTATION)

Frequency Table

A frequency table is a tabular representation that displays the frequency (number of occurrences) of different values or categories within a dataset. It helps to organize raw data into a more understandable format.

Example: The scores of 20 students in a Mathematics test (out of 10) are: 5, 7, 6, 8, 5, 9, 7, 6, 5, 8, 10, 7, 6, 5, 9, 8, 7, 6, 5, 10.

Steps to construct a frequency table:

List the distinct data values in one column.
Use tally marks to count the occurrence of each value.
Write the total frequency for each value.

Score (x)	Tally	Frequency (f)
5	\|\|\|\|\|	5
6	\|\|\|\|	4
7	\|\|\|\|	4
8	\|\|\|	3
9	\|\|	2
10	\|\|	2
Total		20

Pictograms

A pictogram (or pictograph) uses pictures or symbols to represent data. Each symbol usually represents a certain number of units, and a key is provided to explain the value of each symbol.

Steps to construct a pictogram:

Choose a suitable symbol to represent the data.
Decide on a key, specifying what each symbol represents.
Draw the appropriate number of symbols for each category.

Example: If represents 5 cars, then represents 10 cars.

Ordering or Ranking Data

Ordering or ranking data involves arranging the data values in a specific sequence, either in ascending order (from smallest to largest) or descending order (from largest to smallest). This helps to quickly identify the minimum, maximum, and median values.

Example: The scores 5, 7, 6, 8, 5, 9, 7, 6, 5, 8, 10, 7, 6, 5, 9, 8, 7, 6, 5, 10.

Ascending order: 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10, 10.
Descending order: 10, 10, 9, 9, 8, 8, 8, 7, 7, 7, 7, 6, 6, 6, 6, 5, 5, 5, 5, 5.

Bar Charts

A bar chart (or bar graph) uses rectangular bars of varying heights or lengths to represent data. The bars can be vertical or horizontal, and there are usually gaps between them. It is used to compare different categories or show changes over time.

Steps to construct a bar chart:

Draw two axes: a horizontal axis for categories and a vertical axis for frequency/values.
Label the axes clearly.
Choose an appropriate scale for the frequency axis.
Draw bars of equal width for each category, with heights corresponding to their frequencies. Leave equal gaps between the bars.

Example: Favorite colors of 30 students.

Red: 10
Blue: 8
Green: 6
Yellow: 4
Black: 2

Construction Steps:

Draw horizontal axis (Colors) and vertical axis (Number of Students).
Label the horizontal axis with Red, Blue, Green, Yellow, Black.
Choose a scale for the vertical axis, e.g., 1 unit = 2 students.
Draw bars for each color to the corresponding height (Red to 10, Blue to 8, etc.) ensuring equal width and gaps.

Pie Charts

A pie chart (or circle graph) is a circular graph divided into sectors, where each sector represents a proportion of the whole. The size of each sector is proportional to the frequency it represents, measured by its angle at the center of the circle. The sum of all angles in a pie chart is 360°.

Steps to construct a pie chart:

Calculate the total frequency of all data values.
For each category, calculate the angle of its sector using the formula:
Angle = (Frequency of category / Total frequency) × 360°
Draw a circle using a compass.
Use a protractor to draw each sector according to its calculated angle.
Label each sector clearly or provide a key.

Example: Monthly family expenditure.

Food: N15,000
Rent: N10,000
Transport: N5,000
Education: N5,000
Savings: N5,000

Construction Steps:

Step 1: Calculate Total Expenditure.
Total = N15,000 + N10,000 + N5,000 + N5,000 + N5,000 = N40,000.
Step 2: Calculate Angle for Each Category.
- Food: (15,000 / 40,000) × 360° = 0.375 × 360° = 135°
- Rent: (10,000 / 40,000) × 360° = 0.25 × 360° = 90°
- Transport: (5,000 / 40,000) × 360° = 0.125 × 360° = 45°
- Education: (5,000 / 40,000) × 360° = 0.125 × 360° = 45°
- Savings: (5,000 / 40,000) × 360° = 0.125 × 360° = 45°
(Check: 135° + 90° + 45° + 45° + 45° = 360°)
Step 3: Draw the Pie Chart.
Draw a circle. Use a protractor to draw sectors with the calculated angles, starting from any radius. Label each sector.

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 introduces the lesson by asking pupils how they would organize a large amount of information, like test scores or survey results.
Pupils’ Activity: Pupils respond by suggesting ways to group or list the information.
Learning Point: Pupils recall prior knowledge of data handling and are introduced to the concept of data presentation.

Step 2: Frequency Tables

Time: 10 minutes
Teaching Skill: Explanation/Demonstration
Teacher’s Activity: The teacher explains what a frequency table is and demonstrates how to construct one using the provided example of students’ test scores, emphasizing tally marks.
Pupils’ Activity: Pupils observe the demonstration, ask questions, and copy the example into their notes.
Learning Point: Pupils learn to construct frequency tables to organize raw data.

Step 3: Pictograms and Ordering Data

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains pictograms, showing how symbols represent data and how to choose a key. The teacher also explains ordering data in ascending and descending order with an example.
Pupils’ Activity: Pupils identify the symbols used in pictograms and practice ordering data values.
Learning Point: Pupils understand how to use pictograms and order data for better analysis.

Step 4: Bar Charts

Time: 8 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher explains the components of a bar chart and demonstrates how to draw a bar chart using the example of favorite colors, emphasizing labels, scales, and gaps between bars.
Pupils’ Activity: Pupils pay attention to the steps and try to sketch the bar chart as guided by the teacher.
Learning Point: Pupils learn to represent data using bar charts.

Step 5: Pie Charts

Time: 8 minutes
Teaching Skill: Explanation/Calculation
Teacher’s Activity: The teacher explains pie charts, focusing on how to calculate the angle for each sector. The teacher demonstrates the calculation and construction using the family expenditure example.
Pupils’ Activity: Pupils follow the calculations and understand how angles represent proportions in a circle.
Learning Point: Pupils learn to calculate angles and construct pie charts.

Step 6: Class Activity/Practice

Time: 5 minutes
Teaching Skill: Collaborative Learning
Teacher’s Activity: The teacher provides a small dataset and asks pupils to work in pairs to either create a frequency table or sketch a simple bar chart.
Pupils’ Activity: Pupils work collaboratively to apply what they have learned.
Learning Point: Pupils practice the skills acquired and reinforce their understanding.

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 table.
State two differences between a bar chart and a pictogram.
How do you calculate the angle for a sector in a pie chart?
Given the data: 3, 5, 2, 5, 4, 3, 2, 5. Construct a frequency table.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 2 minutes
Teaching Skill: Summarization
Teacher’s Activity: The teacher summarizes the key methods of data presentation discussed: frequency tables, pictograms, bar charts, and pie charts, emphasizing their importance in making data understandable.
Pupils’ Activity: Pupils listen attentively and ask any final questions.
Learning Point: Pupils consolidate their understanding of data presentation techniques.

Lesson Keywords

Frequency Table – A table that organizes data by showing how often each value or category appears.
Pictogram – A graph that uses pictures or symbols to represent data.
Bar Chart – A graph that uses rectangular bars to compare different categories of data.
Pie Chart – A circular graph divided into sectors, where each sector represents a proportion of the whole.
Ordering Data – Arranging data in ascending or descending sequence.

Differentiation

For pupils who grasp concepts quickly, the teacher will provide more complex datasets for them to organize and represent using multiple methods. For pupils needing more support, the teacher will provide simplified data and offer step-by-step guidance, focusing on one data presentation method at a time.

Note for teachers using this lesson plan

Encourage pupils to use appropriate tools (rulers, protractors, compasses) for accurate drawing of charts. Emphasize the importance of clear labeling and choosing appropriate scales for graphs. Practical examples relevant to pupils’ daily lives will enhance understanding and engagement.