Measurement of Central Tendency, Mode and Everyday Uses for Primary 5

Class: Primary 5
Term: 3rd Term
Week: 7
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Nil
Previous Lesson: Data Presentation, Tally, Bar Graph, Pictogram and Pie Chart.
Topic: MEASUREMENT OF CENTRAL TENDENCY.
Subject Matter: Mode of a given data, identifying mode in daily life activities, calculating mode of a given data, mode of a set of data in daily activities, quantitative aptitude on mode.

Specific Objectives

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

Cognitive Domain:

• Define mode as a measure of central tendency.
• Identify the mode from a given set of data.
• Calculate the mode for various data sets.
• Solve quantitative aptitude problems involving mode.

Affective Domain:

• Appreciate the importance of mode in understanding data.
• Relate the concept of mode to real-life situations.

Psychomotor Domain:

• Collect simple data from their environment.
• Organize collected data and prepare a tally.
• Record the mode from collected data.

Social Domain:

• Participate actively in group activities for data collection.
• Collaborate with peers to identify and calculate mode.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum (Primary 4-6) Mathematics.
• Lagos State Unified Scheme of Work for Primary Schools.
• Pre-Vocational Studies for Primary Schools Book 5.
• https://www.mathsisfun.com/data/mode.html
• https://www.splashlearn.com/math-vocabulary/data-management/mode

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart showing examples of data sets.
• Flash cards with different numbers.
• Posters illustrating daily life examples of mode.
• Quantitative aptitude workbook.

Rationale for the Lesson

This lesson helps pupils understand how to find the most frequent item in a group of data. Understanding mode is important for pupils to make sense of information around them, such as knowing the most popular shoe size or favourite colour in their class, which is a useful skill in daily life.

Prerequisite/Previous Knowledge

Pupils have basic knowledge of counting, comparing numbers, and simple data collection.

Lesson Content/Board Summary

MEASUREMENT OF CENTRAL TENDENCY: MODE

What is Mode?

The mode is the number or item that appears most frequently in a set of data. It is the value that occurs with the highest frequency.

How to Find the Mode

To find the mode, follow these steps:

• Arrange the data in ascending or descending order (optional, but makes it easier).
• Count how many times each number or item appears.
• The number or item that appears most often is the mode.

Examples of Calculating Mode

Let’s find the mode for different data sets:

Example 1: Finding a single mode

Find the mode of the following numbers: 2, 3, 5, 2, 4, 2, 6.

Steps:

1. Arrange the numbers in order: 2, 2, 2, 3, 4, 5, 6.
2. Count the frequency of each number:
   • 2 appears 3 times.
   • 3 appears 1 time.
   • 4 appears 1 time.
   • 5 appears 1 time.
   • 6 appears 1 time.
3. Identify the number that appears most often. The number 2 appears 3 times, which is more than any other number.

Answer: The mode is 2.

Example 2: Finding multiple modes (Bimodal)

Find the mode of the following numbers: 10, 12, 15, 12, 18, 10, 14.

Steps:

1. Arrange the numbers in order: 10, 10, 12, 12, 14, 15, 18.
2. Count the frequency of each number:
   • 10 appears 2 times.
   • 12 appears 2 times.
   • 14 appears 1 time.
   • 15 appears 1 time.
   • 18 appears 1 time.
3. Identify the number(s) that appear most often. Both 10 and 12 appear 2 times, which is the highest frequency.

Answer: The modes are 10 and 12 (this is called bimodal).

Example 3: Data with no mode

Find the mode of the following numbers: 7, 8, 9, 10, 11.

Steps:

1. Arrange the numbers in order: 7, 8, 9, 10, 11.
2. Count the frequency of each number: Each number appears only 1 time.
3. Identify the number(s) that appear most often. No number appears more frequently than any other.

Answer: There is no mode for this data set.

NOTE: A data set can have one mode, more than one mode (e.g., bimodal for two modes), or no mode at all.

Identifying Mode in Daily Life Activities

The mode helps us understand what is most common or popular. Here are some daily life examples:

• Favourite colours: If pupils list their favourite colours, the colour chosen by most pupils is the mode.
• Shoe sizes: In a shoe shop, the most frequently sold shoe size is the mode.
• Types of fruits: The type of fruit most commonly bought by customers in a market is the mode.
• Test scores: The score that many pupils achieved in a test can be the mode.

Quantitative Aptitude on Mode

Quantitative aptitude questions on mode often involve finding the mode from a given set of numbers or solving word problems that require identifying the most frequent item.

Example 1:

A shopkeeper recorded the number of loaves of bread sold each day for a week: 25, 30, 25, 28, 30, 25, 29. What is the mode of bread sales?

Steps:

1. List the sales numbers: 25, 30, 25, 28, 30, 25, 29.
2. Arrange in order: 25, 25, 25, 28, 29, 30, 30.
3. Count frequencies:
   • 25 appears 3 times.
   • 28 appears 1 time.
   • 29 appears 1 time.
   • 30 appears 2 times.
4. Identify the most frequent: 25 appears most often.

Answer: The mode of bread sales is 25 loaves.

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 asks them to recall what they understand by “data” and “information”. The teacher then asks pupils to think about what is popular in their class, like the most common favourite colour or most common age.

Pupils’ Activity: Pupils respond to the teacher’s questions, sharing their ideas about data and popular items in class.

Learning Point: Pupils recall prior knowledge and are introduced to the idea of finding the most frequent item.

Step 2: Explanation of Mode

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher defines mode as the number or item that appears most frequently in a set of data. The teacher explains that it helps to know what is most common. The teacher uses simple examples like “If 5 pupils have blue pens and 3 have red pens, blue is the mode.”

Pupils’ Activity: Pupils listen attentively and copy the definition of mode into their notebooks.

Learning Point: Pupils understand the definition of mode and its basic concept.

Step 3: Identifying Mode in Daily Life

Time: 8 minutes

Teaching Skill: Real-world Connection/Brainstorming

Teacher’s Activity: The teacher asks pupils to think of situations in their daily lives where they might want to know the “most common” thing. The teacher writes down their suggestions and adds more examples from the board summary (e.g., favourite fruits, shoe sizes, popular games).

Pupils’ Activity: Pupils actively participate by suggesting daily life examples where identifying the mode would be useful. They discuss how it applies to their experiences.

Learning Point: Pupils connect the concept of mode to real-life situations, making it more meaningful.

Step 4: Calculating Mode (Single Mode Example)

Time: 7 minutes

Teaching Skill: Demonstration/Guided Practice

Teacher’s Activity: The teacher presents a simple data set on the board (e.g., 2, 3, 5, 2, 4, 2, 6). The teacher guides pupils through the steps to find the mode, demonstrating how to arrange the numbers and count frequencies, as shown in Example 1 of the board summary.

Pupils’ Activity: Pupils follow the teacher’s steps, arranging the numbers and counting frequencies to identify the mode. They work on the example in their notebooks.

Learning Point: Pupils practice calculating the mode for a data set with a single mode.

Step 5: Calculating Mode (Multiple/No Mode Examples)

Time: 8 minutes

Teaching Skill: Problem-Solving/Clarification

Teacher’s Activity: The teacher presents more complex data sets (e.g., 10, 12, 15, 12, 18, 10, 14 for bimodal, and 7, 8, 9, 10, 11 for no mode). The teacher guides pupils through these examples, explaining how to handle cases with two modes or no mode, as demonstrated in Examples 2 and 3 of the board summary.

Pupils’ Activity: Pupils work through the new examples, identifying multiple modes or stating when there is no mode. They ask questions for clarification.

Learning Point: Pupils learn to identify multiple modes and understand when a data set has no mode.

Step 6: Quantitative Aptitude on Mode

Time: 5 minutes

Teaching Skill: Application/Problem-Solving

Teacher’s Activity: The teacher presents a quantitative aptitude problem from the board summary or workbook (e.g., the bread sales example). The teacher guides pupils to apply their knowledge of mode to solve the problem, emphasizing the steps involved.

Pupils’ Activity: Pupils attempt to solve the quantitative aptitude problem independently or in pairs, applying the steps learned to find the mode in a real-world context.

Learning Point: Pupils apply the concept of mode to solve practical problems.

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. Define mode in your own words.
2. Given the numbers: 6, 8, 5, 6, 9, 5, 6. What is the mode?
3. Give two examples of how mode can be used in daily life.
4. Can a data set have more than one mode? Explain.

Pupils’ Activity: Pupils answer orally and in writing.

Learning Point: Pupils demonstrate understanding of the lesson.

Step 8: Conclusion

Time: 0 minutes

Teacher’s Activity: The teacher summarizes the lesson by reiterating that mode is the most frequent item in a data set and is useful for understanding common occurrences. The teacher assigns homework.

Pupils’ Activity: Pupils listen to the summary and copy down the homework.

Learning Point: Pupils consolidate their understanding of mode.

Home Task: Solve three new exercises on MEASUREMENT OF CENTRAL TENDENCY. Show each step and check each answer.

Lesson Keywords

• Mode – The number or item that appears most frequently in a set of data.
• Data – Facts and statistics collected together for reference or analysis.
• Frequency – The number of times an event or value occurs.
• Central Tendency – A central or typical value for a probability distribution.

Differentiation

For pupils who grasp the concept quickly, the teacher will provide more challenging data sets, including larger numbers or more complex real-world scenarios. For pupils needing extra support, the teacher will provide simpler data sets, use visual aids more extensively, and offer one-on-one guidance during practice exercises.

Note for teachers using this lesson plan

Teachers should ensure pupils actively participate in data collection and discussion to make the concept of mode relatable. Emphasize that not all data sets have a single mode, and some may have no mode at all. Encourage pupils to create their own simple data sets and find the mode.