This document outlines content standards and learning objectives for sets and real numbers in Grade 7 mathematics. It covers key concepts like well-defined sets, subsets, universal sets, null sets, cardinality of sets, union and intersection of sets, and Venn diagrams. Specific objectives include describing these set concepts, finding unions and intersections, and using Venn diagrams to represent relationships between sets. The document provides references and learning resources to support understanding, including textbook pages, websites, and practice exercises. It also includes sample sets, activities, and questions to help teach the relevant concepts and assess student mastery of sets and real numbers.

1. Annex 1B to Deped Order No. 42 s. 2016
I. OBJECTIVES
A. Content Standards The learner demonstrates understanding of key concepts of sets and the real number system.
B. Performance Standards The learner is able to formulate challenging situations involving sets and real numbers and solve these in a variety of strategies.
C. Learning
Competencies/Objectives
Establish a welcoming classroom
environment.
The learner describes well-defined sets,
subsets, universal sets, and the null set
and cardinality of sets.
(M7NS-Ia-1)
a. Describe well-defined sets, and
null set
b. Identify the elements, subsets
and cardinality of a set.
c. Appreciate the importance of
sets
The learner describes well-defined
sets, subsets, universal sets, and the
null set and cardinality of sets.
(M7NS-Ia-1)
a. Describe well-defined sets,
and null set
b. Identify the elements, subsets
and cardinality of a set.
c. Appreciate the importance of
sets
.
The learner illustrates the union and
intersection of sets and the difference of
two sets.
(M7NS-Ia-2)
a. Describe and define union and
intersection of sets
b. Find the union / intersection of sets
c. Use Venn diagrams to represent the
union and intersection of sets Value
accumulated knowledge as means of
new understanding
II. CONTENT
Acquaintance Sets: An Introduction Sets: An Introduction
Union and Intersection
of Sets
III. LEARNING RESOURCES
A. References
1. Teacher's Guide Pages - pp. 1 - 7 pp. 1 - 7 pp. 8 – 14
2. Learner's Material Pages - pp. 1 - 3 pp. 1 - 3 pp. 5 – 8
3. Textbook Pages
-
Patterns and Practicalities on G7- Math pages: 5-10
Gladys Nievera
Patterns and Practicalities on G7- Math pages: 5-
10 Gladys Nievera
-e-math Work text in Mathematics 7, pages1-11
by Orlando Oronce and Marilyn Mendoza
-e-math Work text in Mathematics 7, pages 6-8 by
Orlando Oronce and Marilyn Mendoza
-Patterns and Practicalities on G7- Math pages: 10-12
Gladys Nievera
4. Additional Material from
___Learning Resource (LR) Portal
- https://en.wikipedia.org/wiki/Set_(mathematics
https://www.google.com.ph/search?q=favorite+car
toon+character&espv=2&biw=1366&bih=667&sour
ce=lnms&tbm=isch&sa=X&ved=0ahUKEwjT5NiU4K
HMAhWDppQ
https://www.mathsisfun.com/activity/subsets.ht
ml
https://en.wikipedia.org/wiki/Set_(mathematics
https://www.google.com.ph/search?q=favorite+c
artoon+character&espv=2&biw=1366&bih=667&s
ource=lnms&tbm=isch&sa=X&ved=0ahUKEwjT5Ni
U4KHMAhWDppQ
http://passyworldofmathematics.com/venn-diagrams-
introduction/
https://www.google.com.ph/search?&biw=1366&bih=
667&tbm=isch&sa=1&q=PHILIPPINE+PRESIDENTS&oq
=PHILIPPINE+PRESIDENTS&gs_l=img.3...4601.15333.0.
15961.50.27.0
B. Other Learning Resources - MATH Grade 7 PIVOT IV-A Learner’s
Material p. 6
MATH Grade 7 PIVOT IV-A Learner’s
Material p. 7
MATH Grade 7 PIVOT IV-A Learner’s
Material p. 8-9
School: SOUTHVILLE 3A NATIONAL HIGH SCHOOL Grade Level: 7
Teacher: JO ANN CHRYSOL S. IRINGAN Learning Area: MATHEMATICS
Teaching Dates & Time: August 29, 2023/6:00-12:30 P.M. Quarter: FIRST
Date: August 29, 2023 Date: August 30, 2023 Date: August 31, 2023 Date: September 1, 2023
SESSION 1 SESSION 2 SESSION 3 SESSION 4
GRADES 1 TO 12
DAILY
LESSON LOG

2. IV. PROCEDURES
A. Reviewing previous lessons or
Presenting new lesson
Introductions and Attendance Motivation
Below are some famous characters and
places. Which do you think does NOT
belong in each group? Why?
Ask the students to find each set:
1. Odd numbers from 1 to 10
2. Multiples of three from 1 to
10
Even numbers from 1 to 20
Answer the follow-up questions:
FAVORITE SUBJECTS
Ana and Jay are talking about their
favorite subjects
1. If we will combine all their
favorite subjects, what are they?
2. Is there a subject that they both
like? What is this?
3. Do you have your favorite
subjects too?
B. Establishing a purpose for the
lesson 1. Introduce yourself and have
students introduce themselves.
2. Establish and discuss guidelines
for discussion.
3. Get the students talking to each
other with discipline
Discuss course and school policies.
Ask the students to look at the objects
below and answer the ff. questions:
Which of the following sets are well-
defined?
b. The set of all large numbers
c. The set of all multiples of 5
d. The set of good writers
The set of nice people in your class
Given the pictures below, answer the
following questions:
TAAL VOLCANO
IMUS CATHEDRAL
PICO DE LORO
SKY RANCH
AMUSEMENT PARK
BORACAY

3. a. Which objects belong together?
b. How many numbers/elements
are there in each set?
Is there an object that belongs to more
than one group? Which one?
Based from the activity, answer the
following questions:
a. Did you group the objects correctly?
b. How many sets elements are there in
each set?
c. Can you give your own examples of
well-defined sets and null set?
d. What is the importance of sets in daily
life?
1. Which of the following shows the
combination of set A and set B? How
many elements are there?
2. What element/s contain/s in both A and
B How many element/s is/are there?

5. C. Presenting examples/instances
of the new lesson
● A set is a collection of objects
,things or symbols which are clearly
defined .In the objects above the sets are;
1. Set of school supplies 3. Set of
things worn by girls
2. Set of gadgets 4. Set of
things worn by boys
The groups are called sets for as long as
the objects in the group share a
characteristics and are thus, well defined.
We have four well-defined sets in the
objects above.
●.The individual objects in a set are called
the members or elements of the set.
Example: three of the elements in set 1
belong to a set of school supplies (ruler,
ballpen, and notebook ).Can you name
elements of other sets? The symbol
is used to indicate that an
object is an element or member of the set.
● When we define a set,if we take
pieces of that set, we can form what is
called a subset. For example, we have the
set { 1,2,3,4,5}.
A subset of this is { 1,2,3,},another subsets
are { 3,4}, {2,3,5} or even { 1 }. However,
{1,6} is not a subset, since 6 is not in the
parent set.
A symbol for subset is ⊆
● The universal set U is the set that
contains all objects under consideration
.At the start, “objects” is our universal set
.
● The null set is an empty set. Example:
If H is the set of boys in an exclusive school
for girls, then H is called empty set since
there were no boys in that school.The null
set is a subset of any set. The symbol
or { } will be used to refer to an empty
set or null set.
● The cardinality of a set is the number
of elements contained in that set.
Recall: SETS
● A set is a collection of objects
,things or symbols which are clearly
defined .In the objects above the sets
are;
1. Set of school supplies 3. Set of
things worn by girls
2. Set of gadgets 4. Set of
things worn by boys
The groups are called sets for as long as
the objects in the group share a
characteristics and are thus, well
defined. We have four well-defined sets
in the objects above.
●.The individual objects in a set are
called the members or elements of the
set. Example: three of the elements in
set 1 belong to a set of school supplies
(ruler, ballpen, and notebook ).Can you
name elements of other sets? The
symbol is used to indicate
that an
object is an element or member of the
set.
● When we define a set,if we take
pieces of that set, we can form what is
called a subset. For example, we have
the set
{ 1,2,3,4,5}.
A subset of this is { 1,2,3,},another
subsets are { 3,4}, {2,3,5} or even { 1 }.
However, {1,6} is not a subset, since 6 is
not in the parent set.
A symbol for subset is ⊆
● The universal set U is the set that
contains all objects under consideration
.At the start, “objects” is our universal
set
.
● The null set is an empty set. Example:
If H is the set of boys in an exclusive
school for girls, then H is called empty set
a. How will you describe the given
diagram?
b. How many sets are there? What are
their elements?
c. Is there a common element/animal
in both sets?
Union and Intersection of sets may be
represented using Venn Diagrams.
These are diagrams that make use of
geometric shapes to show relationships
between shapes
Intersection of Sets
.Universal set of Animals:
E = Everything = { Fish, Eels, Platypus,
Penguins, Eagles, Bats }
We are going to use a Venn diagram to
divide these animals into the following
two sets:
“Water Animals” and “Two Legged
Animals” .
When we do this, we find that Penguins
belong in both groups:

6. Example: In the objects given, the
cardinality of set of gadget is 3, set of
things worn by boys is 2. The cardinality
of a set A is written as n(A).
Ask:
a. Did you group the objects correctly?
b. How many sets elements are there in
each set?
c. Can you give your own examples of
well-defined sets and null set?
What is the importance of sets in daily
life?
since there were no boys in that
school.The null set is a subset of any set.
The symbol or { } will be used to
refer to an empty set or null set.
The cardinality of a set is the number of
elements contained in that set.
Example: In the objects given, the
cardinality of set of gadget is 3, set of
things worn by boys is 2. The cardinality
of a set A is written as n(A).
E = Everything = { Fish, Eels, Platypus,
Penguins, Eagles, Bats }
Water Animals={Fish,
Eels,Platypus, Penguin}
Two Legged Animals = {Eagles,
Bats, Penguins }
This means that on our Venn Diagram, we
will need to have two overlapping circles,
so that we can put Penguins inside both
circles.
Union of Sets
The union of two sets is everything that is
contained within the two circles joined
together.
It is the combined total of the two sets,
where each item is only listed once.
For our Venn Diagram of Two Legged
Animals and Water Animals, we have:
{ Two Legged Animals } Union { Water
Animals } ={ Fish, Eels, Platypus, Penguins,
Eagles, Bats }
Union is often written using a big “U”
symbol, or the word “OR”

7. Guide Questions: (Developmental
Activity )
a. Who are the personalities given
in Activity 1 in Set A? in Set B?
b. Who is common in both sets?
Why?
c. How will you differentiate union
and intersection of sets?
d. Can you give your own real-life
examples of these sets?
D. Discussing new concepts and
practicing new skills #1
Do what is asked:
a. Is the given set well-defined? Justify
your answer.
1. {subjects in Grade 7 } Yes/No
because __________________
1. { popular actors } Yes/No
because
__________________
b. Which of the following are empty
sets and why?
1. Triangles with four sides. It is an
empty set because _______
2. Pandas in the Philippines .It is an
empty set because _______
3. Actors who are politicians. It is a
set because ________
c. Identify the elements, subsets and
cardinality of the given set
Identify the elements, subsets and
cardinality of the given set below.
{mango, banana, guyabano, avocado}
List No. of
subsets
Zero
element
{ }
One
element
Two
element
s
Three
element
s
Given: A = {a,e,i,o,u}
B = {a,b,c,d,e}
Find:
1. A ∩ B
A U B

8. C= { first five counting number}
Elements: 1,2,3,__,__ Subsets: {1}, { 1,2},{
},{ } Cardinality: n( C)=__
Four
element
s
Total
E. Discussing new concepts and
practicing new skills #2
Identify the elements, subsets and
cardinality of the given set.
1. L = {letters of English alphabet up to h}
2. V = {all the vowels of English alphabet}
3. A = {all even numbers less than 10}
4. B = {all odd numbers less than 10}
Determine all the possible subsets of
each set.
a. {1,2}
{1,2,3}
Using the diagram above, find:
1. A U B
2. A ∩ B
3. A U C
A ∩ C
F. Developing Mastery (Leads to
formative assessment)
Complete the table by determining
whether the given set is well-defined,
not well-defined or null set. If well-
defined, give the elements, three
subsets and its cardinality.
Set
1.A={schooldays }
2.B={ baldmen with braided hair}
3.C={wholenumbers less than five }
4.D={vowels in the
alphabet }
5.E={ pretty girls}
Answer each of the ff:
2. Is A a subset of B, where A = {1,
3, 4} and B = {1, 4, 3, 2}?
3. Let A be all multiples of 4 and B
be all multiples of 2. Is A a subset of B?
And is B a subset of A?
4. True or False. The empty set is a
subset of every set, including the empty
set itself.
5. Given the set {1, 2, 3, 4, 5}. A
subset of this is {1, 2, 3}. Another subset
is {3, 4, 5, 6}.
6. {1, 6} is not a subset, since it has
an element (6) which is not in the parent
set.
Given: P= { 1,2,3,4,5,6,},
Q= {2,4,6,8 }, and R= {1,3,5}
Find; a. P
b. P
c. P
d. Q
e. Illustrate
P using Venn diagram
G. Finding practical application of
concepts and skills in daily living
Do the following exercises. Write your
answers on the spaces provided:
1. Give 3 examples of well-defined sets in
real life situations.
THINK-PAIR-SHARE:
Do the following exercises:
1.Give 3 examples of well-defined sets
and null sets
Determine A and A

9. _________________________________
_________________________________
_______________
2. Name two subsets of the set of
whole numbers.
_________________________________
_________________________________
_____________
2.Name 3 elements in each of the given
sets
a. { Municipalities in Cavite}
b. { Cellphone brands}
3. Let B= { a,i,m }.List all the possible
subsets of B.
SET A
Students who has Instagram Account
Angel Valdez
Rachel Dy
Steph Torres
Cherry Cruz
SET B
Students who has Twitter Account
John Angon
Cherry Cruz
Angel Valdez
Phil Reyes
H. Making generalizations and
abstractions of the lesson
Terms to
Remember
Notations and Symbols
1. A set is a
well-
defined
group of
objects,
called
elements
that share a
common
characteris
tic.
2. When a
set is
contained
in another
set B, we
say that set
A is a
1.Uppercase letters will
be used to name sets
and lowercase letters
will be used to refer to
any element of a set. For
example, let M be the
set of all objects on
activity. We write,
M={ballpen,notebook,c
rayon and ruler}. The
symbol is
used to indicate that an
object is an element or
member of the set
Terms to
Remember
Notations and Symbols
6. A set is a
well-
defined
group of
objects,
called
elements
that share
a common
characteris
tic.
7. When a
set is
contained
in another
set B, we
say that set
A is a
1.Uppercase letters will
be used to name sets
and lowercase letters
will be used to refer to
any element of a set.
For example, let M be
the set of all objects on
activity. We write,
M={ballpen,notebook,c
rayon and ruler}. The
symbol is
used to indicate that an
object is an element or
member of the set
⮚ The union of two sets are all the
elements from both sets.
Thus, the union of sets A and B, written as
A , is the set of the elements that
are members of A,or members of B ,or
members of both A and B.
⮚ The intersections of two sets are
those elements that belong to both sets.
Thus, the intersection of sets A and B ,
written as A is a set of
elements that are members of both A and
B.

10. subset of
set B
3. The
universal
set is the
set that
contains all
objects
under
considerati
on
4. The null
set is an
empty set.
The null set
is a subset
of any set.
5. The
cardinality
of a set A is
the number
of
elements
contained
in A.
2 if .A is a subset of (or is
included in) B, then we
write ,
3.Universal set is
denoted by U.
4.The symbol or { }
will be used to refer to
an empty set or null set.
5.The cardinality of a set
A is written as n(A).
subset of
set B
8. The
universal
set is the
set that
contains all
objects
under
considerati
on
9. The null
set is an
empty set.
The null set
is a subset
of any set.
10.The
cardinality
of a set A is
the
number of
elements
contained
in A.
2 if .A is a subset of (or
is included in) B, then
we write ,
3.Universal set is
denoted by U.
4.The symbol or {
} will be used to refer to
an empty set or null set.
5.The cardinality of a
set A is written as n(A).
I. Evaluative learning Answer each of the ff:.
1. Let B = [1, 3, 5, 7, 9}. List all the
possible subsets of B.
2. Answer this question: How
many subsets does a set of n elements
have?
If K={ counting numbers from 1-10},
L={consonants in word art }, and M= {
whole numbers between 9 and 10};
A. Which of the sets are well-defined?
null set?
B. Find;
1. elements of K
2. elements of M
3. subsets of M
4. three subsets of L
5. cardinalities of all the sets
A = {0, 1, 2, 3, 4}
B = {0, 2, 4, 6, 8}
C = {1, 3, 5, 7, 9}
Given the sets above, determine the
elements and cardinality of:
1. A U B =
2. A U C =
3. A ∩ B =
4. B ∩ C =
5. A U B U C =
J. Addition activities for application
or remediation
Consider the sets:
A= {1, 3, 5,}
B= {2,4,6, } Study: Union and Intersection of sets
Given:
A= {1,2,3,4,5,6,7,8}
B= { 2,4,6,8,10}

11. C= {0,1,2,3,4,……}
D= the odd numbers less than 7
E= the whole numbers less than 7
Answer the following;
_____a. Name the elements of set A
_____b Name the elements of set C
_____c. Is set D a subset of set C? Why?
_____d. Is set C a subset of set D? Why?
_____e. Which of the sets are subsets of
set C?
Find:
1. A U B
2. A ∩ B
V. REMARKS
VI. REFLECTION
A. No. of learners who earned 80%
in the evaluation
B. No. of learners who require
additional activities for remediation
C. Did the remedial lessons work?
No. of learners who have caught
up with the lesson
D. No. of learners who continue to
require remediation
E. Which of my teaching strategies
worked well?
F. What difficulties did I encounter
which my principal or supervisor
can help me solve?
G. What innovation or localized
materials did I use/discover which I
wish to share with other teachers?
JO ANN CHRYSOL S. IRINGAN
SUBJECT TEACHER
MARY GRACE R. MACARAEG
SUBJECT COORDINATOR
SHERYLL ANN M. DADAL
OIC/HT IV-FILIPINO