Mathematics - Senior Secondary 1 - Definition of Sets

Definition of Sets

Get it on Google Play
Get it on the Apple App Store
  1. Home
  2. Comprehensive Lesson Plan and Notes
  3. Senior Secondary 1
  4. Definition of Sets

TERM: 1ST TERM

WEEK: 9
Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Definition of Sets
Focus: Set notation (listing/roster method, rule method, set builder notation) and Types of Sets (e.g., universal set, empty set, finite set, infinite set, subset, disjoint set, power set).

SPECIFIC OBJECTIVES:
By the end of the lesson, students should be able to:

  1. Define a set.
  2. Use and apply set notation (listing or roster method, rule method, set builder notation).
  3. Identify and define the types of sets: universal set, empty set, finite set, infinite set, subset, disjoint set, and power set.
  4. Illustrate sets using objects in the classroom, school, and home environments.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practical exercises and examples
  • Use of analogies

INSTRUCTIONAL MATERIALS:

  • Objects in the classroom (e.g., chairs, books)
  • Flashcards with set notation examples
  • Whiteboard and markers
  • Mathematical sets

 

PERIOD 1 & 2: Introduction to Sets and Set Notation

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Sets

Explains the definition of a set: a collection of distinct objects, which are called elements or members of the set.

Students listen attentively, ask clarifying questions.

Step 2 - Set Notation

Introduces the roster or listing method (e.g., A = {1, 2, 3}), rule method (e.g., B = {x

x is an even number}), and set builder notation (e.g., C = {x

Step 3 - Examples

Provides examples from the classroom environment: A = {Chairs, Tables}, B = {Students in class}, and C = {Books on the shelf}.

Students observe, take notes, and ask for clarification where needed.

Step 4 - Guided Practice

Guides students to create their own sets from objects around the school or classroom.

Students create and discuss sets from their surroundings.

NOTE ON BOARD:

  • Roster Method: A = {1, 2, 3, 4}
  • Rule Method: B = {x | x is a positive integer}
  • Set Builder Notation: C = {x | x ∈ Z, x > 0}

EVALUATION (5 exercises):

  1. Write down a set using the roster method for the days of the week.
  2. Use set builder notation to represent the set of all even numbers.
  3. Explain the difference between the roster method and set builder notation.
  4. Create a set using the rule method for all odd numbers less than 10.
  5. What is the set notation for a set containing the colors red, green, and blue?

CLASSWORK (5 questions):

  1. Write a set for the numbers between 1 and 5 using the roster method.
  2. Use set builder notation to describe the set of prime numbers less than 20.
  3. What is the rule method for describing the set of even numbers?
  4. Give an example of a set using the listing method.
  5. What notation would you use to describe the set of natural numbers greater than 0?

ASSIGNMENT (5 tasks):

  1. Research and write the set of primary colors using the listing method.
  2. Create a set of the first 5 square numbers using set builder notation.
  3. Describe a set of students in your class who play sports using the rule method.
  4. Write a set for all even numbers greater than 10 using roster notation.
  5. Explain why the set of all students in your class is a finite set.

 

PERIOD 3 & 4: Types of Sets

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Types of Sets

Defines the types of sets: universal set, empty set, finite set, infinite set, subset, disjoint set, power set. Provides examples from everyday life.

Students take notes and ask clarifying questions.

Step 2 - Universal Set

Introduces the universal set (U) as the set that contains all the elements under consideration.

Students observe examples like U = {1, 2, 3, 4, 5, 6}.

Step 3 - Empty Set and Finite Set

Explains the empty set (∅) and finite sets (sets with a limited number of elements). Examples include ∅ = {} and a finite set of chairs in the classroom.

Students copy examples and understand the concept.

Step 4 - Infinite Set and Subset

Defines infinite sets (sets with unlimited elements, e.g., natural numbers) and subsets (e.g., A = {2, 4, 6} is a subset of B = {1, 2, 3, 4, 5, 6}).

Students participate in the discussion and write down the definitions.

Step 5 - Disjoint Set and Power Set

Explains disjoint sets (sets with no common elements) and power sets (sets of all subsets of a set). Example: If A = {1, 2}, the power set is P(A) = {∅, {1}, {2}, {1, 2}}.

Students take notes and ask questions.

NOTE ON BOARD:

  • Universal Set (U): The set of all elements.
  • Empty Set (∅): A set with no elements.
  • Finite Set: A set with a limited number of elements.
  • Infinite Set: A set with an unlimited number of elements.
  • Subset (⊆): A set that contains elements of another set.
  • Disjoint Set: Sets that have no common elements.
  • Power Set: The set of all subsets of a set.

EVALUATION (5 exercises):

  1. What is a universal set?
  2. Write an example of an empty set.
  3. Explain what an infinite set is with an example.
  4. How is a subset different from a power set?
  5. Give an example of two disjoint sets.

CLASSWORK (5 questions):

  1. Write the power set for the set A = {1, 2}.
  2. Identify the universal set for the numbers 1 to 10.
  3. Give an example of a finite set.
  4. Are the sets A = {1, 3, 5} and B = {2, 4, 6} disjoint?
  5. What is the empty set for the set of months in a year that start with the letter "Z"?

ASSIGNMENT (5 tasks):

  1. Write the power set of the set of vowels in the English alphabet.
  2. Give an example of a subset for the set of odd numbers between 1 and 10.
  3. Research and write about the role of the universal set in mathematics.
  4. Describe a real-life example of an infinite set.
  5. Explain why the set of all students in your school is a finite set.

 

PERIOD 5: Applying Sets to Real-Life Situations

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Application of Sets

Guides students to apply the concept of sets in real life (e.g., classroom objects, school groups, and hobbies).

Students list examples of sets from their school environment.

Step 2 - Group Activity

Students create and discuss sets based on various categories: sports teams, students with pets, subjects they study, etc.

Students work in groups to create and share their sets.

NOTE ON BOARD:

  • Apply sets to categories like student groups, school objects, or even household items.

EVALUATION (5 exercises):

  1. Define the universal set for a set of students.
  2. What is the power set of a set containing your favorite colors?
  3. Describe the disjoint sets in your school.
  4. Give an example of a finite set from the classroom.
  5. What is the subset of a set of even numbers between 1 and 10?

CLASSWORK (5 questions):

  1. What is the power set of A = {apple, banana}?
  2. Write an example of a disjoint set involving sports.
  3. Create a finite set of books in your school library.
  4. What is the universal set for the months of the year?
  5. What is the empty set for students in your class who wear glasses?

ASSIGNMENT (5 tasks):

  1. Create the power set for the set of school supplies.
  2. Write a set for all students who enjoy playing soccer using set notation.
  3. Give an example of a subset of even numbers from 1 to 20.
  4. Describe the universal set for all natural numbers.

Research how sets are used in computer programming.