Lesson Note on Statistics: Data Presentation in Ordered Form for JSS 2

Class: Junior Secondary School 2 (JSS 2 / JS2)
Term: 3rd Term
Week: 7
Age: 13 years
Duration: 45 minutes
Subject: Mathematics
Curriculum Theme: Mathematics
Previous Lesson: Collection of Data.
Topic: STATISTICS
Subject Matter: Data presentation in ordered form, Frequency tables: Pie chart

Specific Objectives

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

Cognitive Domain:

• Define data and ordered data.
• Construct frequency tables from raw data.
• Calculate the angles of sectors for a pie chart.
• Draw a pie chart to represent given data.

Affective Domain:

• Appreciate the importance of presenting data clearly.
• Show interest in analyzing statistical information.

Psychomotor Domain:

• Accurately arrange data in ascending or descending order.
• Use a compass and protractor correctly to draw pie charts.

Social Domain:

• Collaborate in groups to present data in various forms.
• Discuss the advantages of different data presentation methods.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum
• State Unified Scheme of Work
• New General Mathematics for Junior Secondary Schools Book 2
• https://www.studywithjosh.com/lesson-notes/jss2/mathematics/third-term/week-7
• https://www.scholor.ng/lesson-note/jss2-mathematics-lesson-note-for-third-term-week-7

Instructional Materials

The teacher will teach this lesson with the aid of:

• Charts showing examples of ordered data and frequency tables.
• A protractor and compass.
• A ruler and pencil.
• A whiteboard and markers.

Rationale for the Lesson

This lesson helps pupils understand how to organize and display numerical information. It enables them to interpret data more easily and make sense of real-world statistics found in newspapers, reports, and daily life.

Prerequisite/Previous Knowledge

Pupils are expected to have prior knowledge of collecting data, basic arithmetic operations, and measuring angles with a protractor.

Lesson Content/Board Summary

STATISTICS

Data Presentation in Ordered Form

Data refers to a collection of facts, such as numbers, words, measurements, observations, or descriptions of things. Raw data is data collected that has not yet been organized. Ordered data is data arranged in a specific sequence, either from the smallest to the largest (ascending order) or from the largest to the smallest (descending order).

Example: Given the following scores of 10 pupils in a test: 5, 8, 3, 7, 5, 9, 6, 3, 8, 7.

Ordered Data (Ascending): 3, 3, 5, 5, 6, 7, 7, 8, 8, 9

Frequency Tables

A frequency table is a table that shows the number of times each item or value appears in a set of data. It helps to organize raw data into a more manageable form.

Components of a Frequency Table:

• Item/Score: The individual values or categories in the data set.
• Tally: Marks used to count the occurrence of each item. A group of five tally marks is represented as four vertical lines with a diagonal line through them (IIII).
• Frequency: The total number of times an item appears, obtained by counting the tally marks.

Example: Using the ordered data: 3, 3, 5, 5, 6, 7, 7, 8, 8, 9, construct a frequency table.

Pie Chart

A pie chart (or circle graph) is a circular statistical graphic divided into sectors to illustrate numerical proportions. In a pie chart, the arc length of each sector, and consequently its area and central angle, is proportional to the quantity it represents.

The entire circle represents the total frequency (100% or 360°).

Formula for calculating the angle of a sector:

Angle of sector = (Frequency of category / Total frequency) × 360°

Steps to construct a pie chart:

1. Find the total frequency of the data.
2. Calculate the angle for each category using the formula.
3. Draw a circle using a compass.
4. Use a protractor to measure and draw each sector based on its calculated angle, starting from a radius.
5. Label each sector clearly with its category and/or percentage.
6. Give the pie chart a suitable title.

Worked Example 1:

The favourite colours of 20 pupils are given in the frequency table below. Construct a pie chart to represent this data.

Solution:

Step 1: Total frequency = 20

Step 2: Calculate the angle for each colour:

• Angle for Red = (10 / 20) × 360° = 0.5 × 360° = 180°
• Angle for Blue = (5 / 20) × 360° = 0.25 × 360° = 90°
• Angle for Green = (5 / 20) × 360° = 0.25 × 360° = 90°

Step 3: Check: 180° + 90° + 90° = 360°

Step 4: Draw a circle with a compass, then use a protractor to draw sectors with angles 180°, 90°, and 90°. Label the sectors “Red”, “Blue”, and “Green”.

Worked Example 2:

The table below shows how 30 students travel to school. Draw a pie chart for this data.

Solution:

Step 1: Total frequency = 30

Step 2: Calculate the angle for each mode of transport:

• Angle for Walk = (15 / 30) × 360° = 0.5 × 360° = 180°
• Angle for Bus = (10 / 30) × 360° = (1/3) × 360° = 120°
• Angle for Car = (5 / 30) × 360° = (1/6) × 360° = 60°

Step 3: Check: 180° + 120° + 60° = 360°

Step 4: Draw a circle with a compass, then use a protractor to draw sectors with angles 180°, 120°, and 60°. Label the sectors “Walk”, “Bus”, and “Car”.

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 collection of data. The teacher then asks pupils how they might organize large amounts of data to make it easier to understand.
Pupils’ Activity: Pupils respond to the greeting and recall methods of data collection. They suggest ways to organize data.
Learning Point: Pupils connect previous knowledge to the new topic and understand the need for data organization.

Step 2: Data Presentation in Ordered Form

Time: 7 minutes
Teaching Skill: Explanation/Illustration
Teacher’s Activity: The teacher explains what data and ordered data are, giving examples of raw data and demonstrating how to arrange it in ascending and descending order on the board.
Pupils’ Activity: Pupils listen attentively, ask questions for clarification, and practice ordering small data sets provided by the teacher.
Learning Point: Pupils learn to define and arrange data in ordered forms.

Step 3: Frequency Tables

Time: 7 minutes
Teaching Skill: Demonstration/Guided Practice
Teacher’s Activity: The teacher introduces frequency tables, explaining its components (item, tally, frequency). The teacher then demonstrates how to construct a frequency table using the ordered data from Step 2, emphasizing the use of tally marks.
Pupils’ Activity: Pupils observe the demonstration and participate by counting tallies and frequencies. They copy the example into their notebooks.
Learning Point: Pupils understand how to construct and interpret frequency tables.

Step 4: Introduction to Pie Charts

Time: 7 minutes
Teaching Skill: Explanation/Concept Development
Teacher’s Activity: The teacher introduces pie charts as another way to present data, explaining that a circle represents the whole (360 degrees). The teacher writes the formula for calculating sector angles on the board.
Pupils’ Activity: Pupils listen to the explanation and copy the formula into their notebooks. They identify real-life examples of pie charts.
Learning Point: Pupils learn the definition of a pie chart and the formula for calculating its sector angles.

Step 5: Worked Example 1 (Pie Chart Construction)

Time: 7 minutes
Teaching Skill: Problem Solving/Demonstration
Teacher’s Activity: The teacher presents Worked Example 1 from the board summary, guiding pupils step-by-step through calculating the angles for each sector and demonstrating how to draw the pie chart using a compass and protractor.
Pupils’ Activity: Pupils follow the teacher’s steps, calculate angles, and observe the drawing process. They ask questions about using the instruments.
Learning Point: Pupils practice calculating sector angles and understand the practical steps of drawing a pie chart.

Step 6: Worked Example 2 (Pie Chart Construction)

Time: 5 minutes
Teaching Skill: Guided Practice
Teacher’s Activity: The teacher presents Worked Example 2. The teacher guides the pupils to calculate the angles independently and then supervises as they attempt to draw the pie chart in their exercise books.
Pupils’ Activity: Pupils calculate the angles for the sectors and attempt to draw the pie chart, seeking assistance from the teacher where needed.
Learning Point: Pupils consolidate their understanding and skill in constructing pie charts.

Step 7: Evaluation/Review

Time: 5 minutes
Teaching Skill: Questioning/Assessment
Teacher’s Activity: The teacher evaluates the learning by asking the following questions:

1. What is ordered data?
2. State two components of a frequency table.
3. How many degrees are in a full circle used for a pie chart?
4. If 10 out of 40 students chose Mathematics as their favourite subject, what angle would represent Mathematics in a pie chart?

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 learning points about data presentation, frequency tables, and pie charts. The teacher assigns homework, asking pupils to collect data on a simple topic (e.g., favourite fruits of 15 family members) and present it in an ordered list, a frequency table, and a pie chart.
Pupils’ Activity: Pupils listen to the summary and copy down the homework assignment.
Learning Point: Pupils review the main concepts of the lesson and prepare for independent practice.

Lesson Keywords

• Data – Facts and statistics collected together for reference or analysis.
• Ordered Data – Data arranged in a specific sequence, either ascending or descending.
• Frequency Table – A table showing the number of times each item occurs in a data set.
• Tally Marks – Marks used to count items in groups, typically in fives.
• Frequency – The number of occurrences of a repeating event per unit of time.
• Pie Chart – A circular graph divided into sectors, where each sector represents a proportion of the whole.
• Sector – A part of a circle enclosed by two radii and an arc.
• Protractor – An instrument used for measuring and drawing angles.
• Compass – An instrument used for drawing circles or arcs.

Differentiation

For pupils who grasp the concepts quickly, the teacher will provide more complex data sets for frequency table construction and pie chart drawing. For pupils who need additional support, the teacher will offer one-on-one guidance during practical drawing sessions and provide simpler data sets with fewer categories.

Note for teachers using this lesson plan

Ensure pupils have access to rulers, pencils, protractors, and compasses for the practical aspects of drawing pie charts. Emphasize the accuracy required in measuring angles. Encourage pupils to work in pairs during the drawing exercises to foster peer learning and support.