Mathematics - Senior Secondary 1 - Set Operations (Union, Intersection, Complement) & Venn Diagrams

Set Operations (Union, Intersection, Complement) & Venn Diagrams

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  4. Set Operations (Union, Intersection, Complement) & Venn Diagrams

TERM: 1ST TERM

WEEK: 10

  • Class: Senior Secondary School 1
  • Age: 15 years
  • Duration: 40 minutes of 5 periods
  • Subject: Mathematics
  • Topic: Set Operations (Union, Intersection, Complement) & Venn Diagrams
  • Focus: Union of Sets, Intersection of Sets, Complement of Sets, Venn Diagrams, and Application of Venn Diagrams in solving problems with up to 3 sets.

 

SPECIFIC OBJECTIVES:

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

  1. Understand and apply the union of sets (A ∪ B).
  2. Understand and apply the intersection of sets (A ∩ B).
  3. Understand and apply the complement of sets (A').
  4. Draw and interpret Venn diagrams for sets.
  5. Solve problems involving up to 3 sets using Venn diagrams.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Practice exercises
  • Real-life examples and analogies

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Charts with examples of set operations
  • Venn diagram templates
  • Worksheets for practice

PERIOD 1 & 2: Union, Intersection, and Complement of Sets

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concept of sets and the basic operations of union, intersection, and complement. Explains symbols: ∪, ∩, and '.

Students listen and ask clarifying questions about sets.

Step 2 - Union of Sets

Demonstrates the union of sets (A ∪ B), showing how to combine elements from both sets without repetition. Provides an example: A = {1, 2, 3}, B = {3, 4, 5}, then A ∪ B = {1, 2, 3, 4, 5}.

Students observe and note the definition and example of the union of sets.

Step 3 - Intersection of Sets

Demonstrates the intersection of sets (A ∩ B), showing how to find common elements. Example: A = {1, 2, 3}, B = {2, 3, 4}, then A ∩ B = {2, 3}.

Students observe and note the definition and example of the intersection of sets.

Step 4 - Complement of a Set

Introduces the complement of a set (A'), explaining how it contains all elements not in set A within the universal set U. Provides an example: U = {1, 2, 3, 4, 5}, A = {1, 2}, A' = {3, 4, 5}.

Students take notes on the complement of sets.

 

NOTE ON BOARD:

  • Union of Sets (A ∪ B): All elements in A or B.
  • Intersection of Sets (A ∩ B): Only elements that are in both A and B.
  • Complement of a Set (A'): All elements in the universal set that are not in A.

 

EVALUATION (5 exercises):

  1. What is the union of sets A = {1, 2, 3} and B = {2, 3, 4}?
  2. What is the intersection of sets A = {1, 2, 3} and B = {3, 4, 5}?
  3. What is the complement of set A = {1, 2} in the universal set U = {1, 2, 3, 4, 5}?
  4. If A = {3, 5, 7} and B = {4, 5, 6}, what is A ∪ B?
  5. If A = {2, 4, 6} and B = {1, 4, 7}, what is A ∩ B?

CLASSWORK (5 questions):

  1. What is A ∪ B if A = {2, 4, 6} and B = {1, 4, 7}?
  2. Find the intersection of sets A = {1, 3, 5} and B = {2, 4, 6}.
  3. What is the complement of A = {1, 3} in the universal set U = {1, 2, 3, 4, 5}?
  4. If A = {2, 5, 8} and B = {4, 5, 6}, what is A ∩ B?
  5. Determine the union of A = {1, 2, 3} and B = {3, 4, 5}.

 

ASSIGNMENT (5 tasks):

  1. Find the union of A = {a, b, c} and B = {b, c, d}.
  2. Find the intersection of A = {2, 4, 6} and B = {1, 2, 3}.
  3. Write the complement of A = {4, 7} in U = {1, 2, 3, 4, 5, 6, 7}.
  4. If A = {x, y, z} and B = {y, z, w}, what is A ∩ B?
  5. If A = {1, 2} and B = {2, 3}, what is A ∪ B?

 

PERIOD 3 & 4: Introduction to Venn Diagrams

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Venn Diagrams

Introduces Venn diagrams as a visual representation of set operations. Explains how to draw Venn diagrams for two sets.

Students listen and observe the drawing of a Venn diagram for two sets.

Step 2 - Drawing Venn Diagrams

Demonstrates how to draw a Venn diagram for A ∪ B, A ∩ B, and A'.

Students practice drawing Venn diagrams on their own.

Step 3 - Real-Life Applications of Venn Diagrams

Provides real-life examples where Venn diagrams are useful, e.g., categorizing students who passed different subjects.

Students discuss how Venn diagrams can be applied in everyday life.

 

NOTE ON BOARD:

  • Venn Diagram for A ∪ B: Circle A and Circle B, shading the area covering both.
  • Venn Diagram for A ∩ B: Circle A and Circle B, shading only the overlapping part.
  • Venn Diagram for A': Shade everything outside of circle A.

 

EVALUATION (5 exercises):

  1. Draw a Venn diagram for the union of sets A = {1, 2} and B = {2, 3}.
  2. Draw a Venn diagram for the intersection of sets A = {1, 3} and B = {2, 3}.
  3. Draw a Venn diagram for the complement of set A = {4, 5} in U = {1, 2, 3, 4, 5}.
  4. Use a Venn diagram to find the union of A = {1, 2} and B = {2, 3}.
  5. Use a Venn diagram to find the intersection of A = {a, b} and B = {b, c}.

 

CLASSWORK (5 questions):

  1. Draw a Venn diagram for A = {1, 2, 3} and B = {2, 3, 4}.
  2. Draw a Venn diagram for A = {a, b} and B = {b, c, d}.
  3. Solve using a Venn diagram: A = {1, 3, 5}, B = {3, 4, 5}.
  4. Draw a Venn diagram for A = {1, 2, 3} and B = {2, 3, 4, 5}.
  5. Use a Venn diagram to solve for A = {x, y}, B = {y, z}, U = {x, y, z}.

 

ASSIGNMENT (5 tasks):

  1. Draw a Venn diagram for A = {2, 4, 6}, B = {4, 5, 6}, and C = {5, 6, 7}.
  2. Solve a real-life problem using Venn diagrams: Categorize students who passed Mathematics, English, and Physics.
  3. Draw a Venn diagram for A = {apple, banana}, B = {banana, orange}, and C = {orange, mango}.
  4. Find the union of A = {1, 3} and B = {2, 3}.
  5. Find the complement of A = {x, y} in U = {x, y, z, w}.

 

PERIOD 5: Application of Venn Diagrams for up to 3 Sets

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to 3-Set Venn Diagrams

Demonstrates how to use Venn diagrams for three sets and explains the concept of overlapping regions.

Students observe and ask questions about the 3-set Venn diagram.

Step 2 - Real-Life Problem Solving

Guides students through solving a real-life problem with a 3-set Venn diagram.

Students work in pairs to solve problems using 3-set Venn diagrams.

Step 3 - Practice

Provides practice problems for students to solve individually using 3-set Venn diagrams.

Students work independently to draw and interpret 3-set Venn diagrams.

 

EVALUATION (5 exercises):

  1. Solve using a 3-set Venn diagram: A = {1, 2}, B = {2, 3}, C = {3, 4}.
  2. Solve using a 3-set Venn diagram: A = {apple, banana}, B = {banana, cherry}, C = {cherry, date}.
  3. Draw a 3-set Venn diagram and solve: A = {x, y, z}, B = {y, z}, C = {z, w}.
  4. Solve: A = {a, b}, B = {b, c}, C = {c, d}.
  5. Solve: A = {cat, dog}, B = {dog, fish}, C = {fish, bird}.

 

CLASSWORK (5 questions):

  1. Draw a 3-set Venn diagram for A = {1, 2}, B = {2, 3}, C = {3, 4}.
  2. Solve for A = {a, b}, B = {b, c}, C = {c, d}. 3. Draw a Venn diagram for A = {apple, banana}, B = {banana, cherry}, C = {cherry, date}. 4. Solve for A = {x, y, z}, B = {y, z}, C = {z, w}. 5. Solve: A = {cat, dog}, B = {dog, fish}, C = {fish, bird}.