2. Session 1 Session 2 Session 3 Session 4
I. OBJECTIVES
1. Content
Standards
The learner demonstrates understanding of key concepts of sets and the real number system.
2. Performance
Standards
The learner is able to intellectually formulate challenging situations involving sets and real numbers, and solve
these in a variety of strategies.
3. Learning
Competencies /
Objectives The learner writes numbers
in scientific notation and vice
versa. (M7NS-Ii-1)
a. Write numbers in scientific
notation
b. Express scientific notation
in decimal form
c. Appreciate the importance
of scientific notation in
real-life situation
The learner writes numbers
in scientific notation and
vice versa. (M7NS-Ii-1)
a. Express scientific
notation in decimal form
and vice versa
b. Apply scientific notation in
real-life situation
c. Appreciate the
importance of scientific
notation in daily living
The learner represents real-
life situations which involve
real numbers. (M7AL-IIi-1)
a.Identify the subsets of real
numbers.
b.Describe and represent
real-life situations which
involve real numbers.
c. Appreciate the concept of
transformation in real-life
situation
The learner represents real-
life situations which involve
real numbers.( M7AL-IIi-1)
a.Describe real-life
situations which involve
real numbers.
b.Use real numbers to
represent real-life
situations.
c. Appreciate the concept of
transformation in real-life
situation
II. CONTENT
Expressing Numbers in
Scientific Notation and vice
versa
Expressing Numbers in
Scientific Notation and vice
versa
Real-Life Situations Which
Involve Real Numbers
Real-Life Situations Which
Involve Real Numbers
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide pages
2. Learner’s Materials
pages
pp 441-450 pp 441-450 pp 441-450 pp 441-450
3. 3. Textbook pages E-Math 7 worktext
Matatag Curriculum
Orlan A. Orance
Marilyn O. Mendoza
Aarhus M. Dela Cruz
E-Math 7 worktext
Matatag Curriculum
Orlan A. Orance
Marilyn O. Mendoza
Aarhus M. Dela Cruz
E-Math 7 worktext
Matatag Curriculum
Orlan A. Orance
Marilyn O. Mendoza
Aarhus M. Dela Cruz
E-Math 7 worktext
Matatag Curriculum
Orlan A. Orance
Marilyn O. Mendoza
Aarhus M. Dela Cruz
4. Additional Materials from
Learning Resource (LR)
portal
http://mathtec.weebly.com/
uploads/
2/9/0/5/29050183/2524255_
orig.jpg
https://
pghrheumatology.files.word
press.com/2014/08/
dscf2255_v1.jpg
https://
image.slidessharecdn.com/
mathgrade7learnersmodule-
151029032600-Iva1-
app6892/95/math-grade-7-
learners-module-78-
638.jpg?1446089429
https://
image.slidessharecdn.com/
mathgrade7learnersmodule-
151029032600-Iva1-
app6892/95/math-grade-7-
learners-module-78-
638.jpg?1446089429
B. Other Learning
Resources / Materials
Grade 7 LCTG by DepEd
Cavite Mathematics, 2016
Grade 7 LCTG by DepEd
Cavite Mathematics, 2016
Grade 7 LCTG by DepEd
Cavite Mathematics, 2016
Grade 7 LCTG by DepEd
Cavite Mathematics, 2016
IV. PROCEDURES
A. Reviewing previous
lesson or presenting
the new lesson
Using a scientific calculator,
key in the following.
a. Two hundred eighty-five
billion
b. Eighty-seven hundred
thousandth
c. One thousand, five billionth
d. Five trillion, six hundred
nine billion
e. Three ten millionth
Write FACT if the
corresponding number is
the correct scientific
notation of the given
standard form,otherwise
write BLUFF.
UNSCRAMBLE THE
LETTERS
1. ROTAILAN
2. HOWEL
3. TARANUL
4. TARALIRONI
5. GREINETS
Determine what set of
numbers will represent the
following situations:
1. Finding out how many
cows there are in a barn
2. Corresponds to no more
apples inside the basket
3. Describing the temperature
4. STANDARD SCIENTIFIC
FORM NOTATION
1. 23,000 2.3 x 104
2. 0.340 3.4 x 10-3
3. 61,000, 000 6.1 x 106
4. 8.40 8.40 x 100
5. 7,260,000 7.26 x 109
in the North Pole
4. Representing the amount
of money each member
gets when P200 prize is
divided among 3 members
5. Finding the ratio of the
circumference to the
diameter of a circle,
denoted by “π” (read as
“pi”)
B. Establishing a
purpose for the
lesson
Using a scientific calculator,
key in the numbers in the
preliminary activity and then
press the equal sign. Are
these reflected on the screen?
a. Two hundred eighty-five
billion = 2.85 x 1011
b. Eighty-seven hundred
thousandth = 8.7 x 10-4
c. One thousand, five billionth
= 1.005 x 10-6
d. Five trillion, six hundred
nine billion = 5.609 x 1012
e. Three ten millionth
= 3 x 10-7
Express each in decimal
form.
1. The mass of Jupiter is
approximately 1.90 x 1027
kg.
2. The radius of Saturn is
approximately 6.04 x 107
metres.
3. The area of the Atlantic
Ocean is 8.17x107
sq.metres.
4. The mass of Earth is
5.976 x 1024
kg.
5. The area of the Asian
continent is approximately
3 x 108
metres per
second.
Determine the subset of real
numbers to which each
number belongs. Use a
check mark (/) to answer.
Number
Whole
Number
Integer
Rational
Irrational
1. -86
2. 34.74
3.
4.
5. 11
6.-0.125
7. 0
8. 250
9. 1.5
10. -6
The bird Maya live in
families. The family
members collect rice grains
and store them in the trunks
of trees. The table below
shows information about the
number of rice grains
collected and eaten by a
family of Maya on 3 days.
Rice Grains Collected and Eaten
Day Number
Collected
Number
Eaten
Monday 23 8
Tuesday 29 10
Wednesd
ay
42 9
5. Which expression best
describe the information in
the table if the family had
stored 428 grains of rice
before Monday?
a. 428 - 23 + 8 - 29 + 10 -
42 + 9
b. 428 + 23 - 8 + 29 - 10 +
42 - 9
c. 23 - 8 + 29 - 10 + 42 - 9 -
428
d. 23 + 8 - 29 + 10 - 42 + 9
+ 428
C. Presenting examples/
instances of the lesson
Last graduation day,
Danielle’s father gave her a
graduation gift. It was a 64 GB
flash drive. Her brother also
received his graduation gift, a
32 GB flash drive? About how
many bytes is each flash drive
equivalent to? Can these
values be written in a shorter
way? How?
1 gigabyte (1 GB) =
1,073,741,824 bytes or about
1,100,000,000 bytes, so 64
GB is about 65,000,000,000
bytes and 32 GB is about
35,000,000,000.
To write these values in a
1. How about the diameter of
a red blood cell?
It is about 0.000007 mm.
How can it be written in
scientific notation?
0.000007 = 7 x 10-6
2. The sun’s core
temperature reaches close to
2.7 x 107
degrees Fahrenheit.
Represent this temperature
in standard notation.
WHERE DO I BELONG?
Group the following
numbers based on their
classification.
П 1 -1 -2
2 0
3 -3 4
-3 3.79
The famous theorist of the
Pythagorean Theorem,
Pythagoras, once said that,
“All things are number.” Truly,
numbers are everywhere! But
do we really know our
numbers? Sometimes a
person exists in our midst but
we do not even bother to ask
the name or identity of that
person. It is the same with
numbers. Yes, we are
surrounded by these
boundless figures but do we
bother to know what they
really are?
Divide the class into 5 groups
and give each one of the
Real Numbers
Irrational
,
Rational
3.79
Integers
-1
-2
-3
-4 -4
Whole
0
Natural
1, 2, 3, 4
6. shorter way, use scientific
notation.
It is denoted by
m x 10n
, where 1 ≤ m ≤ 10 and
n is an integer.
1,100,000,000 = 1.1 x 109
,
65,000,000,000 = 6.5 x 1010
,
and
35,000,000,000 = 3.5 x 1010
2.7 x 107
= 27, 000, 000 0
F
following questions:
Give a real-life example of
the following:
Natural numbers
(example: counting the
number of homework
problems)
Whole numbers
(example: counting the
number of dates you will get
with a movie star – zero)
Integers
(example: temperature – can
be negative)
Rational numbers
(example: the cost of an item
at the store in dollars)
Absolute value
(example: the distance from
home to school)
D. Discussing new
concepts and
practicing new skills #1
A. Determine the coefficient or
significant in the following
numbers.
a. 38,000,000,000
b. 0.000000001
Doctors should be aware of
blood clotting performing
surgery. Blood clotting
involves a series of chemical
reactions that lead to the
formation of a mesh of fibers
that are too large for blood
Group the following
situations according to its
classification:
1. Monthly income of the
Family
2. Population size of GMA
Below are the ingredients for
chocolate oatmeal raisin
cookies. The recipe yields 32
cookies. Make a list of
ingredients for a batch of 2
dozen cookies.
7. c. 2,016,000,000,000
d. 0.000000001007
e. 0.000000000091306
B. Determine the value of n in
the following scientific
notations.
a. 5.3 x 104
b.1.968 x 10-5
c. 2.071 x 100
d. 1.000001 x 10-3
e. 8 x 102
cells to pass through.
A micron is a unit of
measurement 10-6
m long.
Extremely small objects,
such as the blood cells, are
measured in microns.
Give each measurement 10-6
m long. Explain how you got
your answers.
3. Lot area of GMA Portal
Mall
4. Number of Barangay
Officials of Cavite
5. Parts of Buko Pie
Example:
A typical red blood cell is
0.0000072m wide.
A white cell is 0.000007m
to 0.000012m wide.
A platelet is about
0.000003m wide
1tsp baking soda
1 tsp salt
1cup unsalted butter
2 large eggs
1tsp vanilla extract
12 ounces semi-sweet
cup light-brown
sugar
cup granulated sugar
cups rolled oats
cups raisins
cups all-purpose
flour
Rational Irrational
8. E. Discussing new
concepts and
practicing new skills
#2
Think, Pair ,Share
a. Are you comfortable in
writing very large/small
numbers? Why or why not?
b. Which way do you prefer to
write the largest/smallest
numbers, in whole
number/decimal form or
scientific notation?
c. What is a more convenient
way of expressing very
large and very small
numbers?
d. How do you express very
large or very small numbers
in scientific notation?
a. How do we write a number
that is greater than 1 in
scientific notation?
b. How do we write a number
greater than 0 but less than
1 in scientific notation?
c. For what kinds of numbers
is scientific notation a
useful notation?
1. What are the subsets of
real numbers?
2. What is the difference
between an irrational
number and a rational
number?
3. Can you cite situations in
our daily life which
involves real Numbers?
a. Do you agree with
Pythagoras that all things
are numbers?
b. Can we represent real-life
situations which involve
real numbers?
c. Do we encounter situations
in our everyday life which
involves real numbers? If
yes, cite/ give examples.
F. Developing mastery
(Leads to Formative
Assessment 3)
A. Determine the coefficient or
significant in the following
numbers.
a. 678,000,000,000
b. 0.000005
c. 5,026,000,000,000
d. 0.000000203
e. 0.000000006013
B. Determine the value of n in
the following scientific
Express in standard form.
The distance, in Kilometres,
of the planets from the sun
are as follows:
Pluto 5.90 x 109
Venus 1.08 x 108
Neptune 4.50 x 109
Saturn 1.43 x 109
Mercury 5.79 x 107
Jupiter 7.78 x 108
Write 3 example and an
applicable situation for each
subset of the set of real
numbers
1. Rational Numbers
2. Irrational Numbers
3. Integers
4. Whole Numbers
5. Irrational Numbers
Write 1 example and an
applicable situation for each
subset of the set of real
numbers. Use the table
below.
Subset of Real
Numbers
Applicable
Situation
9. notations.
a. 6.3 x 107
b. 4.921 x 10-4
c. 1.025 x 103
d. 5.0324 x 108
e. 9.421 x 10-5
Irrational
Numbers
Rational
Numbers
Integers
Natural Numbers
Whole Numbers
G. Finding practical
applications of
concepts and skills in
daily living
Complete the table below
with numbers and their
scientific notations.
Standard
form
Scientific
Notation
45, 000, 000
2. 0034 x 10-5
0.0000000108
8 x 104
3.0023 x 100
A. Express the following in
scientific notation
1. 3, 000, 000
2. 0.00056
3. 0.245
4. 256,000
5. 83, 000,000, 000
B. Write the following in
standard form
1. 9.3 x 106
2. 4.12 x 10-4
3. 2.5 x 107
4. 7.2 x 10 -8
5. 1.056 x 105
Use a real number to
represent each real life
situation. Number 1 is done
for you.
Situation Real
Number
1. A population
growth of
1279
2. An oil drilling
platform
extends 325
feet below
sea level.
3. Water boils at
1000
C
4. A child digs a
hole 3 feet
deep in beach
sand.
5. There is a
wind chill
factor of
minus 100
F.
6. A hiker
1279
Determine the subset of real
numbers to which each
number belongs. Use a
check mark (/) to answer.
10. climbs a
mountain that
is 2023 feet
high.
H. Making
generalizations and
abstractions about
the lesson
Procedure for Writing
Numbers in Scientific Notation
Step 1: Determine the
coefficient or significant by
moving the decimal point to
the right of the first non zero
digit. It is understood that the
decimal point of any natural
number is located after the
last digit.
Step 2: Count the number of
places the decimal is moved.
This corresponds to the
exponent of 10 to be used as
a factor. A movement to the
left corresponds to a positive
integral power of 10. A
movement to the right
corresponds to a negative
power of 10.
Step 3: Multiply the number
obtained in step 1 and the
power of 10 obtained in step
2.
Procedure in Writing Numbers
in Scientific Notation to
Decimal Form
Procedure for Writing
Numbers in Scientific
Notation
Step 1: Determine the
coefficient or significant by
moving the decimal point to
the right of the first non zero
digit. It is understood that the
decimal point of any natural
number is located after the
last digit.
Step 2: Count the number of
places the decimal is moved.
This corresponds to the
exponent of 10 to be used as
a factor. A movement to the
left corresponds to a positive
integral power of 10. A
movement to the right
corresponds to a negative
power or 10.
Step 3: Multiply the number
obtained in step 1 and the
power of 10 obtained in step
2.
Procedure in Writing
Numbers in Scientific
Sets and Subsets of Real
Numbers
Real Numbers - is any
element of the set R, which
is the union of the set of a
rational numbers and the
set of irrational numbers.
Rational Numbers - is a
number determined by the
ratio of some integer to
some nonzero natural
number.
Irrational Numbers - is a real
number that cannot be
written as a simple fraction.
Irrational means not
Rational.
Integers - are positive and
negative whole numbers.
Whole Numbers - is a
number consists of the
natural numbers and 0.
Natural Numbers - these
numbers are used for
counting.
Sets and Subsets of Real
Numbers
Real Numbers - is any
element of the set R, which
is the union of the set of a
rational numbers and the
set of irrational numbers.
Rational Numbers - is a
number determined by the
ratio of some integer to
some nonzero natural
number.
Irrational Numbers - is a real
number that cannot be
written as a simple fraction.
Irrational means not
Rational.
Integers - are positive and
negative whole numbers.
Whole Numbers - is a
number consists of the
natural numbers and 0.
Natural Numbers - these
numbers are used for
counting.
11. Step 1: If the exponent of 10 is
positive n, move the decimal
point n places to the right.
Step 2: If the exponent of 10 is
0, do not move the decimal
point.
Step 3: If the exponent of 10 is
negative n, move the decimal
point n places to the left.
Notation to Decimal Form
Step 1: If the exponent of 10
is positive n, move the
decimal point n places to the
right.
Step 2: If the exponent of 10
is 0, do not move the decimal
point.
Step 3: If the exponent of 10
is negative n, move the
decimal point n places to the
left.
I. Evaluating learning Choose the letter of the
correct answer.
1. 5.02 x 102
a. 5.02 c. 502
b. 50.2 d. 5, 020
2. 0.000000108
a. 1.08 x 106
c. 1.08 x 10-6
b. 1.08 x 107
d. 1.08 x 10-7
3. 2 981 000 000
a. 2.981 x 108
c. 2.981 x 109
b. 2.981 x 10-8
d. 2.981 x 10-9
4. 0.00000041230
a. 4.123 x 107
c. 4.123 x 107
Fill in the table by writing the
number in standard notation
or in scientific notation as
indicated.
Quantity
Standard
Notation
Scientific
Notation
1.
Diameter
of the
sun
1.39 x
109
m
2. Wave
length of
ultraviolet
light
1.36 x
10-6
cm
3.
Approxim
ate age
of the
4,00
0,00
0,
000
yr
Determine what set of
numbers will represent the
following situations:
1.Temperature below zero
2.Floors above ground level
3. Number of Siblings
4. Monthly allowance
5. Average height of GMATHS
students in cm.
Determine what set of
numbers will represent the
following situations:
1. Spending and earning
money.
2. The distance from
GMATHS to GMA
Market.
3. Rising and falling
temperatures
4. Ages of students.
5. Number of Family
members.
6. Stock market gains and
losses
7. General average of G7
12. b. 4.123 x 10-7
d. 4.123 x 10-8
5. 6.007 x 10-5
a. 0.00006007
b. 0.0006007
c. 0.000006007
d. 0000006007
Earth
4.
Diameter
of the
Earth
12
700
000
000
m
5.
Frequenc
y of an
AM radio
wave
1.4 x
106
hertz
Students.
8. Vowels in English Alphabet
9. Number of Month starts
with letter X.
10. Gaining or losing yards in
a football game
J. Additional activities
for application or
remediation
Research about 5 smallest
and biggest things. Express
their sizes in scientific
notation.
Study
Problem Solving Involving
Real Numbers
a. What real-life situations
involve real numbers?
b. How do you represent
real-life situations which
involve real numbers?
Give 1 situation each for the
different subsets of real
numbers applied in real-life
situations. Then, give an
example from each subset.
List down the steps in
problem solving
V. REMARKS
VI. REFLECTION
1. No.of learners who
earned 80% on the
formative assessment
2. No.of learners who
require additional
activities for
remediation.
13. 3. Did the remedial
lessons work? No.of
learners who have
caught up with the
lesson.
4. No.of learners who
continue to require
remediation
5. Which of my teaching
strategies worked
well? Why did these
work?
6. What difficulties did I
encounter which my
principal or
supervisor can help
me solve?
7. What innovation or
localized materials
did I use/discover
which I wish to share
with other teachers?
