Intersection and Union of Sets

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Subject: Mathematics

Semester: 1

Period: 1

Week: 2

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School Name:
Teacher’s Name:
Subject: Mathematics
Grade Level: Grade 6
Date: Week 2
Lesson Duration: 45 minutes
Week & Period: Week 2, Period 1
Topic: Intersection and Union of Sets
Sub-topic: Venn Diagrams and Set Operations

Learning Objectives
By the end of the lesson, students should be able to:
Define intersection (∩) and union (∪) of sets
Draw Venn diagrams for intersection and union
Identify empty and disjoint sets

Previous Knowledge
Students already know basic sets, membership, and subsets.

Instructional Materials
Mathematics textbook for Grade 6, chart paper, markers, classroom data (e.g., students who play football/basketball).

Lesson Development – ABC Model
A – Anticipation (Warm-up / Starter)
Time: 5–10 minutes
Teacher asks: “Who plays football, who plays basketball? Can anyone play both?” Collect data and show overlap.

B – Building Knowledge (Main Lesson Body)

Time: 25–30 minutes

Definitions & Explanations

1. Intersection of Sets ( ∩ )

• The intersection of two sets is the set of elements that are common to both sets.
• Symbol: A ∩ B

Examples:

• A = {2, 4, 6, 8}, B = {4, 8, 10, 12} → A ∩ B = {4, 8}
• A = {apple, mango, orange}, B = {orange, banana} → A ∩ B = {orange}
• If A = {boys}, B = {girls}, then A ∩ B = ∅ (no student is both a boy and a girl).

 

2. Union of Sets ( ∪ )

• The union of two sets is the set of all elements that belong to either set (without repeating elements).
• Symbol: A ∪ B

Examples:

• A = {1, 2, 3}, B = {3, 4, 5} → A ∪ B = {1, 2, 3, 4, 5}
• A = {football, basketball}, B = {basketball, volleyball} → A ∪ B = {football, basketball, volleyball}
• A = {red, blue}, B = {green, yellow} → A ∪ B = {red, blue, green, yellow}

 

3. Empty Set ( ∅ )

• The empty set is a set with no elements.
• Symbol: ∅ or {}

Examples:

• Set of students with 10 heads = ∅
• Set of numbers less than 0 but greater than 1 = ∅
• In a class of only boys, the set of girls = ∅

4. Disjoint Sets

• Two sets are disjoint if they have no elements in common.
• Their intersection is empty (A ∩ B = ∅).

Examples:

• A = {1, 2, 3}, B = {4, 5, 6} → A ∩ B = ∅, so they are disjoint.
• A = {cats}, B = {dogs} (disjoint because no animal is both a cat and a dog).
• A = {fruits}, B = {numbers} (disjoint because fruits and numbers are different things).

 

5. Venn Diagrams

• A Venn diagram uses circles to show the relationships between sets.
• Intersection: overlapping area.
• Union: all areas covered by both circles.
• Disjoint sets: two separate, non-overlapping circles.
• Empty set: represented as a circle with nothing inside.

 

Expanded Learners’ Activities

1. Classroom Survey (Practical Activity):

• Teacher asks students: “Who plays football? Who plays basketball?”
• Learners form two sets A and B.
• They identify A ∩ B (students who play both).

2. Venn Diagram Drawing:

• Learners draw two overlapping circles for sets A and B.
• Shade the intersection region and union region.

3. Identify Disjoint Sets:

• Learners suggest examples of disjoint sets (e.g., boys and girls’ names in the class, chalk and books).

4. Empty Set Exploration:

• Learners list sets from the classroom that are empty (e.g., “students with wings,” “triangles with 5 sides”).

5. Group Work:

• Groups are given sets (e.g., A = {2, 4, 6}, B = {3, 6, 9}) and asked to find union, intersection, and check if disjoint.

 

Assessment Checks

1. If A = {2, 4, 6}, B = {4, 6, 8}, find A ∩ B.
2. If A = {red, blue}, B = {blue, green}, what is A ∪ B?
3. True or False: ∅ has no elements.
4. Give an example of two disjoint sets from your classroom.
5. Teacher asks: “If no one plays cricket, what is the intersection of cricket players and football players?” (Answer: ∅).

 

Notes (Expanded & Detailed)

• Intersection ( ∩ ) shows common elements → useful in real life (students who like both football and basketball, people who can speak two languages).
• Union ( ∪ ) shows all elements together → useful in combining groups (all students who like sports).
• Empty sets ( ∅ ) and disjoint sets highlight situations where groups have nothing in common.
• Venn diagrams give a visual understanding of how sets relate, making abstract ideas easier to grasp.

C – Consolidation (Conclusion & Assessment)
Time: 5–10 minutes
Summary: Review intersection, union, empty sets, disjoint sets, and diagram representation.

Evaluation Method (Expanded)
Exit slip/quiz: Draw a Venn diagram for students who like reading and drawing. Identify intersection and union.

Assignment (Expanded):
Create 2 Venn diagrams using classmates’ favorite subjects.

Follow-up Activity:
Observe students’ clubs or activities and identify sets, intersections, and unions.

Differentiation / Inclusive Strategies
Use color-coded diagrams for visual learners. Pair learners for discussion.

Teacher’s Reflection (After Class)
What worked well? ___________________________________________
What needs improvement? ____________________________________
Students’ engagement level: ☑ High ☐ Medium ☐ Low