Essential Math Competencies for Learning

Most Essential Learning Competencies
Department of Education
SDO Pampanga

FOCUS
SDO Pampanga
 Discuss the rationale behind the streamlining of
competencies and how unpacking/integrating of
competencies was done
 Clarify gray areas or issues to deepen teachers’
understanding, skills and confidence in the
implementation of the learning delivery

SDO Pampanga
COVID19 pandemic
continues to impact
various governments
and economies
around the world
ensuring the welfare
of more than 27
million learners
‘Education cannot
wait. If learning
stops, we will lose
human capital.’
(UNESCO 2017)
DepEd’s Sulong
Edukalidad
Framework
Most Essential
Learning
Competencies
(MELCs)
ENDURANCE
as primary
determining factor

Twin Goals
Critical Thinking
Problem Solving
MATH K to 10 Curriculum Framework
Professionalism Integrity Excellence Service

Twin Goals
Critical Thinking
Problem Solving
Content Domains
Numbers and Number
Sense
Geometry
Patterns and Algebra
Measurement
Statistics and Probability

Skills and
Processes
knowing and
understanding
Estimating
computing and solving
visualizing and modelling
representing and
communicating
Conjecturing
Reasoning
proving and decision-
making
applying and connecting

Values and Attitudes
Accuracy
Creativity
Objectivity
Perseverance
productivity
Appropriate Tools
Manipulative objects
Measuring Devices
Calculators
Computers
Smart phones and tablets

SDO Pampanga
The value of
Mathematics as a
learning area should
not be confined in the
corners of a classroom
or any learning space.
Its application to real-
life world problems
should be dealt with
depth and breadth in
order to create
meaning.

SDO Pampanga
Teachers, as
instructional
leaders, should be
deeply informed
on how to identify
the Most Essential
Learning
Competencies
(MELCs)

From LCs to MELCs
Essential
Learning
Competencies
Most Essential
Learning
Competencies

Mapping of Essential and
Desirable Competencies
Identifying the Prerequisite
Knowledge and Skills within the
learning area
Analysis of interconnectedness of
prerequisite knowledge and skills
among learning competencies
across learning areas
From LCs to MELCs

• What the students
need, considered
indispensable to
building skills, to
equip learners for
the next grade
level, and for life
long learning
Essential
LCs
• What may enhance
education but may not
be necessary in
building foundational
skills
Desirable
LCs
From LCs to MELCs

If it remains with learners long after a test or
unit of study is completed
 If it is useful beyond a single test or unit of
study, e.g.
comprehension,
research skills, reading
writing, map reading, and
hypothesis testing, which are essential in many
professions and in everyday life (Reeves, 2002;
Many & Horrell, 2014).
Identifying the MELCs

From LCs to MELCs
• Satisfies the ENDURANCE criterion
Contributes to lifelong learning and a
pre-requisite skill to the next grade
level
Retained
• two or more learning competencies
(LC) that have the same objective or
learning intention are combined into
one comprehensive learning
competency
Merged
• To make the statement of the LC
more concise
Rephrased
• LC that is too specific; recurring;
subsumed in another LC
Dropped

From LCs to MELCs
Curriculum Review of Grade 2, 2nd Quarter: NUMBERS AND
NUMBER SENSE
24. visualizes, represents, and subtracts 2- to 3-digit
numbers with minuends up to 999 without and with
regrouping.
Essential
25. subtracts mentally 1-digit numbers from 1- to 3-digit
numbers without regrouping using appropriate strategies.
Essential
26. subtracts mentally 3-digit numbers by tens and by
hundreds without regrouping using appropriate strategies.
Essential
27. solves routine and non-routine problems involving
subtraction of whole numbers including money with
minuends up to 1000 using appropriate problem solving
strategies and tools.
Essential

From LCs to MELCs
Identification of MELCs for Grade 2, 2nd Quarter: NUMBERS AND NUMBERSENSE
Essential Learning Competency Action Taken/MELCs Reason
24. visualizes, represents, and subtracts
2- to 3-digit numbers with minuends up
to 999 without and with regrouping.
RETAINED Satisfies
ENDURANCE
criterion
25. subtracts mentally 1-digit numbers
from 1- to 3-digit numbers without
regrouping using appropriate strategies.
MERGED, REPHRASED
subtracts mentally the following
numbers without regrouping using
appropriate strategies:
a. 1-digit numbers from 1- to 3-
digit numbers
b.3-digit numbers by tens and by
hundreds
LCs are related,
and may be
harmonized/
unified for a
more focused
development of
the concept/
skill
26. subtracts mentally 3-digit numbers
by tens and by hundreds without
regrouping using appropriate strategies.
27. solves routine and non-routine
problems involving subtraction of
whole numbers including money with
minuends up to 1000 using appropriate
problem solving strategies and tools.
RETAINED Satisfies
ENDURANCE
criterion

From LCs to MELCs
Curriculum Review of Grade 2, 2nd Quarter: NUMBERS AND NUMBERSENSE
28. creates problems involving subtraction of whole numbers including money. Desirable
29. performs orders of operations involving addition and subtractions of small
numbers.
Essential
30. solves multi-step routine and non-routine problems involving addition and
subtraction of 2- to 3-digit numbers including money using appropriate problem
solving strategies and tools.
Essential
31. creates word problems involving addition and subtraction of whole numbers
including money.
Desirable
Identification of MELCs for Grade 2, 2nd Quarter: NUMBERS AND NUMBERSENSE
Essential Learning Competency Action Taken/MeLCs Reason
29. performs orders of operations involving
addition and subtractions of small numbers.
RETAINED Satisfies
ENDURANCE
criterion
30. solves multi-step routine and non-routine
problems involving addition and subtraction of 2-
to 3-digit numbers including money using
appropriate problem solving strategies and tools.
RETAINED

From LCs to MELCs
Curriculum Review of Grade 6, 4th Quarter: MEASUREMENT
70. determines the relationship of the volume between
1. a rectangular prism and a pyramid;
2. a cylinder and a cone; and
70. 3 a cylinder and sphere.
Essential
71. derives the formula for finding the volume of cylinders, pyramids, cones, and
spheres.
Essential
72. finds the volume of cylinders, pyramids, cones, and spheres. Essential
73. solves routine and non-routine problems involving volumes of solids. Essential
74. creates problems involving surface area and volume of solid/space figures,
with reasonable answers
Desirable
75. reads and interprets electric and water meter readings. Essential
76. solves routine and non-routine problems involving electric and water
consumption.
Essential
77. creates problems involving electric and water consumption, with reasonable
answers.
Desirable

From LCs to MELCs
Identification of MELCs for Grade 6, 4th Quarter: MEASUREMENT
Essential Learning Competency Action Taken/
MELCs
Reason
70. determines the relationship of the volume
between
1. a rectangular prism and a pyramid;
2. a cylinder and a cone; and
70. 3 a cylinder and sphere.
RETAINED Satisfy ENDURANCE
criterion
71. derives the formula for finding the volume of
cylinders, pyramids, cones, and spheres.
DROPPED LC is more of a
teacher’s action
72. finds the volume of cylinders, pyramids, cones, and
spheres.
RETAINED Satisfy ENDURANCE
criterion
volumes of solids.
RETAINED SatisfyENDURANCE
criterion
75. reads and interprets electric and water meter
readings.
criterion
electric and water consumption.
criterion

Identification of MELCs (other samples)
Grade 1, First Quarter Action Taken/MELCs Reason
NUMBERS AND NUMBER SENSE
1. visualizes and represents numbers
from 0 to 100 using a variety of
materials
MERGED, REPHRASED
Visualizes, represents, and
counts numbers from 0 to
100 using a variety of
materials and methods
LCs 2 and 8 are
subsumed in LC 1; and
may be sub-tasked
2. counts the number of objects in a
given set by ones and tens.
4. composes and decomposes a given
number. e.g. 5 is 5 and 0, 4 and 1, 3
and 2, 2 and 3, 1 and 4, 0 and 5.
REMOVED Competency repeated in
Patterns and Algebra,
Grade 1, Third Quarter
6. visualizes, represents, and
compares two sets using the
expressions “less than,” “more than,”
and “as many as.”
MERGED, REPHRASED
compares two sets using
the expressions “less
than,” “more than,” and
“as many as” and orders
sets from least to greatest
and vice versa.
LCs are related, and may
be harmonized for a
more focused
development of the skill
7. visualizes, represents, and orders
sets from least to greatest and vice
versa

How to Use the MELCs in Math
Appraise the content standards in each quarter of
your grade level.
1
• The Content Standards guides you in tracking the learning content being focused
per quarter.
Plan the instructional activities based on
performance standard
2
• Design instructional activities/tasks suited for the type of learning delivery
modality being used..
• Contextualize the instructional task whenever necessary.
Examine the identified MELCs for each quarter.
Remember, time allotment is flexible.
3
• The MELC is the learning goal for the quarter. Sub-task if the MELC is of a big
chunk of a learning goal
• Development of Math skill is prioritized over competence on content-knowledge
Design activities/assessment tasks dealing with
problem-solving and analysis
4

Comparison of the number of LCs in original CG, ELCs and MELCs
Grade
Level
Grade 1
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Grade 9
Grade 10
Total
Current ELC MELCs
CG
66 62 38
93 74 54
80 73 57
86 74 67
107 88 74
89 71 62
64 63 53
57 57 52
48 48 46
51 47 40
741 657 543
0
20
40
60
80
100
120
Orig CG ELC MELCs

Comparison of the retained, dropped and merged LCs
from the original CG
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
Grade 1 Grade 2 Grade 10
44% 42%
55%
72%
67%
63%
72%
84%
96%
69%
41%
37%
35%
12%
7%
12%
20%
14%
18%
15%
22%
10%
16%
25% 25%
5%
2% 4%
12%
Grade 3 Grade 4
Retained
Grade 5 Grade 6 Grade 7 Grade 8 Grade 9
Merged, Rephrased Dropped

MATH Grade 1, Quarter 1
Learning Competencies Comments/Recommendation Identified MELCs
Visualizes and represents numbers from 0 to
100 using a
variety of materials
Clustered as counting
the
number of objects
subsumed or is part of
visualizing and
representing numbers
Visualizes and represents numbers from 0 to
100 using a
variety of materials and methods
Counts the number of objects in a given set by
ones and tens
Visualizes and count by 2s, 5s, and 10s through
100
Composes and decomposes a given number,
e.g. 5 is 5 and0, 4 and 1, 3 and 2, 2 and 3, 1
and 4 and 0 and 5
Omitted as this will is
also discussed in
Quarter 3
Visualizes, represents and compares two sets
using
expressions “less than,” “more than,” and “as
many as”
Clustered and rephrased Compares two sets using the expressions “less
than,” “more
than,” and “as many as” and orders sets from
least to greatest and vice versa
Visualizes, represents and orders sets from least
to greatest
and vice versa
Visualizes, represents and compares numbers
up to 100 using
relation symbols
Clustered and rephrased Compares numbers up to 100 using relations
symbols and
ordering them in increasing and decreasing
order
Visualizes, represents and orders numbers up
to 100 in
increasing or decreasing order
Identifies the 1st, 2nd, 3rd up to 10th object in a
given set from
a given point of reference
Clustered and rephrased Identifies, reads and writes ordinal numbers:
1st, 2nd, 3rd, up
to 10th object in a given set from a given point
of reference
Reads and writes ordinal numbers: 1st, 2nd, 3rd
up to 10th

Orientation on the MELCs for the MATHEMATICSSupervisors

Orientation on theMELCs andLearning Delivery Modalities for the CLMD and CID CHIEFS

Orientation on theMELCs for the MATHEMATICSSupervisors

Comparison of the number of LCs in original CG and MELCs
Subject Current
CG
ELC MELCs
Gen.
Math 63 58 54
Stat. and
Proba. 71 65 37
Business
Math 45 35
Pre
Calculus 49 30
Basic
Calculus 39 33
80
70
60
50
40
30
20
10
0
Gen.
Math
Stat.and
Proba.
Business
Math
Pre
Calculus
Basic
Calculus
Current CG ELCs MELCs

Comparison of the retained, dropped and merged LCs
from the original CG
20%
10%
0%
30%
40%
50%
60%
70%
80%
90%
100%
General
Mathematics
Business
Math
Pre Calculus Basic Calculus
84%
73%
60% 57%
69%
24%
10%
18%
13%
3% 27%
16%
33%
13%
Statistics and
Probability
Retained Merged, Rephrased Dropped

General Mathematics, Quarter 1

General Mathematics, 1st Quarter
General Mathematics Action / MELCs Reason
11. graphs rational functions. DROPPED Graphing these
functions may
be augmented
by various
software/
applications
17. graphs inverse functions.
25. graphs exponential functions.
34. graphs logarithmic functions.
29. illustrates the laws of logarithms.
More of a
teacher’s action;
content-focused

General Mathematics, Quarter 2

General Mathematics, 2nd Quarter
49. interprets the theory of
efficient markets.
DROPPED Specialized
topic
53. illustrates a proposition.
MERGED/REPHRASED:
illustrates and
symbolizes
propositions.
Related LCs,
harmonized
to focus on
the skill
54. symbolizes propositions.

General Mathematics, 2nd Quarter
62. illustrates the different
methods of proof (direct and
indirect) and disproof
(indirect and by
counterexample).
DROPPED Specialized topics
63. justifies mathematical and
real-life statements using the
different methods of proof
and disproof.

Statistics and Probability, Quarter 3

Statistics and Probability, 3rd Quarter
Statistics and Probability Action / MELCs Reason
5. constructs the probability mass function DROPPED the
content-
knowledge
is not
widely-
used in
conducting
student
researches
in Senior
High
School
of a discrete random variable and its
corresponding histogram.
12. constructs a normal curve.
24. illustrates point and interval
estimations.
25. distinguishes between point and
interval estimation.
26. identifies point estimator for the
population mean.
27. computes for the point estimate of the
population mean.

28. identifies the appropriate form of DROPPED the
content-
knowledge
is not
widely-
used in
conducting
student
researches
in Senior
High
School
the confidence interval estimator for
the population mean when: (a) the
population variance is known, (b) the
population variance is unknown, and (c)
the Central Limit Theorem is to be used.
30. constructs a t-distribution.
31. identifies regions under the t-
distribution corresponding to different
t-values.

33. computes for the confidence DROPPED the
content-
knowledge
is not
widely-
used in
conducting
student
researches
in Senior
High
School
interval estimate based on the
appropriate form of the estimator for
the population mean.
34. solves problems involving
confidence interval estimation of the
population mean.
35. draws conclusion about the
population mean based on its
confidence interval estimate.

37. computes for the point DROPPED the content-
knowledge is not
widely-used in
conducting
student
researches in
Senior High
School
estimate of the population
proportion.
38. identifies the appropriate
form of the confidence interval
estimator for the population
proportion based on the Central
Limit Theorem.
39. computes for the confidence
interval estimate of the
population proportion.

40. solves problems involving DROPPED the content-
knowledge is not
widely-used in
conducting
student
researches in
Senior High
School
confidence interval estimation of
the population proportion.
41. draws conclusion about the
population proportion based on
its confidence interval estimate

Statistics and Probability, Quarter 4

Statistics and Probability, 4th Quarter
Statistics and
Probability
Action /
MELCs
Reason
47. calculates the
probabilities of
committing a Type I
and Type II error.
DROPPED this may just be
part of the
discussion on types
of errors in
hypothesis testing
68. draws the best-fit
line on a scatter plot.
this may be
obtained from
Statistics software

Business Math, Quarter 1

Business Math, 1st Quarter
Business Math Action / MELCs Reason
1. Perform DROPPED These competencies have been
acquired from elementary and
applied frequently in JHS.
Performing this operation may also
be done using computer applications
and calculators.
fundamental
operations on
fractions and
decimals
2. Express fractions MERGED/REPHRASED: Learning competencies having the
to decimals and Express: same mathematical focus or
percent forms and a. fractions to decimal foundational skills are merged/
vice versa and percent forms clustered and rephrased.
3. Illustrate how b. decimals to
decimals and fractions and percent
fractions can be forms
written in terms of c. percent to fractions
percent and decimal forms

1. Compare and differentiate ratio
and rate
DROPPED Content-focused
2. Write proportions illustrating
real-life situations
MERGED/REPHRASED:
Identify the different
kinds of proportions
and write examples of
real-life situations for
each
Learning competencies
having the same
mathematical focus or
foundational skills are
merged/ clustered and
rephrased.
3. Identify the different kinds of
proportion and give examples for
each

2. Illustrate how Mark-on,
Mark-down, and Mark-up
are obtained
REPHRASED:
obtain Mark-on, Mark-
down, and Mark-up
given price of a product
“illustrating”
how a value
can be
obtained is
more of the
role of
teacher in
these LCs.
These are
rephrased to
state that the
students has
to compute
them.
5. Illustrate how to compute
single trade discounts and
discount series
REPHRASED: Compute
single trade discounts
and discount series
10. Illustrate how interest is
computed specifically as
applied to mortgage,
amortization, and on
services/utilities and on
deposits and loans
REPHRASED: Compute
interest specifically as
applied to mortgage,
amortization, and on
services/utilities and on
deposits and loans

Business Math, Quarter 2

Business Math, 2nd Quarter
13. Illustrate how
to obtain down
payment, gross
balance, and
current increased
balance
REPHRASED:
Compute down
payment, gross
balance and current
increased balance
“illustrating” how a value can
be obtained is more of the
role of teacher in these LCs.
These are rephrased to state
that the students has to
compute them.
2. Compute gross
and net earnings
RETAINED
3. Differentiate
gross from net
earnings
DROPPED Subsumed in LC 2

1. Show samples of business
data
DROPPED Subsumed in LC 2
2. Compare the forms (textual,
tabular, and graphical) of data
RETAINED
3. Identify the essential parts of
a table
DROPPED Subsumed in LC
9/10
4. Draw the table to present the
data
DROPPED Subsumed in LC
9/10
9. Draw the graph/table to
present the data
RETAINED
10. Analyze and interpret the
data presented in a graph/table
RETAINED

6. Describe the MERGED/REPHRASED: Learning competencies
different kinds of Describe the different having the same
graphs for data kinds of graphs and its mathematical focus or
presentation essential parts for data foundational skills are
7. Describe the presentation. merged/ clustered and
essential parts of rephrased.
a graph

Pre-Calculus, 1st Quarter
4. Graph a circle in a DROPPED Graphs may be
rectangular coordinate generated using ICT
system tools. Far more
7. Graph a parabola in a important than
rectangular coordinate graphing is the
system understanding and
10. Graph an ellipse in a interpretation of
rectangular coordinate the graph.
system
13. Graph a circle in a
hyperbola coordinate
system

Pre-Calculus, 1st Quarter

Pre-Calculus, 2nd Quarter

Basic Calculus, 3rd Quarter

Basic Calculus, 4th Quarter

Statistics and Probability, 4th Quarter
Statistics and
Probability
Action
/
MELCs
Reason
47. calculates the
probabilities of
committing a Type I
and Type II error.
DROPPED this may just be
part of the
discussion on types
of errors in
hypothesis testing
68. draws the best-fit
line on a scatter plot.
this may be
obtained from
Statistics software

“Whenever you are asked if you can do
a job, tell 'em, 'Certainly I can!' Then get
busy and find out how to do it.”
― Theodore Roosevelt
SDO Pampanga

Thank You!
SDO Pampanga

Essential Math Competencies for Learning

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