Measurement of Central Tendency, Median, Ordering Data and Finding Middle Value for Primary 5

Class: Primary 5
Term: 3rd Term
Week: 9
Age: 10 years
Duration: 45 minutes
Subject: General Mathematics
Curriculum Theme: Measurement of Central Tendency
Previous Lesson: Measurement of Central Tendency, Mean, Calculation and Daily Applications.
Topic: MEASUREMENT OF CENTRAL TENDENCY (CONT).
Subject Matter: Meaning of median of a data, calculating median of results collected, calculating median as applicable in daily activities, identifying median from a given data, quantitative aptitude on median.

Specific Objectives

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

Cognitive Domain:

• Define median as the middle number in an ordered data set.
• Arrange numbers in ascending or descending order to find the median.
• Calculate the median for both odd and even numbers of data points.
• Identify the median from a given set of data.
• Solve quantitative aptitude problems involving median.

Affective Domain:

• Appreciate the importance of median in understanding data in daily life.
• Participate actively in class discussions and problem-solving.

Psychomotor Domain:

• Accurately arrange data sets in order.
• Correctly apply the steps to calculate the median.

Social Domain:

• Work cooperatively with peers when collecting and analyzing data.

Reference Materials

The following resources were used in planning this lesson:

• 9 Years Basic Education Curriculum for Primary 5 Mathematics.
• State Unified Scheme of Work for Primary 5 Mathematics.
• New General Mathematics for Primary Schools Book 5.
• Quantitative aptitude workbook.

Instructional Materials

The teacher will teach this lesson with the aid of:

• Chart showing examples of data sets.
• Flash cards with numbers.
• Posters illustrating how to find the median.
• Quantitative aptitude workbook.

Rationale for the Lesson

This lesson helps pupils understand how to find the middle value in a set of numbers, which is called the median. This skill is important for making sense of information and data they encounter every day, such as class scores or survey results.

Prerequisite/Previous Knowledge

Pupils have prior knowledge of arranging numbers in ascending and descending order and basic understanding of data collection.

Lesson Content/Board Summary

Median of a Data

Meaning of Median

The median is the middle value in a set of numbers that has been arranged in order (either ascending or descending). It divides the data set into two equal halves.

Calculating Median for an Odd Number of Data Points

When there is an odd number of data points, the median is simply the middle number after arranging the data.

Steps:

• Step 1: Arrange the data in ascending (smallest to largest) or descending (largest to smallest) order.
• Step 2: Identify the middle number. This is the median.

Example 1: Find the median of the following numbers: 5, 2, 8, 1, 6.

Solution:

Step 1: Arrange the numbers in ascending order:

1, 2, 5, 6, 8

Step 2: Identify the middle number.

The middle number is 5.

Therefore, the median is 5.

Calculating Median for an Even Number of Data Points

When there is an even number of data points, there are two middle numbers. The median is the average of these two middle numbers.

Steps:

• Step 1: Arrange the data in ascending or descending order.
• Step 2: Identify the two middle numbers.
• Step 3: Add the two middle numbers and divide the sum by 2 to find their average. This average is the median.

Example 1: Find the median of the following numbers: 7, 3, 9, 2, 5, 4.

Solution:

Step 1: Arrange the numbers in ascending order:

2, 3, 4, 5, 7, 9

Step 2: Identify the two middle numbers.

The two middle numbers are 4 and 5.

Step 3: Calculate the average of the two middle numbers.

Median = (4 + 5) / 2

Median = 9 / 2

Median = 4.5

Therefore, the median is 4.5.

Calculating Median as Applicable in Daily Activities

Median can be used to find the middle value in real-life situations, such as:

• Finding the middle height of students in a class.
• Finding the middle amount of money spent by a group of friends.
• Finding the middle score in a test for a group of pupils.

Example: Five friends spent N50, N80, N30, N60, N40 on snacks. Find the median amount spent.

Solution:

Step 1: Arrange the amounts in ascending order:

N30, N40, N50, N60, N80

Step 2: Identify the middle amount.

The middle amount is N50.

Therefore, the median amount spent is N50.

Identifying Median from a Given Data

To identify the median, the data must always be ordered first.

Example: From the data set {10, 4, 15, 8, 12}, identify the median.

Solution:

Step 1: Arrange in ascending order: 4, 8, 10, 12, 15.

Step 2: The middle number is 10.

Thus, the median is 10.

Quantitative Aptitude on Median

These problems often involve applying the definition of median in slightly more complex scenarios.

Example: The median of the numbers 3, x, 7, 10, 12 is 7. What could be the value of x?

Solution:

Step 1: Arrange the given numbers (excluding x) in ascending order: 3, 7, 10, 12.

Step 2: Since the median is 7, and there are 5 numbers in total, the 3rd number in the ordered list must be 7.

Step 3: For 7 to be the middle number (3rd position), ‘x’ must be less than or equal to 7 but greater than or equal to 3, so when arranged, ‘x’ would be before or at the position of 7. However, if ‘x’ is 7, then the ordered list would be 3, 7, 7, 10, 12. If ‘x’ is 5, the ordered list would be 3, 5, 7, 10, 12. Both give 7 as the median.

Possible values for x are any number from 3 up to 7, inclusive, such that when the numbers are ordered, 7 remains the middle value.

If the numbers are arranged as: 3, (x), 7, 10, 12, for 7 to be the median, x must be less than or equal to 7. A simple answer is that x can be 7 or any number between 3 and 7 (e.g., 5).

Let’s assume x = 5. Ordered list: 3, 5, 7, 10, 12. Median = 7.

Let’s assume x = 7. Ordered list: 3, 7, 7, 10, 12. Median = 7.

Therefore, x can be any number such that when the data is ordered, 7 remains the middle value. For example, x could be 5 or 7.

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 if they remember what they learned about finding the average (mean) of a set of numbers. The teacher then introduces the topic of median as another way to find a “middle” value in data.

Pupils’ Activity: Pupils respond to the teacher’s questions about mean and listen attentively to the introduction of the new topic.

Learning Point: Pupils recall previous knowledge and are prepared for the new lesson.

Step 2: Meaning of Median

Time: 7 minutes

Teaching Skill: Explanation/Definition

Teacher’s Activity: The teacher explains the meaning of median as the middle number in an ordered data set. The teacher uses a simple example like pupils’ ages to demonstrate arranging data and finding the middle. The teacher writes the definition on the board.

Pupils’ Activity: Pupils listen, ask questions for clarification, and copy the definition into their notebooks.

Learning Point: Pupils understand the definition of median.

Step 3: Calculating Median for Odd Number of Data Points

Time: 8 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher guides pupils through the steps to calculate the median for an odd number of data points using examples from the board summary. The teacher demonstrates arranging numbers and identifying the middle value. The teacher encourages pupils to work along with the examples.

Pupils’ Activity: Pupils observe, participate in arranging numbers, and solve example problems in their exercise books.

Learning Point: Pupils learn how to calculate the median for an odd number of data points.

Step 4: Calculating Median for Even Number of Data Points

Time: 8 minutes

Teaching Skill: Demonstration/Problem Solving

Teacher’s Activity: The teacher explains that when there is an even number of data points, there are two middle numbers. The teacher demonstrates how to find the average of these two numbers to get the median, using examples from the board summary. The teacher emphasizes the division by 2.

Pupils’ Activity: Pupils pay attention to the new step, identify the two middle numbers, and practice finding their average to determine the median.

Learning Point: Pupils learn how to calculate the median for an even number of data points.

Step 5: Applying and Identifying Median in Daily Activities

Time: 7 minutes

Teaching Skill: Application/Discussion

Teacher’s Activity: The teacher provides simple scenarios relevant to pupils’ daily lives (e.g., scores in a mini-test, number of siblings) and guides them to identify the median. The teacher also shows how to identify the median from a pre-arranged data set.

Pupils’ Activity: Pupils participate in discussions, identify median in various scenarios, and practice identifying median from given data sets.

Learning Point: Pupils understand the practical application of median and can identify it from data.

Step 6: Quantitative Aptitude on Median

Time: 5 minutes

Teaching Skill: Problem Solving

Teacher’s Activity: The teacher presents a simple quantitative aptitude problem involving median (e.g., finding a missing value if the median is known) and guides pupils on how to approach such problems by using the definition of median.

Pupils’ Activity: Pupils attempt to solve the quantitative aptitude problem with guidance from the teacher.

Learning Point: Pupils develop problem-solving skills related to median.

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 the term “median.”
2. State the first step in finding the median of any data set.
3. Find the median of the following numbers: 10, 3, 7, 5, 12.
4. Find the median of the following numbers: 2, 8, 4, 6, 10, 12.

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

Teacher’s Activity: The teacher summarizes the key points of the lesson, reiterating the importance of arranging data and the methods for finding the median for both odd and even data sets. The teacher gives homework.

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

Learning Point: Pupils reinforce their understanding of the median and its calculation.

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

Lesson Keywords

• Median – The middle value in a data set when the numbers are arranged in order.
• Data – A collection of facts, such as numbers, words, measurements, or observations.
• Ascending Order – Arranging numbers from the smallest to the largest.
• Descending Order – Arranging numbers from the largest to the smallest.
• Average – The sum of a set of numbers divided by the count of numbers in the set.

Differentiation

For pupils who grasp the concept quickly, the teacher will provide more challenging quantitative aptitude problems or ask them to create their own data sets and find the median. For pupils who need more support, the teacher will provide additional guided practice with smaller data sets and visual aids, focusing on the step-by-step process.

Note for teachers using this lesson plan

Ensure pupils understand the importance of ordering data before attempting to find the median. Emphasize the difference in calculation for odd versus even numbers of data points. Encourage group work for data collection and median calculation to foster collaborative learning.