Further Mathematics - Senior Secondary 1 - Set II - Set Operations (Union, Intersection, Venn Diagrams, and Applications)

Set II - Set Operations (Union, Intersection, Venn Diagrams, and Applications)

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TERM: 1ST TERM

WEEK 2

Class: Senior Secondary School 1
Age: 15 years
Duration: 40 minutes of 4 periods
Subject: Further Mathematics
Topic: Set II - Set Operations (Union, Intersection, Venn Diagrams, and Applications)
Focus: Union and Intersection of Sets, Venn Diagrams for up to 3 Sets, and Applications

SPECIFIC OBJECTIVES:

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

  1. Understand and define the concepts of union and intersection of sets.
  2. Draw and interpret Venn diagrams for up to 3 sets.
  3. Solve problems involving set operations (union, intersection) using Venn diagrams.
  4. Apply set operations in real-life contexts.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Use of analogies
  • Group work

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts illustrating union and intersection of sets
  • Venn diagrams for 2-set and 3-set problems
  • Flashcards for different sets and operations
  • Worksheets for practice

 

PERIOD 1 & 2: Introduction to Set Operations: Union and Intersection of Sets

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of sets and set operations. Defines union (A ∪ B) and intersection (A ∩ B) using examples. Explains how union combines all elements from two sets, and intersection shows common elements.

Students listen attentively and ask clarifying questions.

Step 2 - Union of Sets

Demonstrates the union of sets A and B using visual examples on the whiteboard. Shows that A ∪ B includes all elements from both sets without repetition.

Students observe the examples and note down the explanation of union.

Step 3 - Intersection of Sets

Explains the intersection of sets A and B using visual examples on the whiteboard. Shows that A ∩ B includes only the elements that are common to both sets.

Students observe and take notes on intersection.

Step 4 - Real-Life Analogy

Uses real-life analogies to explain set operations. For example, the union of all students who play basketball or football, and the intersection as students who play both.

Students engage with the analogies and ask questions about their relevance.

NOTE ON BOARD:

  • Union (A ∪ B): All elements in A or B (or both).
  • Intersection (A ∩ B): Only the common elements in A and B.

EVALUATION (5 exercises):

  1. What is the union of sets {1, 2, 3} and {3, 4, 5}?
  2. What is the intersection of sets {a, b, c} and {c, d, e}?
  3. Write the union of sets {2, 4, 6} and {1, 3, 5}.
  4. Write the intersection of sets {1, 2, 3} and {3, 4, 5}.
  5. What is the union of sets {x, y} and {y, z}?

CLASSWORK (5 questions):

  1. Find the union of sets {3, 6, 9} and {5, 6, 7}.
  2. Find the intersection of sets {4, 8, 12} and {8, 9, 10}.
  3. Determine the union of sets {a, b, c} and {b, c, d}.
  4. Find the intersection of sets {5, 10, 15} and {0, 5, 10}.
  5. Explain what happens when the union of two sets has no elements in common.

ASSIGNMENT (5 tasks):

  1. Write the union of the sets {p, q, r} and {q, r, s}.
  2. Find the intersection of sets {1, 2, 3} and {4, 5, 6}.
  3. What is the union of the sets {red, green, blue} and {yellow, green}?
  4. Explain in your own words the difference between union and intersection.
  5. Draw a Venn diagram for the sets {2, 4, 6} and {3, 6, 9} and shade the union and intersection areas.

 

PERIOD 3 & 4: Venn Diagrams and Applications

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of Venn diagrams and explains how to represent set operations (union, intersection) visually. Draws Venn diagrams for union and intersection of 2 sets.

Students observe the drawings and ask questions about Venn diagrams.

Step 2 - Venn Diagram for Union

Demonstrates the Venn diagram for union (A ∪ B), shading the entire area that represents both sets. Explains how the union combines all elements.

Students watch the demonstration and take notes on the diagram.

Step 3 - Venn Diagram for Intersection

Demonstrates the Venn diagram for intersection (A ∩ B), shading only the overlapping area. Emphasizes that the intersection contains only common elements.

Students take notes on the Venn diagram for intersection.

Step 4 - 3-Set Venn Diagram

Demonstrates the Venn diagram for three sets, explaining how the union and intersection work when dealing with more than two sets.

Students observe and ask questions about 3-set Venn diagrams.

Step 5 - Guided Practice

Provides several problems for students to solve using Venn diagrams, both for two sets and for three sets. Students work in pairs to solve the problems.

Students work in pairs to solve the problems and share answers with the class.

NOTE ON BOARD:

  • Venn Diagrams: Visual representation of sets and their relationships.
  • Union (A ∪ B): Shade both sets entirely.
  • Intersection (A ∩ B): Shade only the overlapping part.
  • For 3 Sets (A, B, C): Illustrates how union and intersection work with three sets.

EVALUATION (5 exercises):

  1. Draw a Venn diagram for the union of sets {1, 2, 3} and {3, 4, 5}.
  2. Draw a Venn diagram for the intersection of sets {a, b, c} and {b, c, d}.
  3. Solve the Venn diagram for three sets {1, 2}, {2, 3}, and {3, 4}.
  4. Using a Venn diagram, find the union of sets {a, b, c} and {b, c, d}.
  5. Using a Venn diagram, find the intersection of sets {x, y} and {y, z}.

CLASSWORK (5 questions):

  1. Draw a Venn diagram for the union of sets {1, 2, 3} and {4, 5, 6}.
  2. Draw a Venn diagram for the intersection of sets {a, b} and {b, c}.
  3. Solve a Venn diagram for three sets {2, 4}, {4, 6}, and {6, 8}.
  4. Find the union of sets {1, 3, 5} and {2, 3, 6} using a Venn diagram.
  5. Draw a Venn diagram and find the intersection of sets {x, y, z} and {y, z, w}.

ASSIGNMENT (5 tasks):

  1. Draw a Venn diagram for the sets {a, b, c} and {c, d, e} and find their union.
  2. Solve a 3-set problem using Venn diagrams: {2, 4}, {3, 4}, {4, 5}.
  3. Explain in your own words how to use Venn diagrams to represent set operations.
  4. Draw the Venn diagram for the intersection of sets {p, q} and {q, r}.

Solve a word problem involving Venn diagrams (e.g., "There are 30 students in a class. 12 like football, 15 like basketball, and 5 like both. How many like neither sport?").