Grade 7 Mathematics Final.pdf learning a

Practice Personal Hygiene protocols at all times. i
7
Mathematics
First Quarter
LEARNING ACTIVITY SHEETS

Practice Personal Hygiene protocols at all times. i
Learning Activity Sheet in MATHEMATICS
GRADE 7
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Practice Personal Hygiene protocols at all times. ii
Table of Contents
Competency
The learner illustrates well-defined
sets, subsets, universal sets, null set,
cardinality of sets and the difference
of two sets
The learner solves problems involving
sets with the use of Venn Diagram
The learner represents the absolute
value of a number on a number line
as the distance of a number from 0
The learner performs fundamental
operations on integers
The learner illustrates the different
properties of operations on the set of
integers.
Express rational numbers from
fraction form to decimal form and
vice versa.
The learner performs operations on
rational numbers.
The learner describes principal roots
and tells whether they are rational or
irrational
The learner determines between
what two integers the square root of
a number is
The learner estimates the square root
of a whole number to the nearest
hundredth
The learner plots irrational numbers
(up to square roots) on a number
line.
Page Number
----- 1-7
----- 8-13
----- 14-21
----- 22-40
----- 41-45
----- 46-54
----- 55-65
----- 66-69
----- 70-76
---- 77-85
___ 86-89

Practice Personal Hygiene protocols at all times. iii
Illustrates the different subsets of real
numbers
The learner arranges real numbers in
increasing or decreasing order and
on a number line
The Writes numbers in scientific
notation and vice versa
The learner represents real-life
situations and solves problems
involving real numbers
----- 90-96
----- 97-103
----- 104-107
---- 108-115

Practice Personal Hygiene protocols at all times. 1
MATHEMATICS 7
Name of Learner: ________________________________ Grade Level: _____
Section: _________________________________________ Date: ____________
LEARNING ACTIVITY SHEET
The Set Virus
Background Information for Learners
This activity sheet serves as a self-learning guide for the learners. It facilitates lesson
as it specifically aims for students’ mastery on the world of sets.
This is an introductory lesson on sets. A clear understanding of the concepts in this
lesson will help you easily grasp number properties and enable you to quickly identify
multiple solutions involving sets of numbers
Important Terms to Remember
The following are terms that you must remember from this point on.
1. A set is a well-defined group of objects, called elements that share a common
characteristic. The term well defined means that given a set and an object, one can
clearly determine whether that object belongs to the set or not. A set is usually
denoted by a capital letter. For example, set of vowels in the alphabet: V = {a, e, i, o,
u}
2. The set F is a subset of set A if all elements of F are also elements of A. For example,
the even numbers 2, 4 and 12 all belong to the set of whole numbers. Therefore, the
even numbers 2, 4, and 12 form a subset of the set of whole numbers. F is a proper
subset of A if F does not contain all elements of A.
3. The universal set U is the set that contains all objects under consideration. The set of
all letters in the alphabet could be a universal set from which the set {a,b,c,d,…..z}
could be taken.
4. The null set ᴓ is an empty set. The null set is a subset of any set. The set of months in
a year with 35 days is considered as null set because there is no months with 35 days.
5. The cardinality of a set A is the number of elements contained in A. Supposed set A
is the vowels in the alphabet. Its cardinality is 5 because there are just 5 vowels {a, e,
i, o, u} in the alphabet.
6. The difference of two sets A and B, denoted by A – B (read as A minus B), is the set
that contains all elements of A that are not in B. In some cases, the symbol “” is also
used to mean difference. Suppose set A = {1,3,5} and set B = {2,3,4}, when we take
its difference the result will be {1,5}.

Learning Competency with code
The learner illustrates well-defined sets, subsets, universal sets, null set, cardinality of
sets ,union and intersection of sets and the difference of two sets (M7NS-Ia-1,& M7NS-Ia-2)
Directions:
Different activities were prepared for you to be well versed on the concept of Sets.
Activity 1 SET IT UP! Write S if the given group or collection is a set and NS
if it is not. Write your answer on the space provided before each number.
_______1. Collection of students in your class whose surname starts with letter A.
_______2. Countries in Asia affected by covid-19
_______3. Collection of distinct letters of the word “PANDEMIC”
_______4. Group of cities in the province of Isabela
_______5. Group of enjoyable subjects in high school
_______6. Group of students in your class who wear mask
_______7. Collection of hygiene kits for sanitation
_______8. Group of major TV stations in the Philippines
_______9. Group of good schools in Santiago City
_______10. Cities in Metro Manila under ECQ(Enhanced Community Quarantine)
Activity 2. ARE YOU POSITIVE OR NOT? Draw on the space
provided before each item if the given set is a subset of A. If it is not then draw .
Given: A = { c,o,r,o,n,a,v,i,r,u,s,o,u,t,b,r,e,a,k}
_______1. {c, r, n, v, s, t, k}
_______2. {a, e, i, o, u}
_______3. {set of all consonants in the alphabet}
_______4. {x/ x is a vowel in the alphabet}
_______5. {set of even numbers}
_______6. {set of odd numbers}
_______7. {alcohol, sanitizer, soap}
_______8. {USA, China, Italy, Japan, Philippines}
_______9. {a, b, c, d, e}
_______10. {u, v, w, x, y, z}

Activity 3. UNIVERSAL IT IS!
A. List all the elements on the universal set for the following sets
1. A = { a, b, c, d, e}
B = { a, e, i, o, u}
U = ___________________________
2. C= { letters of the word novel}
D = { letters of the word corona}
E = { letters of the word virus}
U = ____________________________
3. F = { 2, 4, 6, 8, 10}
G = {1, 3, 5, 7, 9}
U = ____________________________
4. H = { N95 mask, gloves, goggles}
I = {gowns, aprons, face visors}
U = ____________________________________________________________________
5. J= {set of prime numbers less than 10}
K = { set of even numbers less than 10}
U = ____________________________________________________________________
B. Identify a possible universal set from which the following sets could be chosen.
1. { working pass, travel pass, financial travel pass}
Set of _________________________________________
2. { basketball, volleyball, badminton, futsal, boxing}
Set of _________________________________________
3. { doctors, nurses, police, military, LGU}
Set of _________________________________________
4. { Math, Science, English}
Set of _________________________________________
5. { social distancing, stay at home, hand washing, wear mask, exercise}
Set of _________________________________________
Activity 4. MY EMPTINESS AND PHOBIA!
“Are you afraid of viruses, germs, bacteria? Then you are ____________”

To answer this, cross out the pair of letters that corresponds to null or empty set in the box
below. There will be 5 boxes left after. Decode the remaining letter from left to right, top to
bottom. Place the letter of your answer on the answer box. One letter per box.
AB
Set of 3 legged
human
MY
Set of vowels in the
alphabet
SO
Set of even numbers
CD
Set of months with
33 days
PH
Set of quarantine
pass during ECQ
XY
Set of dogs with 6
legs
UV
Set of squares with 5
sides
OB
Set of qualified
family social status
that will be given
SAP
RP
Set of cars with 10
doors
JR
Set of integers which
are both even and
odd
RH
Set of newly born
babies who can walk
PS
Set of humans living
in planet MARS
EF
Set of schools in the
Philippines who
conducted graduation
S.Y. 2019-2020
physically in their
respective schools
LN
Set of vaccines that
can treat corona virus
TP
Set of humans with
multiple lives
IA
Set of countries
affected by covid-19
Note: Letters that are not crossed out will correspond to the name of the phobia
Answer:
Activity 5. Where does corona virus outbreak started? __________________
To answer this, identify the cardinality of the following set. Match your answer from
the choices on the right and write the corresponding letter of the correct answer in the box
at the left of number.
1. {a, e, i, o, u} N1. 9
2. {set of days in a week} I. 120
3. {set of vowels in the word “PANDEMIC”} H2. 12
4. { set of non-repeated consonant letters in the word H1. 3

“FRONTLINERS”}
5. {rice, coffee, powdered milk, sugar, noodles, sardines,
corned beef, soap, alcohol}
C. 0
6. {empty set} U. 7
7. {set of months in a year} A1. 6
8. {100,200, 300, …….12000} W. 5
9. {USA, Italy, Spain, Germany, China, France, Iran, United
Kingdom, Switzerland, Turkey}
A2. 11
10. {N95 mask, surgical gloves, goggles, medical gowns,
aprons, face visors, face shields, respirators, protective
clothing, helmets, biohazard bags }
N2. 10
Answer: _______________________________________________________________
Activity 6 THE HIDDEN MESSAGE
What is the hidden message written below despite this pandemic outbreak of
corona virus? To answer, shade the elements of the result of the difference of two sets on
each of the following number.
1. A= { c, o, r, o, n, a}
- B= {v, i, r, u, s}
C c c
O v v
O o n
R r n
A a a
2. A = {a, e, i, o, u}
-B = {a, b, c, d ,e}
i i i
a o e
a o e
a u e
a u e
3. A= {2,4,6,8,10}
-B = {1,3,5,7,9}
2 2 2
4 1 8
4 6 8
6 3 10
6 7 10
4. A = {w, e, a, r}
-B = {m, a, s, k}
w a w
w e w
m e s
m r k
a r k
5. A = { r,e,p,a,c,k}
-B = {r,e,l,i,e,f}
P p p
A r e
A a c
L f c
K k k
6. A = {f, a, k, e}
-B = {n, e, w, s}
f f f
a n k
a f k
a w k
a s k
7.A = {1,2,3…10}
-B = {2,4,6…10}
1 1 1
3 2 4
3 7 9
5 6 8
5 10 10
8. A = {4,8,12…40}
-B = {2, 4, 8…64}
12 20 24
12 4 8
28 36 36
28 16 32
40 40 40
Reflection
Complete this statement: I have learned that …

___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
__________________________________________________________________________.
References
Math 7 Teaching Guide
Oronce, O. & Mendoza, M.(2012) E-Math
Malvar, M. et al. (2014) Simplified Math
https://www.who.int/medical_devices/meddev_ppe/en/
https://www.pharmaceutical-technology.com/features/covid-19-coronavirus-top-ten-most-
affected-countries/
Answer Key
Activity 1
1. S
2. S
3. S
4. S
5. NS
6. NS
7. S
8. S
9. NS
10. S
Activity 2
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Activity 3
A.
1. {a,b,c,d,e,i,o,u}
2. { a,c,e,i,l,n,o,r,s,u,v}
3. {1,2,3,4,5,6,7,8,9,10}
4. {aprons, facemask, gloves, goggles,
gowns, N95 mask}
5. {2,3,4,5,6,7,8}
B.
1. quarantine pass
2. sports
3. frontliners
4. major subject
5. rules during covid-19 outbreak

7
X
Activity 4
AB
Set of 3 legged human
MY
Set of vowels in the alphabet
SO
Set of even numbers
CD
Set of months with 33 days
PH
Set of quarantine pass
during ECQ
XY
Set of dogs with 6 legs
UV
Set of squares with 5 sides
OB
Set of qualified family
social status that will be
given SAP
RP
Set of cars with 10 doors
JR
Set of integers which are
both even and odd
RH
Set of newly born babies
who can walk
PS
Set of humans living in
planet MARS
EF
Set of schools in the
Philippines who conducted
graduation S.Y. 2019-2020
physically in their respective
schools
LN
Set of vaccines that can treat
corona virus
TP
Set of humans with multiple
lives
IA
Set of countries affected by
covid-19
Answer:
M Y S O P H O B I A
Activity 5
1. W 6. C
2. U 7. H2
3. H1 8. I
4. A1 9. N2
5. N1 10. A2
Activity 6
1.
c c c
o v v
o o n
r r n
a a a
2.
i i i
a o e
a o e
a u e
a u e
3.
2 2 2
4 1 8
4 6 8
6 3 10
6 7 10
4.
w a w
w e w
m e s
m r k
a r k
5.
p p p
a r e
a a c
l f c
k k k
6.
f f f
a n k
a f k
a w k
a s k
7.
1 1 1
3 2 4
3 7 9
5 6 8
5 10 10
8.
12 20 24
12 4 8
28 36 36
28 16 32
40 40 40
Prepared by:
JOY ALPHA FLOR C. DE LEON
EMERSON R. RESPONZO
T-III, Patul National High School
X
X
X
X
X
X
X
X X
X

MATHEMATICS 7
Section: ________________________________________ Date: ____________
SOLVE PROBLEMS INVOLVING SETS USING VENN DIAGRAM
This learning activity sheet is about solving problems involve using Venn diagram.
The activity encourages students to learn, to help direct students’ learning out-of-class and a
good way to choose practice or drill their skills on the concepts of Venn diagram.
A Venn diagram is used to organize a list of data. Set can be represented in a Venn
diagram. Circle are drawn inside a rectangle representing the universal set.
The overlapping region in the Venn diagram is called the “Intersection” of the set
while the “Union” is the combination of all elements of A and B (or the circle inside the
rectangle).
In a simplest manner, A Venn diagram is a diagram with one or more circles on
closed regions representing sets. A rectangle can be drawn around the Venn diagram to
represent the universal set.
The figures below are the models for representing the operations on sets which is
somewhat similar to the basic operations on numbers.
Four Basic Operations on Sets
1. Union of sets A and B
A U B = set of all elements found in A or B or both
Example :
A = {a, b, c, d, e} , B = {b, c, f, g, h} = { a, b, c, d, e, f ,g }
In General, A U B = {a, b, c, d, e, f ,g}
2. Intersection of Sets A and B
A ∩ B = Set of all elements common to set A and Set B
Example : A ={ 1, 2, 3, 4 } , B={3, 4,5, 6,} = { 3,4}
In General A ∩ B = { 3,4}
3. Complement of a set A
A’ = Set of all elements in the universal set but not found in A
Example:
A = {1,2}, U= {1,2,3,4,5 } A’= {3,4,5}
In General = A’ U U= {3,4,5}

This Photo by Unknown Author is licensed under CC
BY-NC-ND
4. Difference of Sets A and B
A-B = Sets of all elements in A but not in B
B-A = Sets of all elements in B but not in A
Example :
A= {4,5,6,7}, B= {1,6,7,8,9)
A-B {4,5} , B -A {1,8,9}
Example : Soaring with 95%
In a class of 40 students ;
25 got an average of 95 in English ;
17 have an average of 95 in Mathematics ,
7 have an average of 95 in Mathematics and English
U = 40
English Mathematics
18 7 10
5
a. How many students have an average of 95 in English only?
b. How many students have an average of 95 in Math Only?
c. How many student do not have an average of 95 in Math and English?
Solution :
a. For Students who have an average of 95 in English only
25-7 = 18 students have an average 95 in English only
b. For Students who have an average of 95 in Math only
17-7 = 10 students have an average of 95 in Math only
c. Students that does not have an average of 95 in both English and Math
40 - [18 +7 +10 ] = 5 students does not have an average of 95 in both Math and
Science
Learning Competency (Quarter 1, Week 2)
Solve problems involving sets with the use of Venn Diagram. (M7NS-Ib-2)

Activity 1. WEBINAR ! NEW NORMAL
Directions/Instructions:
Let us try to solve the following problem: Venn diagram is already drawn for you, just fill up
your answer on the given illustrations below ,and answer the following questions.
SCIENCE MATH
In a group of 35 students who joined the online activity in Math and Science webinar
28 of these students are in Science club and
20 of them are in Math club
a. How many have joined in Science club only?
b. How many have joined in both Club?
Guide Questions:
1. In evaluating the sets what method did you use? _______________ Why?
2. Did you compare set A and Set B? What relationship exists between the two sets?
How?
3. What symbol did you use to emphasize the intersection? Why?
4. What can you conclude regarding on the operation of sets? Why?

This Photo by Unknown
Author is licensed under CC
BY-SA-NC
Online Actual
Activity 2. I CAN MAKE IT!, BELIEVE ME I CAN !
(Option A) (Option B)
(Option C)
Direction : A Venn diagram is already drawn for you just fill in the empty sets to correspond
your answer inside the universal set.
50 students was surveyed through social media bout their option of classes they most prefer
for this coming opening of school year ,
15 of the students wants online schooling
20 of the students wants actual face to face schooling
7 students want both option.
a. How many students want online schooling only?
b. How many students want actual face to face schooling only?
c. How many students want at least two scheme of classes?
d. How many students do not want any of the two option?
Guide Questions:
1. How did you evaluate the problem?
2. How did you make the intersection of set?
3. Does set A, Set B and Set C related with one another?
4. What operation did you used in finding the intersection of the three sets?
This Photo by Unknown Author is licensed
under CC BY-SA-NC

Author is licensed under
CC BY-NC
Author is licensed under CC
BY-SA
Activity 3: CONGQUER MY TALENT!
(Dancing) (Singing) ( Painting)
Directions: A Venn diagram is already drawn for you just fill in the empty sets to correspond
your answer inside the universal set.
100 students were enrolled in Special Performing Arts Class,
27 are inclined in singing
42 are inclined in dancing
35 are inclined in painting
15 are both inclined in singing and painting
18 are both inclined in dancing and singing
20 are both inclined in painting and dancing
10 are all inclined into the three performing arts
a. How many are into singing only?
b. How many are into dancing only?
c. How many are into painting only?
d. How many students are both inclined in both singing and dancing but not painting?
e. How many students are both inclined in both painting and dancing but not singing?
f. How many students are both inclined in both singing and painting but not dancing
g. How many students are both inclined into either singing or dancing?
h. How many students are both inclined into either dancing or painting?
i. How many students are both inclined into either singing or painting?
j. How many students are not into any of the tree performing arts ?
*** both inclined in singing and dancing
both inclined in painting and dancing
Guide Question:
1. How did you evaluate the problem?
2. What method did you use in identifying sets?
3. How did you make the intersection of the set?
4. Does set A, Set B and Set C related with each other? How?
5. What operation did you used in finding the intersection of the three sets?

Activity 4: Sporty Venn Diagram
Directions/Instructions:
The diagram below shows the different outdoor sports played by ten (10) students last month.
Use the Venn diagram to answer the questions.
Reference:
Volleyball (V)
Basketball (B)
Sepak Takraw (S)
V B
Rona
Rob Bill
S
Questions:
1) How many students played Volleyball and Basketball? _____
2) How many students played Basketball and Sepak Takraw? _____
3) How many students played Volleyball and Sepak Takraw? _____
4) How many students played ONLY Volleyball? _____
5) How many students played ONLY Basketball? _____
6) How many students played ONLY Sepak Takraw? _____
7) V ∪ B _______________________________________________
8) (V ∩ B ) ∪ S _______________________________________________
9) V – B _______________________________________________
10)V ∩ B ∩ S _______________________________________________
Reflection
I have learned that
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
References
Curriculum Guide in Grade 7 Mathematics
Learning Modules in Grade 7 Mathematics
Books : College Algebra with Recreational Mathematics by Benjamin Concepcion, Chastine
Najjar, Prescilla Altares, Sergio Ymas, E-Math Worktext in Mathematics by Orlando
Oronce and Marilyn O. Mendoza
Prepared by:JULIE BACTAD AGCAOILI-Rosario NHS/ JHOANNA D. BALAYAN-
SaganaNHS
Anne
Bing Rey
Ben Fe
Kris
Al

MATHEMATICS 7
Name of Learner: ________________________Grade Level: ______________
Section: _______________________________ Score: ___________________
ABSOLUTE VALUE
A number line is a line with numbers placed in the right order. It is an infinite line which
points represent the real numbers. It is divided into two symmetric halves by the origin that is
the number zero.
The absolute value of a number is the distance on the number line between the number and
zero without any regard to its direction. Since you are only counting the distance, absolute
values are always positive values.
Absolute value bars surround the number being evaluated. Two vertical bars | | denote the
absolute value of a number. For example: |5| = 5 and |-5| = 5. The absolute value of a positive
number is the number itself. The absolute value of a negative number is the opposite of the
negative number and the absolute value of zero is zero. This is best illustrated on the number
line below:
Expressions with absolute value symbol can be simplified. The absolute value of a number is
the number of units it is away from 0 on the number line. For example: |x| = 2. Using the
number line, the distance from 0 to x is 2 units. Therefore x = -2 and x = 2.

Furthermore, to solve and illustrate |x - 4| = 3 using the number line, x must be a number
whose distance from 4 is 3. Thus, think of starting at 4 and moving 3 units in both directions
on the number line. The solutions can be illustrated as the figure below:
Therefore, x is equal to 1 or 7.
The diagram shows that |x - 4| = 3 is equivalent to:
|x - 4| = 3 or |x - 4| = 3
x – 4 = -3 x – 4 = 3
x = -3 + 4 x = 3 + 4
x = 1 x = 7
Represents the absolute value of a number on a number line as the distance of a number from
0 (M7NS-Ic-1)
Directions/Instructions
Exercises 1. GIVE ME MY VALUE! Give the absolute value of each of the following.
Each correct answer corresponds to 1 point.
1. |10| 6. |93|
2. |13| 7. |-103|
3. |48| 8. |-127|
4. |-74| 9. |133|
5. |-85| 10. |165|
Exercises 2. THE SANTIAGO CITY BARANGAY TOUR. Tell whether how far a
barangay in Santiago City from the other barangay as shown in the picture below. Each
correct answer corresponds to 1 point.

1. How far would Calao West be from Dubinan East?
2. How far when you travel from Calao West to Malvar given the route above?
3. If you are from Plaridel and you would like to visit your mom in Malvar, how far
would you travel from your place?
4. Ana travelled from Dubinan West to Calao West while Robert travelled from Plaridel
to Malvar. Who travelled the greater distance, Ana or Robert? Why?
5. What is the total distance travelled by Ana and Robert?
Exercises 3. COME AND ILLUSTRATE. Illustrate using the number line. Each correct
illustration corresponds to 2 points each.

Exercises 4. SOLVE AND PROVE. Solve and illustrate using the number line.
1. |x - 2| = 5
2. |x + 6| = 3
3. |x + 8| = 6
4. |x - 5| = -8
5. |x + 1| = -10
Reflection
Complete the statement below.
I have learned that ____________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________

References
A. Books
1. Orance, O. and Mendoza, M., 2015. E- Math 7. 1st ed. 586 Nicanor Reyes St.,
Sampaloc Manila: Rex Book Store, pp.35-38.
2. De Leon, C. and Bernabe, J., 2002. Elementary Algebra. 1281 Gregorio Araneta
Avenue, Quezon City: JTW Corporation, pp.32-33.
3. 2013. Mathematics Grade 7 Teacher's Guide. 1st ed. 2nd Floor Dorm G, Philsports
Complex, Meralco Avenue, Pasig City, Philippines 1600: Department of Education,
pp.94-100.
4. Aseron, E., Armas, A., Canonigo, A. and Garces, I., 2013. Mathematics – Grade 7
Learner’S Material. 1st ed. 2nd Floor Dorm G, Philsports Complex, Meralco Avenue,
Pasig City, Philippines 1600: Department of Education, pp.70-75.
B. Website
1. Arias, L., 2019. Positive And Negative Numbers, Oh My!. [online] Google Books.
Available at: <https://books.google.com.ph/books?id=TQ-
XDwAAQBAJ&printsec=frontcover&dq=absolute+value+of+a+number&hl=en&sa=
X&ved=0ahUKEwim09GS_cvpAhWuBKYKHd_bB94Q6AEIJjAA#v=onepage&q=a
bsolute%20value%20of%20a%20number&f=false> [Accessed 24 May 2020].
2. Kolby, J., 2020. ACT Math Prep Course. [online] Google Books. Available at:
<https://books.google.com.ph/books?id=NQ_CBgAAQBAJ&pg=PA131&dq=absolut
e+value+of+a+number&hl=en&sa=X&ved=0ahUKEwim09GS_cvpAhWuBKYKHd
_bB94Q6AEIdzAJ#v=onepage&q=absolute%20value%20of%20a%20number&f=fal
se> [Accessed 20 May 2020].
3. Aufmann, R. and Lockwood, J., 2020. Course Companion For Basic College
Mathematics: Powered By Enhanced Webassign. [online] Google Books. Available
at: <https://books.google.com.ph/books?id=BoXbkVg325sC&pg=RA3-
4. Marshall, S., n.d. Rubric For Short-Answer Math Problems. [online]
Hosting.astro.cornell.edu.Available at:
<http://hosting.astro.cornell.edu/~seanm/Sean_Marshall_rubrics.pdf> [Accessed 20
May 2020].
Others:
1. STARBOOKS. 2020. Absolute Value of A Number.
2. Word Search
3. Google Map

Answer Key
Exercises 1. Give Me My Value
1. 10| 6. 93
2. 13 7. 103
3. 48 8. 127
4. 74 9. 133
5. 85 10. 165
Exercises 2. The Santiago City Barangay Tour
1. 2.5 km
2. 10.9 km
3. 5.3 km
4. Robert; 5.3 km > 3.7 km
5. 10.1 km
Exercisers 3. Come and Illustrate.

Exercises 4. SOLVE AND PROVE. Solve and illustrate using the number line.
1. |x - 2| = 5
|x - 2| = 5 or |x - 2| = 5
x - 2 = -5 x - 2 = 5
x = -5 + 2 x = 5 + 2
x = -3 x = 7
Therefore:
2. |x + 6| = 3
|x + 6| = 3 or |x + 6| = 3
x + 6 = -3 x + 6 = 3
x = -3 - 6 x = 3 - 6
x = -9 x = -3
Therefore:
3. |x + 8| = 6
|x + 8| = 6 or |x + 8| = 6
x + 8 = -6 x + 8 = 6
x = -6 – 8 x = 6 – 8
x = -14 x = -2
Therefore:
4. |x - 5| = -8

|x - 5| = -8 or |x - 5| = -8
x - 5 = -8 x - 5 = 8
x = -8 + 5 x = 8 + 5
x = -3 x = 13
Therefore:
5. |x + 1| = -10
|x + 1| = -10 or |x + 1| = -10
x + 1 = -10 x + 1 = 10
x = -10 – 1 x = 10 – 1
x = -11 x = 9
Therefore:
Prepared by:
Gee P. Baltazar Mely C. Paulino
Teacher III Teacher III

RULE # 1
MATHEMATICS 7
Name:_____________________________________ Grade Level_______
Section:____________________________________ Date:____________
Addition of Integers
Background Information for Learner/Concepts
Integers are whole numbers that are positive or negative including zero. Negative
integers are numbers less than zero found at the number line from the left of zero and hold a
negative sign. Examples are -1, -5, -8, -12, -18, etc. while positive integers are numbers
greater than zero located at the right side of zero in the number line. This sign(+) indicates
positive integer. However, the sign is not always needed. Numbers like +3 or 3, +6 or 6, +9
or 9, +13 or 13, etc. are examples of positive integers. Zero on the otherhand is located in
between the positive and negative integers in the number line.
A number line is a horizontal line with numbers that are placed equal distance apart
and are sequentially numbered.
Below is an illustration of negative and positive integers using the number line.
Rules for Adding Integers
In adding two integers
having the same sign,
add the numbers and
copy their common sign.
Examples:
1. 9 + 3 = 12
2. 17 + 6 = 23
3. -5 + -9 = -14
4. – 4 + - 15 = - 19
Number 1 and 2 are both positive while 3 and
4 are negative.
Rule # 2
In adding two integers
with different sign,
subtract and copy the sign
of the larger number.
Examples:
1. -10 + 4 = -6
The difference is 6 and the sign of the
larger number is negative, so the sign of the
sum is negative.
2. -5 + 8 = 3
The difference is 3 and the sign of the
larger number is positive, so the sign of the
sum is positive
3. 15 + (-6) = 9
4. -25 + 17 = -8

Addition of Integers using the number line
1. Use the number line to find the sum of 3 and 7. ( 3 & 7 are both positive)
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
On the number line start with point 3 and count 7 units to the right. At what point on
the number line does it stops? It is at point 10, hence, 3 + 7 = 10.
2. Find the sum of -2 and -5. ( -2 & -5 are both negative)
-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
On the number line start with point -2 and count 5 units to the left. At what point on
the number line does it stops? It is at point -7, hence, -2 + -5 = -7.
3. Find the sum of -8 and 4. ( adding a negative, a larger number and a positive number,
the smaller number)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
On the number line start with point -8 and count 4 units to the right. At what point on
the number line does it stops? It is at point -4, hence, -8 + 4 = -4.
4. Find the sum of -4 and 9.(adding a negative number, smaller and a positive which is
larger number)
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
On the number line start with point -4 and count 9 units to the right. At what point on
the number line does it stops? It is at point 5, hence, -4 + 9 = 5.
SUMMARY:
Addends Addends Sum
┼ ┼ ┼
┼
┼ ┼
LEARNING COMPETENCY and Code
Performs fundamental operations on integers ( M7NS-Ic-d-1)

ACTIVITY
I. SHOW ME THE WAY: Use the number line to find the sum of the following
integers.
1. 3 + 6
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
2. -4 + -1
-7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7
3. -7 + 2
-7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7
4. 8 + -3
3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
5. 10 + -5
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
II. Find the sum of each of the following.
1. 3 + 8 = _____________ 6. -9 + -10 = _________
2. -4 + -2 = _____________ 7. -20 + 7 = __________
3. -10 + 15 = _____________ 8. – 5 + 12 = __________
4. 7 + -10 = _____________ 9. 13 + -6 = __________
5. 15 + 9 = ______________ 10. -4 + 0 = _________
III. BEYOND COMPARE: The table shows the scores obtained by the five players
in a game. Following the rules in adding integers find the total score of each
player.
Name Round 1 Round 2 Total Score
1. Beth 19 8
2. Zeny -2 12
3. Aida -5 -7
4. May 23 -11
5. Jona 16 -7

Use the table to answer the following questions:
1. Find the total score for each player.
2. Whose player had the lowest score?
3. Whose player has the highest score?
4. Who was the best player?
IV. LEARN ON ME. : The integers -10, -8, -6, -4, -2, 0, +2, +4, +6, and +8
are assigned to the letters W, L, E, O, A, T, M, E, H, V respectively. A
word is formed by using these letters. Find the sum of the integers in the word
formed. (Letters can be used more than once)
Example: WE ----------------- -10 + 4 = -6
V. GO for MASTERY: Solve the following problems. Show your solutions.
1. It will be 380
tomorrow. The weatherman predicts it will increase 20
in the
afternoon. What will be the new temperature?
2. A submarine was situated 700 feet below sea level. I it goes up 300 feet, what
is its new position?
3. Leny bought 2 pieces of jeans at 850 pesos each. How much did she pay to
the cashier?
4.
Rubric for rating Activity I and II
Score Descriptions
4 The computations are accurate. A wise use of the rules of addition of integers
are evident.
3 The computations are accurate. Use of the rules of addition of integers are
evident.
2 The computations are erroneous and show some use of the rules of addition of
integers .
1 The computations are erroneous and do not show some use of the rules of
addition of integers .
Rubric for rating Activity III and IV
Score Descriptions
4 Student explains the rules of adding integers and be able to apply in solving
problems..
3 Student demonstrates an understanding the rule of adding integers.
2 Student understands the rule of operations but is inconsistent in solving
1 Student needs assistance in adding integers.
W(-10)
L(-8)
E(-6)
O(-4)
A(-2)
T(0)
M(2)
E(4)
H(6)
V(8)

Rubric for rating the Solving Problem
Score Descriptions
4 The problem is properly modelled with appropriate mathematical concepts
used in the solution and a correct final answer is obtained.
partially used in the solution and a correct final answer is obtained.
2 The problem is not properly modelled other alternative mathematical concepts
are used in the solution and a correct final answer is obtained.
1 The problem is not properly modelled by the solution presented and the final
answer is incorrect.
Reflection
Complete this statement:
I have learned in this activity that…
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
__________________________________________________________________________.
References:
1. Callanta, Melvin T.(2015). Mathematics 10 Learners Module
2. https://www.mathsisfun.com/whole-numbers.html
3. https://brilliant.org/wiki/integers/
Answer Key
Addition of Integers
I. Use the number line to find the sum of the following integers.
1. 3 + 6
-4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(Starts at 3 and move 6 units to the right, it stops at 9 which is the sum)
2. -4 + -1
-7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7
(Starts at -4 and move 1 space to the left, it stops at -5, hence the sum is -5)
3. -7 + 2
-7 -6 -5 -4 -3 -1 0 1 2 3 4 5 6 7
(Starts at -7 and move 2 spaces to the right, it stops at -5, hence the sum is -5)
4. 8 + -3
3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(Starts at 8 and move 3 spaces to the left, it stops at 5, hence the sum is 5)
5. 10 + -5
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
(Starts at 10 and move 5 spaces to the left, it stops at 5, hence the sum is 5)

I.
1. 11 6. -19
2. -6 7. -3
3. 5 8. 7
4. -3 9. 7
5. 24 10 -4
II. 1. Beth ------ 27
2. Zeny ----- 10
3. Aida ----- -12
4. May ----- 12
5. Jona ----- 9
1. 3. Beth
2. Aida 4. Beth
IV. LET --------------- -8 + (-6) + (0) = -14
ME __________ ( 2) + ( -6 ) = -4
VOTE ___________ 8 + (-4) + (0) + (-6) = -2
(Sample words only)
V. 1. 400
2. 1000 feet
3. 1700 pesos
Prepared by
OFELIA V. CAGUIN
Cabulay High School

MATHEMATICS 7
Name:__________________________________________ Section:___________
Section:_________________________________________ Date:_____________
Subtraction of Integers
Background Information for Learner/Concepts
Integers are whole numbers that are positive or negative including zero. Negative
integers are numbers less than zero found at the number line from the left of zero and hold a
negative sign. Examples are -1, -5, -8, -12, -18, etc. while positive integers are numbers
greater than zero located at the right side of zero in the number line. This sign(+) indicates
positive integer. However, the sign is not always needed. Numbers like +3 or 3, +6 or 6, +9
or 9, +13 or 13, etc. are examples of positive integers. Zero on the other hand is located in
between the positive and negative integers in the number line.
The number line is used as a model to help us visualize adding and subtracting of
signed integers. Just think of addition and subtraction as directions on the number line. There
are also several rules and properties that define how to perform these basic operations.
Subtraction of an integer is just by adding its opposite.
Rules in subtracting integers:
1. Copy the first number(minuend)
2. Change the operation from subtraction to addition.
3. Get the opposite sign of the second number(subtrahend)
4. Proceed with the addition of integers.
Example:
1. What is -13 minus 4?
Subtraction
-13 - 4 = -13 + - 4 = 17
Minuend Subtrahend
2. Using the number line
-8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
a. 5 - 3 5 + -3 = 2
b. -4 – 4 -4 + -4 = -8
Subtraction of integers is just the
opposite of adding integers. It can be
done by adding the opposite.
Start at point 5, then move 3
units to the left, so it stops at 2.
Start at point -4, then move 4
units to the left, it stops at -8,
hence the difference is -8.

Learning Competency and Code
Performs fundamental operations on integers. M7NS-Ic-d-1
DIRECTIONS: Different activities were given for you to measure how deep is your
understanding on how to subtract integers.
Activity 1. IN WHAT WAY?
Find the difference using the number line.
-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11
1. -6 - (+3) = _______________ 6. -5 - (+7) = __________
2. 9 - (-4) = _______________ 7. 8 – (-6) = __________
3. -8 – (+5) = _______________ 8. 10 – (3) = __________
4. 10 - (-6) = _______________ 9. 1 – (-5) = __________
5. 7 - ( +2) = _______________ 10. -7 – ( -7) = __________
I. Subtract the following. (Show your solutions)
1. 26 - (15) = ___________ 6. 12 - (0) =___________
2. -50 - (-32) = __________ 7. -63 – (-14) = __________
3. 46 - (20) = __________ 8. 87 - (-52) = __________
4. 100 - (-150) = __________ 9. -69 – (84) = __________
5. -33 - (18) = ___________ 10. -26 – (-12) = __________
II. FITS ME WELL: Subtracting Squares(Show your solutions).
Minuend Subtrahend
- 8 10
-4 1. 2.
-7 3. 4.
- -15 -6
14 5. 6.
10 7. 8.
- -18 20
-9 9. 10.
12 11. 12.
III. I AM BRAVE!: Find the difference, then determine the letter that matches your
answer. When you are done you will be able to decode the word and proved you
are really brave.
R 1 -8 - (6)
O 2 12 - (-4)
G 3 -10 - (8)
T 4 13 - (10)
U 5 0 – (-14)
E 6 -8 - (1)

C 7 6 - (-5)
A 8 -11 - (-7)
____ ____ ____ ____ ____ ____ ____
11 16 14 -15 4 -18 -9
IV. Solve what is being asked:
1. Henry prepared 50 glasses of orange juice to sell. He sold 32 glasses. How
many glasses of orange juice does he have left?
2. Mary Ann’s cat gave birth to 5 kittens, and she gave 2 to her friends. How
many kittens he have now?
3. Peter saved 500 pesos and he spent 175 pesos in buying his shirt. How much
money does Peter have now?
4. It will be 380
tomorrow. The weatherman predicts it will be 20
colder by night.
What will be the temperature by night tomorrow?
5. The table below shows the amount of money donated by the faculty and staff
of a certain school and the amount spent to purchase relief goods for the needy
families.
Amount Collected Amount Spent
3,245.00 2,875.35
Question:
Find the amount of money left, if one staff needs to buy 1 pack of plastic
bag to be used in the packaging of relief goods that costs 40.50.
Rubric for rating Activity I and II
Score Descriptions
4 The computations are accurate. A wise use of the rules of subtraction of
integers are evident.
3 The computations are accurate. Use of the rules of subtraction of integers are
evident.
2 The computations are erroneous and show some use of the rules of subtraction
of integers .
1 The computations are erroneous and do not show some use of the rules of
subtraction of integers .
Rubric for rating Activity III and IV
Score Descriptions
4 Student explains the rules of subtracting integers and be able to apply in
solving problems..
3 Student demonstrates an understanding the rule of subtracting integers.
2 Student understands the rule of operations but is inconsistent in solving
1 Student needs assistance in subtracting integers.
Rubric for rating the Solving Problem
Score Descriptions
used in the solution and a correct final answer is obtained.
partially used in the solution and a correct final answer is obtained.
2 The problem is not properly modelled other alternative mathematical concepts

are used in the solution and a correct final answer is obtained.
1 The problem is not properly modelled by the solution presented and the final
answer is incorrect.
Reflection
Complete this statement:
I have learned in this activity that …
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
________________________________________________________________________.
References:
1. https://www.chilimath.com/lessons/introductory-algebra/subtraction-of-integers/
2. http://www.math.com/school/subject1/lessons/S1U1L11DP.html
3. Callanta, Melvin T.(2015). Mathematics 10 Learners Module
ANSWER KEY
Subtraction of Integers
1. -9 II. 1. 11
2. 13 2. -18
3. -13 3. 26
4. 16 4. 250
5. 5 5. -21
6. -12 6. 12
7. 14 7. -49
8. 7 8. 139
9. 6 9. -153
10. 0 10 -14
III.1.-12 7. 25
2.-14 8. 16
3. -15 9. 9
4. -17 10. -29
5. 29 11. 30
6. 20 12. -8
IV.
R 1 -8 - (6) -14
O 2 12 - (-4) 16
G 3 -10 - (8) -18
T 4 13 - (10) 3
U 5 0 – (-14) 14

E 6 -8 - (1) -9
C 7 6 - (-5) 11
A 8 -11 - (-7) 4
__C__ _O_____U__ __R_ __A__ __G__ _E___
11 16 14 -15 -14 -18 -9
V. Solving Problem:
1. 18 2. 3 3. 325 4. 400
5. 329.15
Prepared by
OFELIA V. CAGUIN
Teacher - III
Cabulay High School

Hi, here are some
activities for you to
master multiplication
of integers.
MATHEMATICS 7
Name of learner : _______________________________________ Grade Level ___________
Section : ______________________________________________ Date : ________________
Multiplying Integers
Background of Information for Learners
In multiplying integers you just do as multiplying whole numbers, but
you should be aware of the signs. We have to remember the rules, the product of
two positive integers is Positive. The product of two negative integers is Positive. The
product of a positive integer and a negative integer is Negative. And remember too that any
number multiplied by zero is equal to zero.
Examples.
1. (15) ( 10) = 150
2. (-25) (- 8) = 200
3. (-12) ( -30) = - 360
4. (-345) (0 ) = 0
Learning Competency with Code:
Performs fundamental operations on integers M7NS-1c-d-1
Activity 1. POSITIVE OR NEGATIVE?
DIRECTIONS : Tell whether the product of the integers
is Positive or Negative. Write your answer on the space
before each number.
______________ 1. ( 7) ( 9 )
______________ 2. ( - 10) ( 8)
______________ 3. ( - 5) ( -3)
______________ 4. ( - 63) ( 2) ( --9)
______________ 5. ( -8 ) ( -7) ( 5 ) ( - 4)
______________ 6. ( 11)(6)(-2)
_______________7. ( 31) (- 117)
_______________8.( 140)(12)
_______________9. (-13)(-406)(0)
_______________10.( 22)(-7)(-102)

Activity 2
Direction: Find the products of the following :
1. ( 6) ( -3) = __________
2. (- 4) ( -8) = __________
3. ( 12 ) ( 9) = __________
4. ( - 7) ( 10) = __________
5. ( 42) ( - 15) = __________
6. ( -11) (-112) = __________
7. ( 5) ( 13) = __________
8. ( - 9) ( -5) = __________
9. ( 14) ( -130) = ___________
10. ( -6) ( - 74) = __________
11. ( 89)(-7)( 2) = __________
12. (-10)(-51)(-4) = __________
13. ( 920)(0)( 11) = __________
14. (- 12)(8)(-2) (31)= _________
15. ( 320) ( - 167) = __________
Activity 3. GUESS WHAT?
.
Direction: What was the mathematical name for # (number sign)?
To answer this, find the products of the integers then write the letter inside
the box that corresponds to their products.
- 60 63 42 -60 42 - 96 - 60 80 -120 -180
H . ( 6) (4) (-4)
T. ( 3) (- 7) ( -2)
C. ( 7) ( -1 ) ( -9)
P. ( 2) ( -6) ( 1) ( 10)
R. ( 16) ( 5)
O. ( 5) ( 4) ( -3)
E. ( -15) ( -3) ( -2) ( 2)
Let us see if
you can find
the products?

Rubrics for Scoring
0 mistakes Outstanding
1-2 mistakes Very Good
3-4 mistakes Good
5- above mistakes Try again
Reflection:
Now ,Rate yourself, put a check
.
Score Remarks
35 Outstanding
34-26 Very Good
25-15 Good
0-14 Try Again
Try to ponder on this:
When something good (+) happens to someone good (+), it is Good (+).
When something good (+) happens to someone bad (-), it is Bad (-).
When something bad (-) happens to someone good (+), it is Bad (-).
When something bad (-) happens to someone bad (-), it is Good (+).
How will you deal with your negative attitudes?
______________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
__________________________________________________
References:
Learner’s Module
Grade 7, Math Lesson 4.3 : Fundamental Operation on Integers: Multiplication of
Integers
Book : e – Math edition 2012 revised edition 2015 by Orlando A. Oronce and
Marilyn O Mendoza.
Internet : byjus.com>videos
Answer Key
Activity 1
1. Positive
2. Negative
3. Positive
4. Positive

5. Negative
6. Negative
7. Negative
8. Positive
9. Negative
10. Positive
Activity 2
1. – 18 6. 22 11. – 1246
2. 32 7. 65 12. 2040
3. 108 8. 45 13. 0
4. -70 9. -1820 14. 5952
5. – 15 10. 444 15.53,440
Activity 3
O C T O T H O R P E
- 60 63 42 - 60 42 - 96 - 60 80 -120 -180
Prepared by
ALELI C. VALERIANO
Teacher - III
Cabulay High School

Ready for
this?
MATHEMATICS 7
Name of Learner :___________________________________________ Grade level :_________
Section: ___________________________________________________ Date: ______________
Dividing Integers
Background of Information for Learners
If multiplication is spreading of numbers, division is the distribution of numbers.
Dividing integers is opposite operation of multiplication. But the rules for division of integers
are same as multiplication rules. Though, it is not always necessary that the quotient will
always be an integer.
Rule 1: The quotient of two positive integers will always be positive.
Rule 2: The quotient of two negative integers will always be positive.
Rule 3: The quotient of a positive integer and a negative integer will always be
negative.
Examples:
1. ( 45) ÷ ( 9) = 5
2. ( -100) ÷ ( -5) = 20
3. ( 88) ÷ ( -4) = -22
4. ( -14) ÷ (7) = -2
Learning Competency with Code:
Performs fundamental operations on integers M7NS-1c-d-1
Activity 1. TRUE OR FALSE ?
Directions: Identify whether the given expression below is TRUE or FALSE. Write T if it is true
and F if it is false.
_____ 1. (- 9) ÷ ( - 3 ) = 27
_____ 2. ( 42) ÷ ( - 7) ÷ ( -6) = 1
_____ 3. ( 85 ) ÷ ( - 17 ) = 5
_____ 4. ( - 112) ÷ ( 16 ) = 7
_____ 5. ( 20) ÷ ( - 2) ÷ ( 5) = 2
_____ 6. ( 81) ÷ ( 9)÷ (- 1) = 9
_____ 7. ( - 36) ÷ ( -6) = -6
_____ 8. ( 515) ÷ (- 5) = 103
_____ 9. ( 24) ÷( 3) ÷(4) = -2
_____10. ( -60) ÷ ( -6) = 10

Looks like
easy, you
can do it.
Want to discover?
Solve the problem.
Activity 2
Direction: Find the quotient of the following:
1. ( 18) ÷ ( 9) = _____
2. ( -75) ÷ ( - 5) = _____
3. ( - 40) ÷ (- 4) = _____
4. ( -156) ÷ ( 12) = _____
5. ( 66) ÷ ( -11) = _____
6. (- 84) ÷ ( 7) ÷ ( - 3) = _____
7. ( 78) ÷ ( -13) ÷( 2) = _____
8. ( -64) ÷( 4) ÷ ( -8) = _____
9 .( 162) ÷ (-9) ÷ (-6) = _____
10. (- 136) ÷ (17) ÷(-2)=_____
Activity 3 What was the division slash (/) called?
DIRECTION: To find the answer , , match the letter in column II with number that corresponds to the
numbers in column I.
____1. ( 322) ÷ ( 14) U . – 7
____2. ( -198) ÷ ( 22 ) E. 7
____3. (186) ÷ ( 6) G. 53
____ 4. ( -212) ÷ ( -4) I. – 9
____5. ( 280) ÷ ( -40) R. 31
____ 6. (720) ÷ ( 9) ÷( -8) V. 23
____ 7. (560) ÷ ( 8) ÷ ( 10) L. – 10
B. – 23
Rubrics for Scoring
0 mistakes Outstanding
1-2 mistakes Very Good
3-4 mistakes Good
5 – above mistakes Try again
Reflection:
Now ,Rate yourself, put a check
.
Score Remarks
22 Outstanding
21- 16 Very Good
15 -11 Good
0-10 Try Again

Try to ponder on this:
When something good (+) happens to someone good (+), it is Good (+).
When something good (+) happens to someone bad (-), it is Bad (-).
When something bad (-) happens to someone good (+), it is Bad (-).
When something bad (-) happens to someone bad (-), it is Good (+).
Do you have any experience which have the same result like the above statement? Can you
share it?
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
__________________________________________________________________________________
________________________________________________________________
References:
.Learner’s Module
Grade 7 Math Lesson 4.3 : Fundamental Operation on Integers: Multiplication of Integers
Book : e – Math edition 2012 revised edition 2015 by Orlando A. Oronce and Marilyn O Mendoza.
Internet : byjus.com>videos
Answer Key
Activity 1
1. T
2. F
3. F
4. F
5. F
6. F
7. F
8. F
9. F
10. T
Activity 2
1. 2
2. 15
3. 10
4. – 13
5. – 6
6. 4
7. -2
8. 2
9. 3
10. – 4

Activity 3
1. V
2. I
3. R
4. G
5. U
6. L
7. E
Prepared by:
ALELI C. VALERIANO
Teacher – III
Cabulay High School

MATHEMATICS 7
Name: _____________________ Grade Level: ____
Date: ______________________ Score: _________
Properties of Real Numbers
Understanding the properties of real numbers will help us simplify numerical and
algebraic expressions, solve equations, and more as you progress in studying algebra.
For clarity, “properties” in this context refer to the characteristics or behaviors of real
numbers under the operations of addition and/or multiplication that are accepted even without
proof.
Here are the main properties of the Real Numbers:
1. Commutative
Example
a. a + b = b + a 2 + 6 = 6 + 2
b. ab = ba 4 × 2 = 2 × 4
2. Associative
Example
a. (a + b) + c = a + ( b + c ) (1 + 6) + 3 = 1 + (6 + 3)
b. (ab)c = a(bc) (4 × 2) × 5 = 4 × (2 × 5)
3. Distributive
Example
a. a × (b + c) = ab + ac 3 × (6+2) = 3 × 6 + 3 × 2
b. (b+c) × a = ba + ca (6+2) × 3 = 6 × 3 + 2 × 3
Real Numbers are closed (the result is also a real number) under addition and
multiplication:
4. Closure
Example
a. a+b is real 2 + 3 = 5 is real
b. a×b is real 6 × 2 = 12 is real
Adding zero leaves the real number unchanged, likewise for multiplying by 1:
5. Identity
Example
a. a + 0 = a 6 + 0 = 6
b. a × 1 = a 6 × 1 = 6

For addition the inverse of a real number is its negative, and for multiplication the inverse
is its reciprocal:
6. Additive Inverse
Example
a + (−a ) = 0 6 + (−6) = 0
7. Multiplicative Inverse
Example
a × (1/a) = 1 6 × (1/6) = 1
*But not for 0 as 1/0 is undefined
Multiplying by zero gives zero (the Zero Product Property):
8. Zero Product
Example
If ab = 0 then a=0 or b=0, or both a × 0 = 0 × a = 05 × 0 = 0 × 5 = 0
The learner illustrates the different properties of operations on the set of integers.
(M7NS-Id-2)
Activity 1
Directions: Each of the given instructions is about two things. In column II, the order has
been changed around. Put a check before the number if the results in the two columns are the
same.
A B
1. Put on your socks and then put on
your shoes.
Put on your shoes and then put on your
socks.
2. Kill the snake and then pick it up. Pick up the snake and then kill it.
3. Walk 10 paces south and then two
paces north.
Walk two paces north and then 10 paces
South.
4. Add 7 and 12 Add 12 and 7
5. Divide 6 by 3. Divide 3 by 6.
Activity 2.
Directions: Do the following calculations in the quickest way you can find.
1. 18 + 6 + 4
2. 65 + 35 + 19
3. 17 + 129 + 1
4. 19 x 5 x 2
5.
1
2
+
5
2
+ 1
2
3

Activity 3
Directions: Identify if the following instructions is commutative or not. Write C if
commutative, NC if not commutative.
__________1. Wash the shirt and the iron it.
__________2. Fetch water and turn on the TV
__________3. Find x if 3 is a factor of 12. Find x if 12 is a factor of 3.
__________4. Eat dinner and clean the bathroom.
__________5. Attend the review class and take the exam.
Activity 3.1
Directions: Complete each statement to illustrate the indicated property.
1. 3 + ( 2 +11) = 3 + (11 +____) Commutative Property
2. 3∙ ( 8 + 12 ) = 3∙ ( 12 + ____ ) Commutative Property
3. (15 + 8) + 7 = _____ + (8 + ____) Associative Property
4. 11∙ ( 9 + 2 ) = 11∙ 9 + 11∙ ____ Distributive Property
5. 11 + ____ = 11 Identity Property
6. -17 + 17 = _______ Inverse Property
7.
7
3
× = 1 Inverse Porperty
8. 19 × 0 = _____ Zero Property
Activity 4
Directions: Identify the real number property that justifies each statement.
1. 19 + x = x + 19 ___________________________________
2. 7(x – 6) = 7x – 42 ___________________________________
3. 17 + (-17) = 0 ___________________________________
4. 0 +
7
3
=
7
3
___________________________________
5. (0.1)(10) = 1 ___________________________________
6. xy + y = y(x + 1) ___________________________________
Activity 5
Directions: Complete each statement using the indicated property.
1. a + b = ____________________ Commutative
2. 7x + 7 = _______________________ Distributive
3. 19(bc) = _______________________ Associative
4. (p + 9) + 1 = _____________________ Associative
5. 0.13 + (____) = 0 Inverse Property
6. 4 (___) = 1 Multiplicative Inverse
7. 25 + ______ = 25 Identity
8.
13
9
𝑘 +
13
9
= ______________________ Distributive

REFLECTION
In this lesson, I learned
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___
REFERENCES
Oronce, O & Mendoza, M (20156). E-Math: Workbook in Mathematics. Rex Printing
Company.),
ANSWER KEY
Activity 1
Directions: Each of the given instructions is about two things. In column II, the order has
been changed around. Put a check before the number if the results in the two columns are the
same.
A B
1. Put on your socks and then put on
your shoes.
Put on your shoes and then put on your
socks.
2. Kill the snake and then pick it up. Pick up the snake and then kill it.
3. Walk 10 paces south and then two
paces north.
Walk two paces north and then 10 paces
South.
/ 4. Add 7 and 12 Add 12 and 7
5. Divide 6 by 3. Divide 3 by 6.
Activity 2.
Directions: Do the following calculations in the quickest way you can find.
1. 18 + 6 + 4 = 28
2. 65 + 35 + 19 = 119
3. 17 + 129 + 1 = 147
4. 19 x 5 x 2 = 190
5.
1
2
+
5
2
+ 1
2
3
= 5
Activity 3.
Directions: Identify if the follwing instructions is commutative or not. Write C if
commutative, NC if not commutative.
NC 1. Wash the shirt and the iron it.
NC 2. Fetch water and turn on the TV
NC 3. Find x if 3 is a factor of 12. Find x if 12 is a factor of 3.
C 4. Eat dinner and clean the bathroom.

NC 5. Attend the review class and take the exam.
Activity 3.1
Directions: Complete each statement to illustrate the indicated property.
1. 3 + (2 +11) = 3 + (11 + 2) Commutative Property
2. 3∙ (8 + 12) = 3∙ ( 12 + 8) Commutative Property
3. (15 + 8) + 7 = 15 + (8 + 7) Associative Property
4. 11∙ (9 + 2) = 11∙ 9 + 11∙ 2 Distributive Property
5. 11 + 0 = 11 Identity Property
6. -17 + 17 = 0 Inverse Property
7.
7
3
×
3
7
= 1 Inverse Porperty
8. 19 × 0 = 0 Zero Property
Activity 4.
Directions: Identify the real number property that justifies each statement.
1. 19 + x = x + 19 COMMUTATIVE
2. 7(x – 6) = 7x – 42 DISTRIBUTIVE
3. 17 + (-17) = 0 INVERSE
4. 0 +
7
3
=
7
3
IDENTITY
5. (0.1)(10) = 1 INVERSE
6. xy + y = y(x + 1) DISTRIBUTIVE
Activity 5.
Directions: Complete each statement using the indiciated property.
1. a + b = b + a Commutative
2. 7x + 7 = 7(x+ 1) Distributive
3. 19(bc) = (19b)c Associative
4. (p + 9) + 1 = p+(9+1) Associative
5. 0.13 + (-0.13) = 0 Inverse Property
6. 4 (1/4) = 1 Multiplicative Inverse
7. 25 + 0 = 25 Identity
8.
13
9
𝑘 +
13
9
=
13
9
(𝑘 + 1) Distributive
dule Fourth Year · Triangle
Trigonometry, Mo, Module 2 (LPrepared by:
GERALDINE S. CANLAS
Teacher

MATHEMATICS 7
Name: _____________________ Grade Level: ____
Date: ______________________ Score: _________
THE TRANSFORMER!
Express rational numbers from fraction form to decimal form
(vice versa).
This activity sheet serves as a supplement learning material guide for the learners. It
will direct the students to familiarize in expressing rational numbers from fraction form to
decimal form (vice versa) to be used in solving real life activity.
The steps in expressing rational numbers from fraction form to decimal form (vice
versa) can be modified using the operations on whole number. Always remember that any
rational number can be changed from fractional form to decimal form by dividing the
numerator by the denominator. On the other hand, a decimal can be changed to a fraction
using the power of 10 as the denominator. Then, reduce it to its simplest form.
Express rational numbers from fraction form to decimal form and vice versa.
(M7NS-Ie-1)
Activity 1: Hunt me if you can!
Instruction: Encircle all terminologies use in expressing rational number from fraction
form to decimal form (vice versa). Words can be spelled forward, backward, diagonally up or
down.

Activity 2: TRANSFORM ME!
Express the given fraction to decimal.
1.
3
4
= ______
2.
2
5
= ______ 3.
1
4
= ______
4.
3
10
= ______ 5.
3
8
= ______
6.
1
8
= ______ 7.
4
10
= ______
8.
3
5
= ______ 9.
15
60
= ______
10.
3
16
= ______
Activity 3: GETTING TO KNOW!
State wether the following fraction are terminating or nonterminating decimals
_____________ 1.
4
5
_____________ 2.
7
8
_____________ 3.
3
7
_____________ 4.
8
11
_____________ 5.
9
20
_____________ 6.
1
6
_____________ 7.
3
15
_____________ 8.
1
3

_____________ 9.
12
42
_____________10.
5
6
Activity 4: Follow Stictly!
To answer this, you will express the rational number from decimal form to
fraction form. Match your answer from the choices on the right and write the corresponding
answer on the left before the number. Then decode the message below.
( Clue:It is the deliverate increase of physical space between people to prevent them
spreading illness.)
_________1. 0.75 G
71
500
_________2. 0.328 L
4
5
_________3. 0.8 C
5
8
_________4. 0.625 I
3
4
_________5. 0.25 D
41
125
_________6. 0.88 T
7
20
_________7. 0.35 N
19
25
_________8. 0.825 A
7
40
_________9. 0.152 J
49
50
________10. 0.365 M
39
50
________11. 0.175 O
22
25
________12. 0.78 B
1
4
________13. 0.142 U
33
40
________14. 0.18 S
73
200
________15. 0.98 P
9
50
__ __ __ __ __ __ __ __ __ __ __ __ __ __ __ __
10 6 4 1 11 3 2 1 10 7 11 9 4 1 9 13

Activity 5: Make Me Simple!
Express the repeating, nonterminating decimals to fraction. The illustrative
example were shown for your reference. Rubric for scoring is given below.
Illustrative example:
Express 0.44… to fraction.
a. 0.44…
Let x = 0.44
10x= 4.44
- x= 0.44
9x = 4
9x = 4
9 9
x =
𝟒
𝟗
1. 0.33… 2. 0.66… 3. 0.55…
4. 0.1212… 5. 0.3232… 6. 0.1515…
7. 0.135135… 8. 0.123123… 9. 0.125125…
Solution Solution Solution

CRITERIA OUTSTAND
ING
(4)
SATISFACTOR
Y
(3)
DEVELOPIN
G
(2)
BEGINNING
(1)
Representation Represent the
problem into
equation.
Represent the
problem into
equation with
missing parts.
The
representation is
not clear.
Doesn't understand
enough to get
started or make
progress.
Solution Shows correct
computation.
Proficient
evidence in
expressing
decimals to
fraction.
80% of the problem
got correctly. There
is basic evidence in
expressing decimal
to fraction.
50% of the
problem got
correctly. There
is basic evidence
in expressing
decimal to
fraction.
There is no
evidence of
computation.
Neatness Work is clear
and organize.
Work is clear but
not organize.
Work is fairly
neat.
Work is not clear
and lack of
organization.
Reflection
I have learned that____________________________________________

Answer key
Activity 1: Hunt me if you can!

Activity 2: TRANSFORM ME!
1.
3
4
= _0.75_
2.
2
5
= __0.4__ 3.
1
4
= _0.25_
4.
3
10
= __0.3__ 5.
3
8
= _0.375
6.
1
8
= _0.125__ 7.
4
10
= __0.4__
8.
3
5
= __0.6__ 9.
15
60
= __0.25__
10.
3
16
= _0.1875_
Activity 3: GETTING TO KNOW!
__Terminating__ 1.
4
5
__Terminating__ 2.
7
8
Nonterminating 3.
3
7
Nonterminating 4.
8
11
__Terminating__ 5.
9
20
Nonterminating 6.
1
6
__Terminating__ 7.
3
15
Nonterminating 8.
1
3
Nonterminating 9.
12
42
Nonterminating 10.
5
6

Activity 4: Follow Stictly!
____ I ___ 1. 0.75 G
71
500
____D____2. 0.328 L
4
5
____L ___ 3. 0.8 C
5
8
____C____4. 0.625 I
3
4
____B____5. 0.25 D
41
125
____O____6. 0.88 T
7
20
____T____7. 0.35 N
19
25
____U____8. 0.825 A
7
40
____N____9. 0.152 J
49
50
___ S____10. 0.365 M
39
50
___ A____11. 0.175 O
22
25
___M____12. 0.78 B
1
4
____G__ 13. 0.142 U
33
40
____P___ 14. 0.18 S
73
200
____J ___15. 0.98 P
9
50
_S_ _O_ _C_ _I_ _A_ _L_ _D_ _I_ _S_ _T_ _A_ _N_ _C_ _I_ _N_ _G_
10 6 4 1 11 3 2 1 10 7 11 9 4 1 9 13
Activity 5: Make Me Simple!
1. 0.33… 2. 0.66… 3. 0.55…
4. 0.1212… 5. 0.3232… 6. 0.1515…
Solution
Let x = 0.33
10x= 3.33
- x= 0.33
9x = 3
9x =3
9 9
x =
3
9
x =
𝟏
𝟑
Solution
Let x = 0.66
10x= 6.66
- x= 0.66
9x = 6
9x = 6
9 9
x =
6
9
x =
𝟐
𝟑
Solution
Let x = 0.55
10x= 5.55
- x= 0.55
9x = 5
9x =5
9 9
x =
𝟏
𝟑

7. 0.135135… 8. 0.123123… 9. 0.125125…
References
Mathematics 7 Teaching Guide, p. 61 - 63
Bernabe, J. & De Leon, C. (2002). Elementary Algebra
https://www.everydayhealth.com/coronavirus/coronavirus-glossary-key-terms-about-the-
pandemic-explained/
Prepared by
ROMMEL A. SIMON/PRIMAROSE A. SALES
Teacher III
Solution
Let x = 0.12
100x= 12.12
- x = 0.12
99x = 12
99x = 12
99 99
x =
12
99
x =
𝟒
𝟑𝟑
Solution
Let x = 0.32
100x =32.32
- x = 0.32
99x = 32
99x = 32
99 99
x =
𝟑𝟐
𝟗𝟗
Solution
Let x = 0.15
100x =15.15
- x = 0.15
99x = 15
99x = 15
99 99
x =
15
99
x =
𝟓
𝟑𝟑
Solution
Let x = 0.135
1000x= 135.135
- x = 0.135
999x = 135
999x = 135
999 999
x =
135
999
x =
𝟒𝟓
𝟑𝟑𝟑
Solution
Let x = 0.123
1000x= 123.123
- x = 0.123
999x = 123
999x = 123
999 999
x =
𝟏𝟐𝟑
𝟗𝟗𝟗
Solution
Let x = 0.125
1000x= 125.125
- x = 0.125
999x = 125
999x = 125
999 999
x =
𝟏𝟐𝟓
𝟗𝟗𝟗

MATHEMATICS 7
Name: ________________________________________ Grade Level: _____
Section: _______________________________________Date: ____________
LEARNING ACTIVITY SHEETS
Operations on Rational Numbers
This activity sheet serves as a self-learning guide for you. It is expected that you will
learn or master operations on rational numbers. How do you operate using rational
numbers?
We have learnt about fractions earlier, and we saw how different operators can be
used on different fractions. Well, all the rules and principles that govern fractions can also be
applied to rational numbers. The one thing to be kept in mind is that rational numbers also
include negatives. So, while 1/5 is a rational number, it is also true that −1/5 is also a
rational number.
Rational
Integers
Whole
Numbers

To understand the concept of negative rational numbers, we need to understand a
number line. A number line is simply a line on which numbers are marked at equal intervals.
A number line can be extended infinitely in both directions. One of the points of a number
line is zero. All points to the right of the zero mark are positive numbers, while all the
numbers to the left of zero are negative numbers.
A number line also makes it very easy to visualize additions and subtractions of
positive numbers and negative numbers. For example, if we wish to
add −3−3 with +2,+2, then it means that the first number is three spaces to the left of zero,
while the second number is two spaces to the right of zero. Therefore, their sum will be just
one space to the left.
Addition of Rational Numbers
As we saw above, a rational number is a ratio of two numbers p and q, where q is
non-zero number. Here p is called the numerator and q is called the denominator. When it
comes to addition of two such rational numbers, there can be four possible variations.
First, both the rational numbers could have the same denominator. For example, when we
wish to add ⅓ and ⅔, the answer is simply the sum of 1 and 2, divided by the common
denominator 3. So
⅓+⅔ = (1+2)/3 = 3/3
Next, the two rational numbers could have the same denominator, but one of them could be
negative. So, when you need to add 3/5 and −1/5, then we can write the calculation in this
way
3/5+(−1/5)=(3+(−1)/5=(3−1)/5=2/5
The third variant is when the two rational numbers to be added have different coefficients.
Like we have seen earlier, we will make the two numbers similar to each other by taking the
lowest common multiple of both denominators as the denominator of the answer. So, to
add 5/6 and 7/9, we first need to find the LCM of 6 and 9, which is 18. So, we can
write 5/6 as 15/18 and 7/9 as 14/18. Then the addition of these two rational numbers can be
expressed in the following way
5/6+7/9=15/18+14/18=(15+14)/18=29/18

The final variant is when one of the two rational numbers with different denominators
is negative. So, if we need to add 5/6 and −7/9, then the addition can be carried out in the
following manner
5/6+(−79)=15/18+(−14/18)=(15+(−14)/18=1/18
Subtraction of Rational Numbers
If you can understand the concept of additive inverse, then you do not need to
understand anything extra outside the addition we saw above, when we need to subtract two
rational numbers. The additive inverse of a fraction is the number which when added to it
gives a result zero. So, if you have a variable x, and its additive inverse is i, then x+i = 0,
= > i = −x. So, when expressed simply, the additive inverse of any number is the same
number with a negative sign.
Now let us see how we can express how to subtract 3/7 from 5/7. The additive
inverse of 3/7 is −3/7 So, the subtraction can be expressed as the addition to additive
inverse.
Therefore,
5/7−3/7=5/7+(−3/7)=2/7
Multiplication and Division of Rational Numbers
Just like we saw above that subtraction can be quite easily understood once addition is
clear, similarly, division of two rational numbers is quite easy to comprehend once
multiplication is clear. First, let us look at multiplication. When two rational numbers are to

be multiplied together, then the simple thing to do is to multiply both numerators together to
get the new numerator, and then the two denominators to get the new denominator. So when
we multiply 3/5 and 4/7, the answer is
3/5×4/7=(3×4)(5×7)=12/35.
For division, we need to find the multiplicative inverse of the second rational number.
Therefore
(3/4)(5/7)=3/4×7/5=(3×7)(4×5)=21/20.
Source: https://www.cuemath.com/maths/operations-on-rational-numbers/
Learning Competency with Code
The learner performs operations on rational numbers. (M7NS-If-1)
Directions: In doing the different given activities, remember that honesty is the best policy.
Apply what you have learned about the operations of rational numbers. Hope you will enjoy!
Activity 1: Reveal the Real Me!
Perform the indicated operations and connect the dots in the order you created to
reveal the image.

Activity 2: The colors of my life!
Perform the indicated operations and color the shapes with corresponding answers.

Activity 3: Flower Fractions!
Solve each problem. Color the picture using the answer key below.

Activity 4: Make It A Habit!
Match the columns. Then write the letters on the space provided that match the
numbers on the correct lines to solve the missing word. (Clue: We must do this always to
prevent Covid – 19.)
1. _____ 3.5 ÷ 2 = N 52.31
2. _____ 78 𝑥 0.4 = B 124.8
3. _____ 9.6 𝑥 13 = I 52
4. _____ 3.24 ÷ 0.5 = C 68.25
5. _____ 1.248 ÷ 0.024 = G 54.6822
6. _____ 27.3 𝑥 2.5 = E 326.9
7. _____ 9.7 𝑥 4.1 = W 1.75
8. _____ 3.415 ÷ 2.5 = F 48.783
9. _____ 53.61 𝑥 1.02 = A 6.48
10. _____ 1948.324 ÷ 5.96 = J 1.366
11. _____ 5.231 ÷ 0.1 = H 39.77
12. _____ 70.1 𝑥 2.03 = L 0.8322
13. _____ 41.61 𝑥 0.02 = D 0.8625
14. _____0.345 ÷ 0.4 = P 142.303
15. _____ 23.23 𝑥 2.1 = S 31.2
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____ _____
7 4 11 14 1 4 2 7 5 11 9

Activity 5: My Real World
Read the problem carefully and solve. Rubric for scoring is given below.
1. Maria brought 7
1
4
meters of silk, 4
1
2
meters of satin and 5
3
8
meters of velvet. How many
meters of cloth did she buy?
2. After boiling, the 18
1
4
liters of water was reduced to 7
1
5
liters. How many water was
evaporated?
3. Marjorie and Crisel are comparing their heights. If Marjorie’s height is 167
3
4
cm and Crisel’s
height is 155
1
2
cm. What is the difference in their heights?
4. A drum full of rice weight 43
1
2
kg. If the empty drum weights 14
1
4
kg. Find the weight of rice
in the drum.
5. A basket contains three types of fruits weighing
87
4
kg in all. If
23
4
of these are oranges,
48
7
kg
are mangoes, and the rest are apples. What is the weight of the apples in the basket?
6. Marjorie spent 3
1
2
hours doing her assignment. Crisel did his assignment for 1
2
3
times as
many hours as Marjorie did. How many hours did Crisel spend doing his assignment?
7. How many thirds are there in six-fifths?
8. Marjorie donated
2
5
of her monthly allowance to the Santiago City frontliners. If her monthly
allowance is P3500, how much did she donate?
9. The enrolment for this school year is 2340. If
1
6
are sophomores and
1
4
are seniors, how many
are freshmen or juniors?
10. At the end of the day, a store had
2
5
of a cake leftover. The four employees each took home
the same amount of leftover cake. How much of the cake did each employee take home?
Rubric for Scoring
CRITERIA OUTSTANDING
(4)
SATISFACTORY
(3)
DEVELOPING
(2)
BEGINNING
(1)
Understands the
problem
Identifies special
factors that
influences the
approach before
starting the
problem.
Understands the
problem.
Understands
enough to solve
part of the
problem or to get
part of the
solution.
Doesn't
understand
enough to get
started or make
progress.
Accuracy The computations
are accurate. A
wise use of key
concepts of
operations on
rational numbers.
The computations
are accurate. Use of
key concepts of
operations on
rational numbers.
The computations
are erroneous and
show some use of
key concepts of
operations on
rational numbers.
The
computations are
erroneous and do
not show some
use of key
concepts of
operations on
rational numbers.
Reflection

I have learned that ____________________________________________
References
K to 12 Curriculum Guide in Mathematics. Available at:https://lrmds.
deped.gov.ph/detail/5455
Mathematics 7 Teaching Guide, p. 78 – 79
https://www.cuemath.com/maths/operations-on-rational-numbers/
Answer Key
Activity 1: Reveal the Real Me!

Activity 2: The colors of my life!
Activity 3: Flower Fractions!

Activity 4: Make It A Habit!
1. ___W__ 3.5 ÷ 2 = N 52.31
2. ___S__ 78 𝑥 0.4 = B 124.8
3. ___B__ 9.6 𝑥 13 = I 52
4. ___A__ 3.24 ÷ 0.5 = C 68.25
5. __I___ 1.248 ÷ 0.024 = G 54.6822
6. ___C__ 27.3 𝑥 2.5 = E 326.9
7. __H___ 9.7 𝑥 4.1 = W 1.75
8. ___J__ 3.415 ÷ 2.5 = F 48.783
9. ___G__ 53.61 𝑥 1.02 = A 6.48
10. ___E__ 1948.324 ÷ 5.96 = J 1.366
11. ___N__ 5.231 ÷ 0.1 = H 39.77
12. ___P__ 70.1 𝑥 2.03 = L 0.8322
13. ___L__ 41.61 𝑥 0.02 = D 0.8625
14. ___D__0.345 ÷ 0.4 = P 142.303
15. ____F_ 23.23 𝑥 2.1 = S 31.2
_____ _____ _____ _____ _____ _____ _____ _____ _____ _____
_____
7 4 11 14 1 4 2 7 5 11 9
HANDWASHING
Activity 5: My Real World
1. 17
1
8
m 6.
35
6
or 5
5
6
hours
2. 11
1
20
liters 7.
18
5
or 3
3
5
3. 12
1
4
cm 8. P1,400.00
4. 29
1
4
kg 9. 1,365 students are freshmen or juniors
5. 9
1
7
kg 10.
1
10
of the cake
Prepared by:
CRISEL C. BISTANTE
MARJORIE INGRARAN
ROMMEL A. SIMON

MATHEMATICS 7
Name: ___________________________________________ Grade Level: ____
Date: ____________________________________________ Score: __________
Principal Roots and Irrational Numbers
This learning activity sheet serves as a self-learning guide for the learners. It
facilitates lesson comprehension as it specifically aims for students’ mastery on principal
square root and describe whether rational or irrational numbers.
Squaring a number is like multiplying a number by itself. The square of 4, written as
42
, and read as “four squared”, is like (4)(4) = 16. The square of -4 is (-4)2
= (-4)(-4) = 16.
Otherwise, 16 is the result of squaring a number, 16 is an example of a perfect square. Below
are the listed perfect squares.
Perfect Square Factored Form Square Root
1 12
= (1)(1) 1
4 22
= (2)(2) 2
9 32
= (3)(3) 3
16 42
= (4)(4) 4
25 52
= (5)(5) 5
36 62
= (6)(6) 6
49 72
= (7)(7) 7
64 82
= (8)(8) 8
81 92
= (9)(9) 9
100 102
= (10)(10) 10
The square root of a number is one of the two equal factors of a perfect square. The
square root of 16 is 4, since (4)(4) = 16. However, since (-4)(-4) = 16, therefore -4 is also a
square root of 16. Every nonzero real number has two square roots, one positive and one
negative.
The square root of a number n is written in symbol as √𝑛. The symbol √ is called
radical sign, and the numbers n under the radical sign is called radicand.
Model: √144 = 12 since 122
= (12)(12) = 49
√0.25 = 0.5 since 0.52
= (0.5)(0.5) = 0.25
Rational numbers such as 0.16,
4
100
, and 4.84 are also perfect square. The square roots of
perfect squares are rational numbers while the square root of numbers that are not perfect
squares are irrational numbers.

Examples: Determine whether the following is rational or irrational.
a. √169 b. √41
Answer
a. Since 169 is a perfect square, √169 is rational. √169 = 13
b. Since 41 is not a perfect square, √41 is irrational.
Learning Competency
Describes principal roots and tells whether they are rational or irrational (M7NS-Ig-1)
Activity 1:
Directions: Find each square root.
1. √25
2. √225
3. √196
4. √576
5. √
9
25
6. √961
7. √529
8. √361
9. √77.44
10. √
1
81
Activity 2:
Directions: Write two integers between which the given square root lies.
1. √70 6. √92
2. √134 7. √189
3. √215 8. √334
4. √406 9. √509
5. √700 10. √1001
Activity 3:
Direction: Tell whether the following is a rational or irrational.

1. √121 6. √441
2. √84 7. √0.09
3. √105 8. √2601
4. √289 9. √503
5. √600 10. √104.04
Activity 4:
Multiple Choice:
1. Which set below includes only irrational numbers?
a. {-√12, −3.7666 … , √36, 4.3858 …} c. {-5.6, √14, 6.3245, √256}
b. {-7.23222…, √5, √15, 8.27451…} d. {-√8, 3.77…,3.265165065…, √900}
2. Which list contains only rational numbers?
a. -4, 0,
1
4
, √
9
4
b. 0,
1
2
, 1.5, √8 c. -2, 1, 2.6…,
3
2
d. 0, 0.3636…, 4, √24
3. What type of number is √26?
a. Whole number b. Integer c. Rational number d. Irrational
number
4. Which element below is an element in the set of irrational number?
a. √4 b. 3.45 c. -8.7 d. √8
5. Which irrational number is between 4 and 5?
a. √12 b. √20 c. √34 d. √80
Activity 5:
Solve each problem and write whether the answer is rational or irrational.
1. A standard classroom measures 7 meters by 9 meters. Its diagonal is √140 meters.
Find the value of √140.
2. The length of a rope is √1369 centimeters. Find its length.
3. The area of a square is determined by squaring the length of its side. If the area is 361
square meters, what is the length of its side?
4. Mr. Cruz is buying a square piece of land which is 506.25 square meters in area. What
is the length of each side of the land?
Reflection
I have learned that…
√4, 3.45, -8.7, √8

_____________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
_______________
References
Next Century Mathematics 7, Elementary Algebra I, E-MATH 7 Revised Edition
Year
Answer Key
Triangle
Prepared by:
RANDY B. TOLENTINO
T-I
Activity 4:
1. b
2. a
3. d
4. d
5. b
Activity 5:
1. 11.8321 – irrational
2. 37 – rational
3. 19 – rational
4. 22.5 - rational
Activity 3:
1. rational
2. irrational
3. irrational
4. rational
5. irrational
6. irrational
7. rational
8. rational
9. irrational
10. rational
Activity 2:
1. 8 & 9
2. 11 & 12
3. 14 & 15
4. 20 &21
5. 26 & 27
6. 9 & 10
7. 13 & 14
8. 18 & 19
9. 22 & 23
10. 31 & 32
Activity 1:
1. 5
2. 15
3. 14
4. 24
5.
3
5
6. 31
7. 23
8. 19
9. 8.8
10.
3
5
.

MATHEMATICS 7
Name: ______________________________________ Score: __________
Grade & Section: ______________________________ Date: ___________
LEARNING ACTIVITY SHEET 1
Perfect Match!
Background Information For Learners
Taking the square root of a number is like doing the reverse operation of squaring a
number. For example, both 5 and –5 are square roots of 25, since 52
= 25, and (–5)2
= 25.
Meaning, the product of multiplying a number to itself is perfect square.
In both 5 and –5, 5 is the positive square root or it is called as principal square root,
and the other one is negative square root.The square roots of perfect squares are rational
numbers while the square roots of numbers that are not perfect squares are irrational
numbers.
You will learn in this learning activity sheet on how to classify perfect squares and
principal roots.
The learner determines between what two integers the square root of a number is.
Code: M7NS-Ig-2
Activity 1.Encircle the perfect squares found in the box.
Activity 2.Match column A to column B. Write the letter of your choice on the space
provided before the number.
Column A Column B
(Principal Roots) (Perfect Squares)
_____ 1. 5 A. 49
_____ 2. 8 B. 16
_____ 3. 2 C. 144
45169 16 49 81 3 16
200 1 8 64 90 9 7121
754 214 20 225 24 265
36 101 164 30 289 326 17 196
19 2 6 100 42 99 68
Practice Application
and

_____ 4. 10 D. 25
_____ 5. 4 E. 529
_____ 6. 12 F. 225
_____ 7. 7 G. 4
_____ 8. 15 H. 100
_____ 9. 19 I. 64
_____10. 23 J. 361
Reflection.
What I have learned in this activity?
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
References:
Learners Manual in Mathematics 7, pp. 63 – 68.
Answer key:
Activity 1 (in any order)
1. 169 6. 1 11. 225
2. 16 7. 64 12. 36
3. 49 8. 9 13. 289
4. 81 9. 121 14. 196
5. 16 10. 4 15. 100
Activity 2
1. D 6. C
2. I 7. A
3. G 8. F
4. H 9. J
5. B 10. E
Prepared by:
JUN – JUN P. DARIANO
Teacher III

MATHEMATICS 7
Name: ______________________________________ Score: __________
Thorn Between Two Perfect Squares!
Perfect squares are numbers that have rational numbers as square roots. If a principal root is
irrational, the best you can do is to give an estimate of its value. Estimating is very important for all
principal roots that are not roots of perfect nth
powers.
For example, between which two integers does √20 lie? In this question, you have to
determine the closest perfect squares between √20. The closest perfect squares are √16 and √25 or
you can expressed as √16<√20<√25, then by getting the principal root, you can write in integers as 4
<√20< 5. Therefore, the two consecutive integers between √20 are 4 and 5.
You will learn in this learning activity sheet on how to write the perfect squares or principal rootsand
determining what two consecutive integers each square root is between.
Code: M7NS-Ig-2
Activity 1.Write the perfect square into its equivalent principal root and vice versa.
Principal Roots Perfect Squares Principal Roots Perfect Squares
1. 9 1. ____ 6. 11 6. ____
2. 7 2. ____ 7. ____ 7. 400
3. ____ 3. 169 8. ____ 8. 529
4. 6 4. ____ 9. 14 9. ____
5. ____ 5. 16 10. ____ 10. 324
Activity 2.Determine what two consecutive integers each square root is between.
Square Root Between of Perfect Square Between of integers Consecutive Integers
1. √40 1. ___ <√40<___ 1. ___ <√40<___ 1. ___ and ___
2. √54 2. ___ <√54<___ 2. ___ <√54<___ 2. ___ and ___
3. √75 3. ___ <√75<___ 3. ___ <√75<___ 3. ___ and ___
4. √112 4. ___ <√112<___ 4. ___ <√112<___ 4. ___ and ___
5. √147 5. ___ <√147<___ 5. ___ <√147<___ 5. ___ and ___
6. √205 6. ___ <√205<___ 6. ___ <√205<___ 6. ___ and ___
7. √238 7. ___ <√238<___ 7. ___ <√238<___ 7. ___ and ___
8. √462 8. ___ <√462<___ 8. ___ <√462<___ 8. ___ and ___
9. √717 9. ___ <√717<___ 9. ___ <√717<___ 9. ___ and ___
and

10. √947 10. ___ <√947<___ 10. ___ <√947<___ 10. ___ and ___
Reflection
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
References
Answer key
Activity 1
1. 81 6. 121
2. 49 7. 20
3. 13 8. 23
4. 36 9. 196
5. 4 10. 18
Activity 2
Square Root Between Perfect Square Between integers Consecutive Integers
1. √40 1. √36<√40<√49 1. 6 <√40<7 1. 6 and 7
2. √54 2. √49<√54<√64 2. 7<√54<8 2. 7 and 8
3. √75 3. √64<√75<√81 3. 8 <√75<9 3. 8 and 9
4. √112 4. √100<√112<√121 4. 10<√112<11 4. 10 and 11
5. √147 5. √144<√147<√169 5. 12<√147<13 5. 12 and 13
6. √205 6. √196<√205<√225 6. 14<√205<15 6. 14 and 15
7. √238 7. √225<√238<√256 7. 15<√238<16 7. 15 and 16
8. √462 8. √441<√462<√484 8. 21<√462<22 8. 21 and 22
9. √717 9. √676<√717<√729 9. 26<√717<27 9. 26 and 27
10. √947 10. √900<√947<√961 10. 30<√947<31 10. 30 and 31
Prepared by:
Teacher III

MATHEMATICS 7
Name: ______________________________________ Score: __________
Perfect Combination!
Combining two closest perfect squares between the square root of an irrational
number is the key in determining two consecutive integers. These two perfect squares are
rational numbers.
You will learn in this learning activity sheet the concepts of square roots of rational
and irrational numbers.
Learning Competency.
Code: M7NS-Ig-2
Activity 1. True or False. Write true if the statement is correct and false if it’s not. Write
your answer on the space provided before the number.
_____1. Rational numbers are numbers that can be expressed as a ratio of two numbers,
where a non zero for denominator.
_____2. The product of multiplying a number to itself is a perfect square.
_____3. The principal root of √784 is –28.
_____4. 22 and 23 are two consecutive integers of √508.
_____5. If 17 is the first consecutive integer, then the second integer of √275 is 18.
Activity 2. Multiple Choice. Write the letter of your choice on the space provided before
the number.
_____1. What is the √441?
A. ±20 C. ±22
B. ±21 D. ±23
_____2. Which of the following is an example of rational number?
A. non-terminating decimal C. pi (Π)
B. non –repeating decimal D. principal root
____3. Between what two consecutive integers does √128 lie?
A. 10 and 11 C. 12 and 13
and

B. 11 and 12 D. 13 and 14
_____4. What is the sum of the principal roots of √324 and √626?
A. 22 C. 44
B. 34 D. 52
_____5. Which of the following is correct?
I. √81 II. √144 III. √225
A. I < II C. II > III
B. III < I D. I > III
_____6. What are the two consecutive integers of this notation: √4<√6<√9?
A. 2 and 3 C. 4 and 9
B. 4 and 6 D. 6 and 9
_____7. If x is the first consecutive number, then which of the following illustrates the
second number?
A. x – 1 C. x + 1
B. x + 2 D. x – 2
_____8. Between what two consecutive integers does √1198 lie?
A. 31 and 32 C. 33 and 34
B. 32 and 33 D. 34 and 35
_____9. Does the product of the root of √81 and √144 a perfect square?
A. Yes C. Cannot be determined
B. No D. None of the above
_____10. Which of the following is correct notation between two consecutive integers of
the square root of irrational number?
A. √121<√132<√144 C. √169<√157<√196
B. √256<√290<√324 D. √49<√71<√64
Reflection
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
References
Answer key

Activity 1
1. True
2. True
3. False
4. True
5. False
Activity 2
6. B
7. D
8. B
9. C
10. A
11. A
12. C
13. D
14. C
15. A
Prepared by:
Teacher III

MATHEMATICS 7
Section: _________________________________________ Date: ____________
Estimates the Square Root of a Whole Number to the Nearest Hundredth
In Mathematics, a square root of a number is a value that, when multiplied by itself,
gives the number. Example: 4 × 4 = 16, so a square root of 16 is 4. Exponent can be used to
show that the number has been multiplied by itself one or more times. A perfect square is
the square of a whole number. The number 9 is a perfect square because 9= 32
. The number 7
is not a perfect square because there is no whole number that can be squared to get 7.
However, to estimate square root, numbers to be illustrated must not be perfect square.
In this module, learners will be learning how to estimate the square root of a whole
number to the nearest hundredth. It has an important concept of standard deviation that is
used in probability theory and statistics.
As part of the learning activity the learners will be able to accomplish exercises to
practice skills in solving square root. It is also strengthen and stimulate the learners creative
thinking skills to be ready for the activity. Having this kind of activity will help the learners
solve the drill at ease.
To give you an idea on to how estimate the square root of a whole number to the
nearest hundredth, divide and average method will be used to illustrate.

Illustration 1. How to get Non- Perfect Square Root
Approximating Square Roots

Illustration 1.1 How to get square root?
Illustration 2
Approximate √112 to the nearest hundredths.
Step 1: Find the value of the whole number.
100 < 112 < 121 Find the perfect squares nearest to 112.
√100 < √112 < √121 Find the square roots of the perfect squares.
10 < √112 < 11 The number will be between 10 and 11.
The whole number part of the answer is 10.
Step 2: Find the value of the decimal.
112 – 100 = 12 Find the difference between the given number,
112, and the lower perfect square.
121 – 100 = 21 Find the difference between the greater perfect
square and the lower perfect square.
𝟏𝟐
𝟐𝟏
Write the difference as a ratio.
12 ÷ 21 ≈ 0.571 Divide to find the approximate decimal value.
The decimal part of the answer is approximately 0.571.

Step 3: Find the approximate value.
10 + 0.571 = 10.571 Combine the whole number and decimal.
10.571 ≈ 10.57 Round to the nearest hundredth.
The approximate value of √112 to the nearest hundredth is 10.57.
The learner estimates the square root of a whole number to the nearest hundredth
(M7NS-lg-3)
EXERCISE 1: UNCOVER THE SQUARE ROOT
Directions: Estimate the square root to the nearest hundredths. Use the number line illustrated
below. Solve the mark number.
1.
2.
3.
4.
5.
EXERCISE 2: NUMBERED LETTER EXERCISE
Direction: Step 1. Unlock the numbers using the Alphabets.
Step 2. Write your answer from the box provided.
Step 3. Add all the number to get the exact whole number.
Step 4. Solve the added number by estimating the square root to the
nearest hundredths.

A R T Q B U P C S V O D N W M E L X F K Y G Z H I J
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

EXERCISE 3: COMPLETING THE BOX EXERCISE
1. .
2.

3.
4.

Processing Activity
Answer the following question:
1. How do you find the activity?
_____________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________.
2. How to estimate the square root of non perfect square?
_____________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________.
Reflection:
Complete the statement:
I have learned that
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
_________________________________________________.
References:
Pictures and Illustration by Cristobal A. Felipe
http://images.pcmac.org/SiSFiles/Schools/GA/MaconCounty/MaconMiddle/Uploads/Docum
entsSubCategories/Documents/Estimating%20Square%20Roots_1.pdf

Answer Key:
EXERCISE 1. UNCOVER THE SQUARE ROOT
1 2.40
2 3.43
3 3.86
4 3.14
5 4.22
EXERCISE 2. NUMBERED LETTER EXERCISE
EXERCISE 3: COMPLETING THE BOX EXERCISE
1. 9.11
2. 6.86
3. 12.04
4. 8.49
Prepared by:
CRISTOBAL A. FELIPE
Teacher

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