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Agenda
Session 10A: Numbers and
Number Sense
Session 10B: Place Value and
Decimal System
Session 11: Multi-Digit
Addition and Substraction
02/07/2023 INSERVICE TRAINING- SESSION 10-A-11 1

Session 10A: The
Concept of Number
Sense and Counting
Venia G. Asuero

Number Sense
and
Numeration
Overview of Big Concept

Numbers & Number Sense
• is one of the key contents in K-12 Mathematics Curriculum
• Numbers and Number Sense as a strand include concepts of
numbers, properties, operations, estimation, and their
applications.
• person’s ability to understand, relate, and connect numbers.

Numbers and
Number Sense
• The big ideas or major concepts in
Number Sense and Numeration are
the following:
• counting
• operational sense
• quantity
• relationships
• representation

General Principles of
Instruction
1. Representations of concepts
promote understanding and
communication.

General Principles
of Instruction
2. Problem solving should be the
basis for most mathematical
learning.

General Principles
of Instruction
3. Students need frequent
experiences using a variety of
resources and learning
strategies.
This Photo by Unknown Author is licensed under CC BY-NC-ND

General Principles
of Instruction
4. As students confront
increasingly more complex
concepts, they need to be
encouraged to use their reasoning
skills

Counting
Its Key Concept and
Instruction/Strategies in Teaching
Counting

Key Concepts of Counting
• Counting includes both the recitation of a series of
numbers and the conceptualization of a symbol as
representative of a quantity.
• Making the connection between counting and quantity
• Counting is a powerful early tool intricately connected with
the future development of students’ conceptual
understanding of quantity, place value, and the
operations.

Key Concepts of Counting
Stable order –
the idea that the
counting
sequence stays
consistent; it is
always 1, 2, 3, 4,
5, 6, 7, 8, . . . , not
1, 2, 3, 5, 6, 8
1
Order
irrelevance – the
idea that the
counting of
objects can begin
with any object in
a set and the total
will still be the
same.
2
Conservation –
the idea that the
count for a set
group of objects
stays the same no
matter whether
the objects are
spread out or are
close together
3
Abstraction – the
idea that a
quantity can be
represented by
different things
(e.g 5 apples)
4
One-to-one
correspondence
– the idea that
each object being
counted must be
given one count
and only one
count.
5
Cardinality – the
idea that the last
count of a group
of objects
represents the
total number of
objects in the
group.
6
Movement is
magnitude – the
idea that, as one
moves up the
counting
sequence, the
quantity increases
by 1
7
Unitizing – the
idea that, in the
base ten system,
objects are
grouped into
tensonce the
count exceeds 9
8

General Strategies For Teaching
Counting
• link the counting sequence with objects (especially fingers)
or movement on a number line, so that students attach the
counting number to an increase in quantity or, when counting
backwards, to a decrease in quantity;
• model strategies that help students to keep track of their count
(e.g., touching each object and moving it as it is counted);
• provide activities that promote opportunities for counting
both inside and outside the classroom (playing hide-and-
seek and counting to 12 before “seeking”; counting students as
they line up for recess);

Counting
• link the counting sequence with objects (especially fingers)
or movement on a number line, so that students attach the
counting number to an increase in quantity or, when counting
backwards, to a decrease in quantity;
• model strategies that help students to keep track of their count
(e.g., touching each object and moving it as it is counted);
• provide activities that promote opportunities for counting
both inside and outside the classroom (playing hide-and-
seek and counting to 12 before “seeking”; counting students as
they line up for recess);

Counting
• continue to focus on traditional games and songs that
encourage counting skills for the earliest grades but also adapt
those games and songs, so that students gain experience in
counting from anywhere within the sequence (e.g., counting
from 4 to 15 instead of 1 to 10), and gain experience with the
teen numbers, which are often difficult for Kindergarteners;
• link the teen words with the word ten and the words one to
nine (e.g., link eleven with the words ten and one; link twelve
with ten and two) to help students recognize the patterns to the
teen words, which are exceptions to the patterns for number
words in the base ten number system;

Counting
• help students to identify the patterns in the numbers
themselves (using a hundreds chart). These patterns in the
numbers include the following:
– The teen numbers (except 11 and 12) combine the number term and
teen (e.g., 13, 14, 15).
– The number 9 always ends a decade (e.g., 29, 39, 49). – The pattern of
10, 20, 30, . . . follows the same pattern as 1, 2, 3, . . . .
– The tens follow the pattern of 1, 2, 3, . . . within their decade; hence, 20
combines with 1 to become 21, then with 2 to become 22, and so on.
–The pattern in the hundreds chart is reiterated in the count from 100 to
200, 200 to 300, and so on, and again in the count from 1000 to 2000,
2000 to 3000, and so on

Teacher , how do you
teach counting?
Please share your classroom
strategies

Session 10B: Place
Value and the
Decimal System
Venia G. Asuero

Place Value
and Decimal
System
Key Concepts in Teaching

What is
Place
Value?
Place value is the numeric
value of a digit, which changes
depending upon its position in
a number.
This Photo by Unknown Author is licensed under CC BY-SA-NC

Key Concepts in Teaching Place value
and Decimal System
• The numeration system currently used in the Philippines, the Hindu-Arabic or
decimal system, is a numeration system that employs place or positional
value (the position or place of a numeral defines its value in multi-digit
numerals)
• Learning about place value entails the ability to count groups as though
they were individual objects
• Using the place value system requires the conservation of number
• Children need to explore the place value system first by manipulating
materials (concept/concrete level), then by relating these experiences with
their corresponding symbols (connecting stage) and eventually by
recording these experiences using their corresponding symbols
(symbolic stage)

Its time to showcase your strategy:
• Group yourself according to the grade level you are
in.
• You have 5 minutes to list down the strategies you
do to introduce place value and decimal system.
• Choose only the best 2 strategies you are familiar
with and the best strategy for the grade level you
are teaching and prepare to demonstrate it to the
entire group.

Some of the strategies to teach place
value and decimal system:
Use Manipulatives to Introduce
and Teach Place Value-
Manipulatives include any hand-on
materials, tools or resources that
help students to build conceptual
understanding through concrete
activities.
1
Use Money as a Manipulative
When Teaching Place Value-
consider money (REAL money –
not plastic coins and paper play
money!!) to be one of the best
manipulatives you can use when
teaching place value.
2
The CPA (Concrete, Pictorial,
Abstract) approach helps pupils
connect a physical representation of
a number (concrete manipulatives)
to that same quantity as shown in
drawings or graphics (pictorial), and
finally to the actual written name
and symbol for that number
(abstract).
3
Give Many Opportunities for Your
Students to Practice Place Value-
explore activities that your children
will have fun and enjoy.
4

Session 11: Multi-
Digit Addition and
Substraction
Venia G. Asuero

Operational
Sense
Key Concepts in Teaching

Key Concepts in Teaching Basic
Operations
• Students’ effectiveness in using operations depends on the
counting strategies they have available, on their ability to
combine and partition numbers, and on their sense of
place value.
• Students learn the patterns of the basic operations by
learning effective counting strategies, working with
patterns on number lines and in hundreds charts, making
pictorial representations, and using manipulatives.

Key Concepts in Teaching Basic
Operations
• The operations are related to one another in various
ways (e.g., addition and subtraction are inverse
operations). Students can explore these relationships to
help with learning the basic facts and to help in problem
solving.
• Students gain a conceptual understanding of the operations
when they can work flexibly with algorithms, including those
of their own devising, in real contexts and problem-
solving situations.

General Instruction in the Operations
• The following are general strategies for teaching the operations.
Teachers should:
• focus on problem-solving contexts that create a need for
computations;
• create situations in which students can solve a variety of
problems that relate to an operation (e.g., addition) in many
different ways, so that they can build confidence and fluency;

• encourage students to use manipulatives or pictorial
representations to model the action in the problems;
• allow students to discover their own strategies for solving the
problems;
• use open-ended probes and questioning to help students
understand what they have done and communicate what they
are thinking;

• prompt students to move to more efficient strategies (e.g.,
counting on, counting back, using derived facts, making tens);
• most importantly, encourage students to talk about their
understandings with the teacher and with their classmates;
• use what they have learned about the mathematical thinking of
individual students to “assess on their feet” in order to provide
immediate, formative feedback to students about their
misconceptions and about any of their ideas that need more
exploration.

Thank you
VENIA G. ASUERO
Email address: vinia.galasi@deped.gov.ph

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