This document discusses sets and set operations. It introduces key concepts about sets such as defining and describing well-defined sets, subsets, unions and intersections of sets. It explains how to use Venn diagrams to represent sets and set operations. The document provides examples and questions to help students learn about sets and assess their understanding. It emphasizes that understanding sets is important as the concept is used in other fields and in mathematics.

1. Mathematics 7
Number Sense:
Sets and Set Operations
BY-ABISHEK KRISHNA

2. Essential Questions
• How do we know when an object is
intrinsically part of a set or not? Why do we
have to consider objects as such?
• Why do you think the study of the concept of
sets important?
• How is the concept of sets being used in other
fields of study?
• Which is more essential: the learning of the
concept of sets or the acquisition of
knowledge of the set of real numbers?

3. What You’ll learn?
KWLH Chart
• Describe and illustrate well-defined sets,
subsets, universal set, and null set.
• Define and describe the union and
intersection of sets and the complement of a
set.
• Use Venn diagram to represent sets, subsets,
and set operations.
• Explain the concept of Venn diagram.
• Create a Venn diagram of elements classified
in different sets.
• Solve problems involving sets.

4. Self-assessment questions
• Personality Development
1. Why do we have to consider ourselves as part of a
group?
2. Is it possible for someone to be part of more than one
group?
3. Is it beneficial to be part of any group?
4. How did you relate the lessons with your personal
experiences as a teenager?
5. How do you think these lessons will affect your
personality and outlook in life?
• Learning Process
1. How did you learn the lesson on sets?
2. Which part of the lesson struck you the most? Why?

5. Exploration
• Identify the object that does not belong to the
group.
a. boat, kalesa, car, bus, airplane
b. carabao, chicken, cow, pig, goat
c. Camiguin, Bukidnon, Basilan, Cebu, Davao del Sur
d. hexagon, quadrilateral, rectangle, rhombus,
square
e. 2, 12, 24, 11, 30

6. Guide Questions
• How do you know when an object does not
belong to a group?
• How do we know if a group is considered a
set?
• How do you identify objects that belong to a
particular group?
• What is your intuitive concept of a set?
• What do you call objects that belong to a
given set?
• Can you give everyday experiences that use
the concept of sets?
• What is the main characteristic of a set in
Mathematics?

7. definition
¤ A group or collection of well-defined distinct objects is
called a __________.
When do we say that a collection
is “well-defined”?
set
When do we say that an object
belongs to a group?
¤ Each object in a set is called a __________
or an __________ of a set.
member
element

8. Dyad activity no.1
• Determine whether the following is a set or
not:
1. The collection of all ESS teachers.
2. Tall students in Grade 7.
3. Rich people in the Philippines.
4. Planets in the Solar System.
5. Beautiful girls in the class.
6. People living on the moon.
7. The collection of all large numbers.
8. The set of all multiples of 5.
9. A group of good writers.
10.Nice people in your class.

9. Global Issue
“Racism is man’s gravest threat to man - the
maximum of hatred for a minimum reason”
Abraham J. Heschel
(Jewish theologian and philosopher)
“At the heart of racism is the religious
assertion that God made a creative mistake
when He brought some people into being”
Friedrich Otto Hertz

10. Exploration
• Can you provide possible members of the
following groups, if possible?
a. Students over 12 years old in the class.
b. Counting numbers less than 5.
c. Set of letters in the word Philippines.
d. Prime numbers which are even.

11. Guide questions
How do you define the terms contained in a
set?
When do we know if a set if null or empty?
Why do we have to identify whether a set is
finite or infinite?
How do you think these terms can be
presented?

12. Here are ways of describing a set.
• The Roster Notation or Listing Method
This is a method of describing a set by
listing each element of the set inside the
symbol { }. In listing the elements of the set,
each distinct elements is listed once and the
order of the elements does not matter.
ex. Colors of the rainbow
R = {red, orange, yellow, green, blue, indigo, violet}
[List the elements in Exploration # 2]

13. Here are ways of describing a set.
• The Set Builder Notation
It is a method that lists the rules that
determine whether an object is an element
of the set rather than the actual elements.
ex. All cities in the Philippines
A = {x| x is a city in the Philippines}
read as:
“A is the set of all x such that x is a city in the
Philippines.”

14. Formative assessment
• Describe the following sets using the
specified methods.
A. Write a verbal description for each of the
following sets:
1. D = {1, 3, 5, 7, . . . }
2. E = {a, b, c, . . . , z}
3. F = {4, 8, 12, 16, . . . , 96}
Answer:
1. The set of odd numbers.
2. The set of small letters in the English
alphabet.

15. Formative Assessment
• Describe the following sets using the
specified methods.
B. List the elements of the following sets:
1. M = {x|x > 7, x is an odd integer}
2. A = {x|7 < x < 8, x is a counting number}
3. T = {x|x is a city in Metro Manila}
4. H = {x|x is a counting number between 7 and 10}
Answers:
1. M = {9, 11, 13, 15, 17, . . . }
2. A = { } or 
3. T = {Manila, Caloocan, Las Piñas, . . . Pasig}

16. Formative assessment
• Describe the following sets using the
specified methods.
C. Write a rule for the following:
1. S = {a, e, i, o, u}
2. E = {3, 6, 9, . . . , 30}
3. T = {Monday, Tuesday, Wednesday, . . . , Sunday}
Answers:
1. S = {x  x is a vowel in the English alphabet}
2. E = {x  3  x  30, x is a multiple of 3}

17. Summing up
Can you share to the class some new
terms you learned today?
Which definition struck you the most?
If you can share a topic that you learned
today to a friend, what would it be?
Why?

18. Homework
• Bring a photo of your favorite actors
• Define the following:
1. Equal
2. Equivalent
3. cardinality of a set
4. Universal Sets
5. Subsets