3. TABLE OF CONTENT
LEARNING
PRINCIPLES
AND THEORIES
Discovery and
Inquiry-Based
Learning
Reflective
Learning
Experiential and
Situated Learning
Cooperative
Learning
Constructivism
4. EXPERIENTIAL
AND SITUATED
LEARNING
·Experiential Learning as advocated by David Kolb
is learning that occurs by making sense of direct
everyday experiences.
·Experiential learning theory defines learning as
“the process whereby knowledge is created
through the transformation of experience”.
·Knowledge results from the combination of
grasping and transforming experience. (Kolb,1984,
p. 41)
·Situated learning, theorized by Lave and Wenger,
is learning in the same context on which concepts
and theories are applied.
5. Mixture of content and process
There must be a balance between the
experiential activities and the underlying
content or theory.
Absence of excessive judgment
The instructor must create a safe space for
students to work through their own process
of self-discovery.
Engagement in purposeful endeavors
In experiential learning, the learner is the
self-teacher, therefore there must be
“meaning for the student in the learning.”
The learning activities must be personally
relevant to the student.
Chapman et al. have provided a list of
characteristics that should be present in
order to define an activity or method as
experiential. These characteristics include:
6. Encouraging the big picture perspective
Experiential activities must allow the students to
make connections between the learning they are
doing and the world. Activities should build in
students the ability to see relationships in
complex systems and find a way to work within
them.
The role of reflection
Students should be able to reflect on their own
learning, bringing “the theory to life” and gaining
insight into themselves and their interactions with
the world.
Creating emotional investment
Students must be fully immersed in the
experience, not merely doing what they feel is
required of them. The “process needs to engage
the learner to a point where what is being learned
and experience strikes a critical, central chord
Chapman et al. have provided a list of
characteristics that should be present in
order to define an activity or method as
experiential. These characteristics
include:
7. The re-examination of values
By working within a space that has been made
safe for self-exploration, students can begin to
analyze and even alter their own values.
The presence of meaningful relationships
One part of getting students to see their learning
in the context of the whole world is to start by
showing the relationships between “learner to
self, learner to teacher, and learner to learning
environment.”
Chapman et al. have provided a list of
characteristics that should be present in
order to define an activity or method as
experiential. These characteristics
include:
8. THE EXPERIENTIAL LEARNING CYCLE
Kolb's experiential learning style theory is typically
represented by a four- stage learning cycle in which
the learner 'touches oll the bases':
9. LEARNING STYLES
Kolb's learning theory
(1984) sets out four
distinct learning styles,
which are based on a
four-stage learning
cycle (see above). Kolb
explains that different
people naturally prefer
a certain single different
learning style.
10. LEARNING STYLES
These people are able to look at things from
different perspectives. They are sensitive. They
prefer to watch rather than do, tending to
gather information and use imagination to solve
problems. They are best at viewing concrete
situations from several different viewpoints.
11. LEARNING STYLES
The assimilating learning preference involves a
concise, logical approach. Ideas and concepts
are more important than people.
These people require good clear explanation
rather than a practical opportunity. They excel at
understanding wide-ranging information and
organizing it in a clear, logical format.
12. LEARNING STYLES
People with a converging learning
style can solve problems and will use
their learning to find solutions to
practical issues. They prefer
technical tasks, and are less
concerned with people and
interpersonal aspects.
13. LEARNING STYLES
The Accommodating learning style is
'hands-on,' and relies on intuition rather
than logic. These people use other people's
analysis, and prefer to take a practical,
experiential approach. They are attracted
to new challenges and experiences, and to
carrying out plans.
14.
15. REFLECTIVE
LEARNING
·Reflective learning refers to learning that
is facilitated by reflective thinking.
·It is not enough that learners encounter
real-life situations.
·Deeper learning occurs when learners
are able to think about their experiences
and process these allowing them the
opportunity to make sense and meaning
of their experiences.
17. CONSTRUCTIVISM
·Constructivism is the theory that argues that
knowledge is constructed when the learner is
able to draw ideas from his own experiences
and connects them to new ideas that are
encountered.
·Constructivism is the theory that says learners
construct knowledge rather than just passively
take in information. As people experience the
world and reflect upon those experiences, they
build their own representations and
incorporate new information into their pre-
existing knowledge (schemas).
18. TRADITIONAL CLASSROOM CONSTRUCTIVIST CLASSROOM
Curriculum begins with the parts of the whole. Emphasizes basic
skills.
Curriculum emphasizes big concepts, beginning with the whole and
expanding to include the parts.
Strict adherence to fixed curriculum is highly valued. Pursuit of student questions and interests is valued.
Materials are primarily textbooks and workbooks.
Materials include primary sources of material and manipulative
materials.
Learning is based on repetition. Learning is interactive, building on what the student already knows.
Teachers disseminate information to students. Students are
recipients of knowledge.
Teachers have a dialogue with students, helping students construct
their own knowledge.
Teacher's role is directive, rooted in authority. Teacher's role is interactive, rooted in negotiation.
Assessment is through testing and correct answers.
Assessment includes student works, observations and points of
view, as well as tests. Process is as important as product.
Knowledge is seen as inert.
Students work primarily alone.
Knowledge is seen as dynamic, ever changing with our experiences.
Students work primarily in groups.
23. COOPERATIVE
LEARNING
Cooperative Learning, sometimes called
small-group learning, is an instructional
strategy in which small groups of students
work together on a common task. The task
can be as simple as solving a multi-step
math problem together, or as complex as
developing a design for a new kind of
school. In some cases, each group member
is individually accountable for part of the
task; in other cases, group members work
together without formal role assignments.
24. FIVE BASIC ELEMENTS OF
COOPERATIVE LEARNING
Students feel
responsible for their
own and the group's
effort.
POSITIVE
INTERDEPENDENCE
Students encourage and
support one another; the
environment encourages
discussion and eye contact.
FACE-TO-FAE
INTERACTION
Each student is
responsible for doing their
part; the group is
accountable for meeting its
goal.
INDIVIDUAL AND
GROUP
ACCOUNTABILITY Group members gain
direct instruction in the
interpersonal, social,
and collaborative skills
needed to work with
others occurs.
GROUP
BEHAVIORS
GROUP
PROCESSING
Group members analyze
their own and the
group's ability to work
together.
26. • The group has only one pencil, paper, book, or other
resource.
• One paper is written by the group.
• A task is divided into jobs and can't be finished unless
all help.
• Pass one paper around the group on which each
member must write a section.
• Each person learns a topic and then teaches it to the
group (Jigsaw method).
• Offer a reward (e.g. bonus points) if everyone in the
group succeeds.
WAYS TO ENSURE
POSITIVE
INTERDEPENDENCE
27. • Students do the work before bringing it to the
group.
• One student is chosen at random and questioned
on the material the group has studied.
• Everyone writes a paper; the group certifies the
accuracy of all their papers; the instructor
chooses only one paper to grade.
• Students receive bonus points if all do well
individually.
• Instructor observes students taking turns orally
rehearsing information.
WAYS TO ENSURE
INDIVIDUAL AND
GROUP
ACCOUNTABILITY
28. • Be on time for group meetings and start them on time.
• Listen to others. Don't be so busy rehearsing what you
are going to say that you miss other group members'
points and ideas.
• Don't close the road to mutual learning by interrupting
or using language that can be regarded as a personal
attack.
• Make sure everyone has the opportunity to speak.
• Don't suppress conflict, but do control and discipline it.
WAYS TO ENSURE
INTERPERSONAL
AND SMALL GROUP
SKILLS
29. • A student orally explains how to solve a problem.
• One group member discusses a concept with
others.
• A group member teaches classmates about a
topic.
• Students help each other connect present and
past learning.
WAYS TO ENSURE
FACE-TO-FACE
PROMOTIVE
INTERACTION:
30. • Group members describe each other's helpful
and unhelpful behaviors and actions.
• As a group, make decisions about which
behaviors to continue and which behaviors to
change.
WAYS TO ENSURE
GROUP
PROCESSING:
31. • ü Form an group and each one will be assigned
to a place to take the air temperature for 7 days.
• ü Compare the temperature for each person.
• ü Why is there a variation in the temperature
• ü Report the findings.
• ü Students form three groups and are assigned
to measure the floor area of the classroom.
• ü One group will only use a one inch paper clip.
• ü One group will use an 8 inches pencil.
• ü One group will use a 15 inches long stick.
• ü Which group do you think will measure the
floor area the fastest? Why?
SAMPLE
ACTIVITIES
32. DISCOVERY AND
INQUIRY-BASED
LEARNING
·The mathematics curriculum allows
students to learn by asking relevant
questions and discovering new ideas.
·Discovery and Inquiry-based learning
(Bruner. 1961) support the idea that
students learn when they make use of
personal experiences to discover facts,
relationships and concepts.
33. THE 5 PRINCIPLES OF
DISCOVERY LEARNING
MODEL
Principle 1: Problem Solving
Instructors should guide and motivate learners to seek
for solutions by combining existing and newly acquired
information and simplifying knowledge. This way,
learners are the driving force behind learning, take an
active role and establish broader applications for skills
through activities that encourage risks, problem-solving
and probing.
Principle 2: Learner Management
Instructors should allow participants to work
either alone or with others, and learn at their
own pace. This flexibility makes learning the
exact opposite of a static sequencing of
lessons and activities, relieves learners from
unnecessary stress, and makes them feel they
own learning.
34. THE 5 PRINCIPLES OF
DISCOVERY LEARNING
MODEL
Principle 3: Integrating and Connecting
Instructors should teach learners how to combine prior
knowledge with new, and encourage them to connect to
the real world. Familiar scenarios become the basis of
new information, encouraging learners to extend what
they know and invent something new. Principle 4: Information Analysis and
Interpretation
Discovery learning is process-oriented and not
content-oriented, and is based on the assumption
that learning is not a mere set of facts. Learners
in fact learn to analyze and interpret the acquired
information, rather than memorize the correct
answer.
35. THE 5 PRINCIPLES OF
DISCOVERY LEARNING
MODEL
Principle 5: Failure and Feedback.
Learning doesn’t only occur when we find the right
answers. It also occurs through failure. Discovery
learning does not focus on finding the right end result,
but the new things we discover in the process. And it’s
the instructor’s responsibility to provide feedback, since
without it learning is incomplete.
Sample Activities
Students will ask their parents
at home the different tools they
use to measure length of
objects.
The students will bring
materials and demonstrate to
their classmates how the tools
are used.
Self-study on the procedure to
convert ℃ to ℉
Show how it is done in class.
36. DISCOVERY AND
INQUIRY-BASED
LEARNING
Inquiry" is defined as "a seeking for
truth, information, or knowledge --
seeking information by questioning.
The natural way in which scientist
create knowledge, present it for
review and try it out in new settings
37. THE PROCESS OF
INQUIRY...
begins with gathering information and
data through applying the human
senses -- seeing, hearing, touching,
tasting, and smelling.
is complex and involves individuals
attempting to convert information and
data into useful knowledge.
38. TRADITIONAL CLASSROOM INQUIRY CLASSROOM
focused on mastery of content
Focused on using and learning content as a means to
develop information-processing and problem solving
skills
Lectures, assigned readings, problem sets and lab
work
Student centered, with the teacher as a facilitator of
learning
k teacher centered, with the teacher focused on
giving out information about "what is known”
There is more emphasis on "how we come to know"
and "what we know"
Students learn to ask too many questions, instead to
listen and repeat the expected answers
Studetns are more involded in the construction of
knowledge through active involvement
39. STUDENTS VIEW
THEMSELVES AS
LEARNERS IN THE
PROCESS OF
LEARNING
• They look forward to learning
• They demonstrate a desire to
learn more
• They seek to collaborate and
work cooperatively with teacher
and peers
• They are more confident in
learning, demonstrate a
willlingess to modify ideas and
take calculated risks, and display
approrpiate skepticism
40. STUDENTS ACCEPT AN
"INVITATION TO LEARN"
AND WILLINGLY ENGAGE
IN AN EXPLORATION
PROCESS
• They exhibiit curiosity and
ponder observations
• They move around, selecting
and using the materials they
need
• They confer with classmates
and teachers about
observations and questions
• They try out some of their
ideas.
41. STUDENTS RAISE
QUESTIONS, PROPOSE
EXPLANATIONS, AND USE
OBSERVATIONS
• They ask questions (verbally and through
actions)
• They use questions that lead them to
activities generating further questions or
ideas
• They observe critically, as opposed to
casually looking or listening
• They value and apply questions as an
important part of learning
• They make connections to previous ideas.
STUDENTS PLAN AND
CARRY OUT LEARNING
ACTIVITIES
• They design ways to try out their ideas, not always
expecting to be told what to do
• They plan ways to veryfiy, extend, confirm, or discard
ideas
• They carry out activities by: using materials, bserving,
evaluating, and recording information
• They sort out information and decide what is
important
• They see detail, detect sequences and events, notice
change, and detect differences and similarities.
42. • He plans ways for each learner to be actively engaged in
the learning process.
• She understands the necessary skills, knowledge, and
habits of mind needed for inquiry learning.
• He understands and plans ways to encourage and enable
the learner to take increasing responsibility for his
learning.
• She insures that classroom learning is focused on relevant
and applicable outcomes.
• He is prepared for unexpected questions or suggestions
from the learner
• She prepares the classroom environment with the
necessary learning tools, materials, and resources for
active involvement of the learner.
TEACHER'S ROLE
THE TEACHER REFLECTS ON THE
PURPOSE AND MAKE PLANS OF
RINQUIRY LEARNING
43. • The teacher's daily, weekly, monthly, and yearly
facilitation plans focus on setting content learning in a
conceptual framework.
• They also stress skill development and model and
nurture the development of habits of mind.
• She accepts that teaching is also a learning process.
• He asks questions, encouraging divergent thinking that
leads to more questions.
• She values and encourages responses and, when these
responses convey misconceptions, effectively explores
the causes and appropriately guides the learner.
• He is constantly alert to learning obstacles and guides
learners when necessary.
• She asks many Why? How do you know? and What is the
evidence? type of questions.
• He makes student assessment an ongoing part of the
facilitation of the learning process.
TEACHER'S ROLE
THE TEACHER FACILITATES
CLASSROOM LEARNING
45. 02
“Teacher, can you spare a sign?”
My worst experience with a teacher was
during our Math class. I loved math and really
thought I knew and understood math. But my math
teacher sent me home crying everyday because
she marked my homework and test wrong since I
used to get my positive and negative signs wrong. I
knew how to do the problems, but I always got my
answers with wrong sign.
46. 03
Reflect: The scenario
illustrates the difficulties experienced
by some unfortunate learners. But can
we afford to let such kind of teachers?
They affect the way our learners feel
about math. Let’s hope not.
47. 04
• Therefore, it depends upon every
teacher to strive to improve her/his
teaching style to increase the number
of children liking, and even loving
Mathematics. Such should start as
early as in the elementary grades.
Furthermore, the use of varied and
appropriate teaching approaches can
entice more learners to like and love
math.
49. 05
A. DISCOVERY APPROACH
The ultimate goal of this approach is that
learners learn how to learn rather than what
to learn.
•for developing their higher-order thinking
skills.
•This approach refers to an “Inductive Method”
of guiding learners to discuss and use ideas
already acquired as a means of discovering
new ideas.
50. A. DISCOVERY APPROACH
Template
It is "International Learning”,
both the teacher and the
learner play active roles in
discovery learning.
52. 02
B. INQUIRY TEACHING
-providing learners with content-related
problems that serve as the foci for class
research activities.
-The teacher provides/presents a
problem then the learners identify the
problem.
-Such problem provides the focus which
lead to the formulation of the hypothesis
by the learners
54. 03
B. DEMONSTRATION
APPROACH
-providing learners with content-related problems
that serve as the foci for class research activities.
-The teacher provides/presents a problem then the
learners identify the problem.
-Such problem provides the focus which lead to
the formulation of the hypothesis by the learners.
-Once the hypotheses have been formulated, the
learners’ task is to gather data to test hypotheses.
-The gathered data are being organized then data
analysis follow to arrive to
conclusion/generalization.
56. 03
B. DEMONSTRATION
APPROACH
✓Once thehypotheses have
been formulated, the learners’
task is to gather data to test
hypotheses.
✓Thegathered data are being
organized then data analysis
follow to arrive to
conclusion/generalization.
58. 04
C. MATH-LAB APPROACH
•children in small groups
work through an
assignment/task card, learn
and discover mathematics
for themselves.
59. 04
C. MATH-LAB APPROACH
•The children work in an
informal manner, move
around, discuss and choose
their materials and method of
attacking a problem,
assignment or task.
60. 05
D. PRACTICAL WORK
APPROACH (PWA)
-The learners in this approach, manipulate
concrete objects and/or perform activities to
arrive at a conceptual understanding of
phenomena, situation, or concept. The
environment is a laboratory where the natural
events/phenomena can be subjects of
mathematical or scientific investigations.
Activities can be done in the garden, in the
yard, in the field, in the school grounds, or
anywhere as long as the safety of the learners
is assured. That’s why elementary schools are
encouraged to put up a Math park.
61. 05
D. PRACTICAL WORK
APPROACH (PWA)
-The learners in this approach, manipulate
concrete objects and/or perform activities to
arrive at a conceptual understanding of
phenomena, situation, or concept. The
environment is a laboratory where the natural
events/phenomena can be subjects of
mathematical or scientific investigations.
Activities can be done in the garden, in the
yard, in the field, in the school grounds, or
anywhere as long as the safety of the learners
is assured. That’s why elementary schools are
encouraged to put up a Math park.
62. 05
D. PRACTICAL WORK
APPROACH (PWA)
✓The environment is a laboratory where
the natural events/phenomena can be subjects
of mathematical or scientific investigations.
✓Activities can be done in the garden, in the
yard, in the field, in the school grounds, or
anywhere as long as the safety of the learners
is assured. That’s why elementary schools are
encouraged to put up a Math park.
64. 01
• This permits the learners to
progress by mastering steps
through the curriculum at his/her
own rate and independently of
the progress of other pupils.
65. 01
• Individualizing instruction does not imply
that every pupil in the class must be
involved in an activity separates and distinct
from that of every other child. There are
many ways of individualizing instruction:
grouping, modules- self-learning
kits/materials, programmed materials, daily
prescriptions, contracts, etc.
67. 02
BRAINSTORMING
• teacher elicits from the learners as many
ideas as possible but refrains from
evaluating them until all possible ideas
have been generated.
• It is an excellent strategy for stimulating
creativity among learners.
69. 03
PROBLEM-SOLVING
• a learner-directed strategy in which
learners “think patiently and
analytically about complex situations in
order to find answers to questions”.
70. PROBLEM-SOLVING04
When using problem-solving for the first time:
❑select a simple problem that can be
completed in a short amount of time.
❑Consider learners’ interest, ability level, and
maturation level.
❑Make sure resources (materials or
equipment) are available.
❑Make sure that learners are familiar with
brainstorming before you implement problem-
solving.
72. 05
COOPERATIVE LEARNING
•eliminates competition among learners.
It encourages them to work together
towards common goals.
•It fosters positive intergroup attitudes in
the classroom. It encourages learners
to work in small groups to learn.
75. 02
B. INQUIRY TEACHING
-providing learners with content-related problems
that serve as the foci for class research activities.
✓The teacher provides/presents a problem
then the learners identify the problem.
✓Such problem provides the focus which lead to
the formulation of the hypothesis by the learners.
✓Once the hypotheses have been formulated,
the learners’ task is to gather data to test
hypotheses.
✓The gathered data are being organized then
data analysis follow to arrive to
conclusion/generalization.
77. 03
INTEGRATIVE TECHNIQUE
-The Integrated Curriculum Mode
(Integrative teaching to some) is
both a “method of teaching and a
way of organizing the instructional
program so that many subject areas
and skills provided in the curriculum
can be linked to one another”.
79. 04
Modes of Integration:
❖Some topics/content in
Sibika at Kultura and
Heograpiya/ Kasaysayan/
Sibika were used as vehicle
for the language skills
development in Filipino.
80. 04
Modes of Integration:
❖Using Thematic
Teaching: Some themes
can center on celebrations,
current issues, learner’s
interests/hobbies, priority
82. 1. Use dramatizations
• Invite children pretend to be in a ball
(sphere) or box (rectangular prism),
feeling the faces, edges, and corners
and to dramatize simple arithmetic
problems such as: Three frogs
jumped in the pond, then one more,
how many are there in all?
83. 2. Use children's
bodies
• Suggest that children show how many feet,
mouths, and so on they have. Invite children to
show numbers with fingers, starting with the
familiar, "How old are you?" to showing numbers
you say, to showing numbers in different ways
(for example, five as three on one hand and two
on the other).
84. 3. Use children's play
• Engage children in block play that
allows them to do mathematics in
numerous ways, including
sorting, creating symmetric
designs and buildings, making
patterns, and so forth
85. 4. Use children's toys
• Encourage children to use
"scenes" and toys to act out
situations such as three cars on
the road, or, later in the year, two
monkeys in the trees and two on
the ground.
86. 5. Use children's stories
• Share books with children
that address Mathematics
but are also good stories.
Later, help children see
Mathematics in any book.
87. 6. Use children's natural
creativity
•Children's ideas about
mathematics should be
discussed with all
children.
88. 7. Use children's problem-
solving abilities
• Ask children to describe how they would
figure out problems such as getting just
enough scissors for their table or how
many snacks they would need if a guest
were joining the group. Encourage them to
use their own fingers or manipulatives or
whatever else might be handy for problem
solving.
89. 8. Use a variety of
strategies
• Bring mathematics everywhere you go in
your classroom, from counting children at
morning meeting to setting the table, to
asking children to clean up a given
number or shape of items. Also, use a
research-based curriculum to incorporate
a sequenced series of learning activities
into your program.
90. 9. Use technology
• Try digital cameras to record children's
mathematical work, in their play and in planned
activities, and then use the photographs to aid
discussions and reflections with children,
curriculum planning, and communication with
parents. Use computers wisely to mathematize
situations and provide individualized instruction.
91. 10. Use assessments to measure
children's mathematics learning
• Use observations, discussions with children, and small-group activities
to learn about children's mathematical thinking and to make informed
decisions about what each child might be able to learn from future
experiences.
92.
93. REFLECTION:
• Choose the best strategy
suited to you and your
students. Explain how will
you employ it in your
class.
95. All subjects extend to difficult
levels; the reason so many
people think math is difficult
is the inaccessible way it is
often taught. We need to
change the thinking around
this if we are open to
mathematics to more people.
Jo Boaler
02
CONTENT
OF
K-12
MATHEMATICS
96. CONTENT OF K-12 MATHEMATICS
The Philippine mathematics education
program at the elementary and
secondary levels aims to teach the
most fundamental and useful contents
of mathematics and organizes these
into the following strands: Numbers
and Number Sense; Measurement;
Geometry; Patterns, Functions and
Algebra and Data, Analysis and
Probability. This organization of the
contents was influenced by the 1995,
1999 and 2003 TIMSS studies.
03
97. NUMBER
AND
NUMBER
SENSE
The general objectives of this strand include enabling students to:
• Read, write and understand the meaning order and relationship
among numbers and number systems;
• Understand the meaning, use and relationships between operations
on numbers;
•Choose and use different strategies to compute and estimate.
This strand focuses on students’ understanding of numbers (counting
numbers, whole numbers, integers, fractions, decimals, real numbers
and complex numbers), properties, operations, estimation and their
applications to real-world situations. Te learning activities must
address students’ understanding of relative size, equivalent forms
of numbers and the use of numbers to represent attributes of real
world objects and quantities.
98. NUMBER
AND
NUMBER
SENSE
Students are expected to have mastery of the operations of whole
numbers, demonstrate understanding of concepts and perform skills on
decimals, fractions, ratio and proportion, percent and integers.
Students are expected to demonstrate an understanding of numerical
relationships expressed in ratios, proportions and percentages. They
are also expected to understand properties of numbers and
operations, generalize from numerical patterns and verify results.
Students are expected to perform basic algorithms and use technology
appropriately.
99. BRIEF COURSE
DESCRIPTION
Mathematics from K-12 is a skills subject. By itself, it is all about
quantities, shapes and figures, functions, logic and reasoning.
Mathematics is also a tool of Science and a language complete with it's
own notations, and symbols and "grammar" rules, with which
concepts and ideas are effectively expressed.
The content of Mathematics include:
• Number and Number Sense
• Measurement
• Geometry
• Patterns ad Algebra
• Statistics and Probability
100. BRIEF COURSE
DESCRIPTION
Measurements as a strand includes:
The use of numbers to describe
Understand and compare mathematical and concrete objects
Applications involving perimeter
• Area
• Surface area
• Angle measure
It focuses on attributes such as
• lenght
• Mass and weight
• Capacity
• Time
• Money and temperature and among others
101. BRIEF COURSE
DESCRIPTION
GEOMETRY as a strand includes:
• Properties of two and three dimensional figures and their
relationships
• Spatial visualization
• Reasoning, and
• Geometric modeling and proofs
102. BRIEF COURSE
DESCRIPTION
PATTERNS and ALGEBRA as a strand studies:
• Patterns
• Relationships and changes among shapes and quantities and
includes the use of algebraic notations and symbols
• Equations and most importantly
• Functions to represent and analyze realtionships
103. BRIEF COURSE
DESCRIPTION
STATISTICS and PROBABILITY as a strand is all about:
• Developing skills in collecting and organizing data using
charts, tables and graphs
• Understanding, analyzing and interpreting data
• Dealing with uncertainty
• Making predict ions and outcomes
104. The K to 10 Mathematics Curriculum
provides a solid foundation for
Mathematics at Grades 11 to 12. More
importantly, it provides necessary
concepts and life skills needed by
Filipino learners as they proceed to
the next stage in their life as
learners and as citizens of our
beloved country, the Philippines.
105. This are the defined
expectancies for learners at
the end of the four key stages
KEY STAGE STANDARDS
Key Stage 1: (at the end of Grade 3)
Key Stage 2 : (at the end of Grade 6)
Key Stage 3: (at the end of Grade 10)
Key Stage 4: )at the end of Grade 12)
106. GRADE
LEVEL
STANDARDS
are the
defined
expectancies
for the
learners in a
particular
level
PERFORMANCE
STANDARDS
Answer the
questions : "What
do we want students
to do with their
learning or
understanding? and
"How do we want
them to use their
learning or
understanding.
CONTENT
STANDARDS
answer the
question:
"What do we
want the
students to
know, be able
t o do and
understand?
LEARNING
COMPETENCIES
are the specific
skills, knowledge,
vales and attitudes
in a partiular
learning area that
learners should
develop and master
in order to meet the
standards. These are
the unpacked content
and performance
standards
107. The learner demonstrates
understanding and
appreciation of key concepts
and principles of Mathematics
as applied, using appropriate
technology, in problem solving,
communicating, reasoning,
making connections,
representations, and decisions
in real life.
LEARNING AREA
STANDARDS
108. At the end of Grade 3, the learner
demonstrates understanding and
appreciation of key concepts and
skills involving whole numbers up
to ten thousand, fractions,
measurement, simple geometric
figures, pre-algebra concepts and
data representation and analysis as
applied, using appropriate
technology in critical thinking,
problem solving, reasoning,
communicating, making
KEY STAGE STANDARDS 1-
3
109. At the end of Grade 6, the learner
demonstrates understanding and
appreciation of key concepts and
skills involving rational numbers,
measurement, geometric figures,
pre-algebra concepts, simple
probability and data analysis as
applied, using appropriate
technology, in critical thinking,
problem solving, reasoning,
communicating, making
connections, representations and
KEY STAGE STANDARDS 4-
6
110. At the end of Grade 10, the learner
demonstrates understanding and
appreciation of key concepts and
skills involving number sense,
measurement, algebra, geometry,
probability and statistics, and
trigonometry as applied, using
appropriate technology in critical
thinking, problem solving,
communicating, reasoning, making
connections, representations, and
KEY STAGE STANDARDS 7-
10
111. The learner demonstrates
understanding and appreciation of key
concepts and skills involving whole
numbers up to 100, fractions,
measurement, simple geometric
figures, pre-algebra concepts, data
collection and representations as
applied, using appropriate technology
in critical thinking, problem solving,
reasoning, communicating, making
connections, representations and
GRADE LEVEL STANDARDS
GRADE 1
112. The learner demonstrates
understanding and appreciation of key
concepts and skills involving whole
numbers up to 1,000, fractions,
measurement, simple geometric
figures, pre-algebra concepts, data
collection and representations as
applied, using appropriate technology
in critical thinking, problem solving,
reasoning, communicating, making
connections, representations and
GRADE LEVEL STANDARDS
GRADE 2
113. The learner demonstrates
understanding and appreciation of key
concepts and skills involving whole
numbers up to 10,000, fractions,
measurement, simple geometric
figures, pre-algebra concepts, data
collection, representation and analysis
as applied, using appropriate
technology in critical thinking, problem
solving, reasoning, communicating,
making connections, representations
GRADE LEVEL STANDARDS
GRADE 3
114. The learner demonstrates understanding and
appreciation of key concepts and skills involving whole
numbers up to 100,000, fractions, decimals including
money, ratio, angles, plane figures like square,
rectangle and triangle, measurement (perimeter, area
of triangle, parallelogram and trapezoids), volume of
cubes and rectangular prisms, pre-algebra concepts,
data collection, representation and analysis as applied,
using appropriate technology in critical thinking,
problem solving, reasoning, communicating, making
connections, representations.
GRADE LEVEL STANDARDS
GRADE 4
115. The learner demonstrates understanding and
appreciation of key concepts and skills involving whole
numbers up to 10,000,000, fractions, decimals including
money, ratio, percent, geometry (circles and five more-
sided polygons) measurement (circumference, area of
circle, volume of cubes and rectangular prisms,
temperature) pre-algebra concepts, data collection,
representation and analysis as applied, using
appropriate technology in critical thinking, problem
solving, reasoning, communicating, making
connections, representations and decision in real life.
GRADE LEVEL STANDARDS
GRADE 5
116. The learner is expected to have mastered the concepts
and operations on whole umbers; demonstrate
understanding and appreciation of the key concepts
and skills involving fractions, decimals including
money, ratio and proportion, percent, rate integers,
geometry (spatial figures), measurement (surface area,
volume, meter reading) pre-algebra concepts, data
collection, representation and analysis, probability,
expressions and equations as applied, using
appropriate technology in critical thinking, problem
solving, reasoning, communicating, making
connections, representations and decision
GRADE LEVEL STANDARDS
GRADE 6
117. The learner demonstrates understanding of key
concepts and principles of number sense,
measurement, algebra, geometry, probability and
statistics as applied using appropriate technology in
critical thinking, problem solving, reasoning,
communicating, making connections, representations
and
GRADE LEVEL STANDARDS
GRADE 7
118. The learner demonstrates understanding of key
concepts and principles of algebra, geometry,
probability and statistics as applied using appropriate
technology in critical thinking, problem solving,
reasoning, communicating, making connections,
representations and decision in real life.
GRADE LEVEL STANDARDS
GRADE 8
119. The learner demonstrates understanding of key
concepts and principles of algebra, geometry, and
trigonometry as applied using appropriate technology
in critical thinking, problem solving, reasoning,
communicating, making connections, representations
and decision in real life.
GRADE LEVEL STANDARDS
GRADE 9
120. The learner demonstrates understanding of key
concepts and principles of number sense, algebra,
geometry, and statistics as applied using appropriate
technology in critical thinking, problem solving,
reasoning, communicating, making
connections.
GRADE LEVEL STANDARDS
GRADE 10
