FMT3701
Assignment 2 2025
Unique number:
Due Date: 26 July 2025
QUESTION 1
1.1 Explain the concept “number sense” and its development
Number sense refers to a learner’s ability to understand numbers and how they work. It
involves knowing how to count, compare, and manipulate numbers flexibly in real-life
contexts. According to the Ontario Ministry of Education (2005), number sense includes
understanding the relationships between numbers, their representation, quantity, and
the four operations. Cunningham (2018) adds that learners with number sense can
compare quantities, identify patterns, and solve problems logically. Number sense
develops through counting, identifying patterns, using place value, and practising
operations in meaningful ways. Teachers play a key role in helping learners apply
numbers confidently and accurately.
Terms of use
By making use of this document you agree to:
Use this document as a guide for learning, comparison and reference purpose,
Terms of use
Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
By making use of this document you agree to:
Use this document
Fully accept the consequences
solely as a guide forshould you plagiarise
learning, reference,or and
misuse this document.
comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
QUESTION 1
1.1 Explain the concept “number sense” and its development
Number sense refers to a learner’s ability to understand numbers and how they
work. It involves knowing how to count, compare, and manipulate numbers flexibly in
real-life contexts. According to the Ontario Ministry of Education (2005), number
sense includes understanding the relationships between numbers, their
representation, quantity, and the four operations. Cunningham (2018) adds that
learners with number sense can compare quantities, identify patterns, and solve
problems logically. Number sense develops through counting, identifying patterns,
using place value, and practising operations in meaningful ways. Teachers play a
key role in helping learners apply numbers confidently and accurately.
1.2 Distinguish between verbal and object counting, giving two examples for
each
Verbal counting, also known as rote counting, is when learners recite number names
from memory, often in sequence, without necessarily understanding the value each
number represents. This type of counting often appears in early learning through
songs, rhymes, and chants. Learners may count rhythmically but do not yet grasp
one-to-one correspondence between numbers and objects. Examples include a
learner singing “one, two, three, four…” while skipping or saying numbers aloud
during a song but without counting real items.
Object counting, or rational counting, involves matching number names to actual
objects, following the one-to-one correspondence principle. In this case, learners
understand that each object must be counted once and that the last number said
represents the total quantity. This type of counting reflects deeper number sense, as
it involves understanding the concept of quantity. Examples include a learner placing
one block at a time while counting aloud “one, two, three…” and understanding that
three blocks are present. Another example is a child counting how many apples are
in a basket, saying one number for each apple, and concluding “five apples.”
In short, verbal counting demonstrates memorisation of the counting sequence, while
object counting shows understanding of quantity. For effective development of
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
number sense, learners must move from verbal to object counting. Teachers should
provide hands-on activities using real items to help learners make this connection.
Both forms are essential in early numeracy but serve different developmental
purposes, with object counting being more accurate for evaluating number
understanding. The image provided shows how verbal counting involves memory
and rhythm, whereas object counting uses number names in meaningful and logical
ways to represent actual amounts.
1.3.1 Order Irrelevance
Order irrelevance is the understanding that the order in which objects are counted
does not affect the total quantity. This means a learner can count five blocks starting
from any point and in any direction, and the total will still be five, as long as each
object is counted once. Learners who have not grasped this concept may think
changing the order changes the answer. Developing order irrelevance helps learners
count flexibly and with confidence. Teachers can support this concept by
encouraging children to count the same set of items in different orders and still arrive
at the same total.
1.3.2 Movement is Magnitude
Movement is magnitude refers to the misconception that the physical position or
movement of an object changes its quantity. For instance, a learner may believe that
spreading objects out means there are more, or that pushing them together means
there are fewer. This misunderstanding often appears in early childhood when
learners focus on the visual layout rather than the actual count. To address this,
teachers should provide experiences where learners count sets before and after
rearranging them to show that quantity remains constant. This understanding is
important in building a strong foundation for conservation of number in mathematics.
1.3.3 Abstraction
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
Assignment 2 2025
Unique number:
Due Date: 26 July 2025
QUESTION 1
1.1 Explain the concept “number sense” and its development
Number sense refers to a learner’s ability to understand numbers and how they work. It
involves knowing how to count, compare, and manipulate numbers flexibly in real-life
contexts. According to the Ontario Ministry of Education (2005), number sense includes
understanding the relationships between numbers, their representation, quantity, and
the four operations. Cunningham (2018) adds that learners with number sense can
compare quantities, identify patterns, and solve problems logically. Number sense
develops through counting, identifying patterns, using place value, and practising
operations in meaningful ways. Teachers play a key role in helping learners apply
numbers confidently and accurately.
Terms of use
By making use of this document you agree to:
Use this document as a guide for learning, comparison and reference purpose,
Terms of use
Not to duplicate, reproduce and/or misrepresent the contents of this document as your own work,
By making use of this document you agree to:
Use this document
Fully accept the consequences
solely as a guide forshould you plagiarise
learning, reference,or and
misuse this document.
comparison purposes,
Ensure originality of your own work, and fully accept the consequences should you plagiarise or misuse this document.
Comply with all relevant standards, guidelines, regulations, and legislation governing academic and written work.
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is" without any express or
implied representations or warranties. The author accepts no responsibility or liability for any actions taken based on the
information contained within this document. This document is intended solely for comparison, research, and reference purposes.
Reproduction, resale, or transmission of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
QUESTION 1
1.1 Explain the concept “number sense” and its development
Number sense refers to a learner’s ability to understand numbers and how they
work. It involves knowing how to count, compare, and manipulate numbers flexibly in
real-life contexts. According to the Ontario Ministry of Education (2005), number
sense includes understanding the relationships between numbers, their
representation, quantity, and the four operations. Cunningham (2018) adds that
learners with number sense can compare quantities, identify patterns, and solve
problems logically. Number sense develops through counting, identifying patterns,
using place value, and practising operations in meaningful ways. Teachers play a
key role in helping learners apply numbers confidently and accurately.
1.2 Distinguish between verbal and object counting, giving two examples for
each
Verbal counting, also known as rote counting, is when learners recite number names
from memory, often in sequence, without necessarily understanding the value each
number represents. This type of counting often appears in early learning through
songs, rhymes, and chants. Learners may count rhythmically but do not yet grasp
one-to-one correspondence between numbers and objects. Examples include a
learner singing “one, two, three, four…” while skipping or saying numbers aloud
during a song but without counting real items.
Object counting, or rational counting, involves matching number names to actual
objects, following the one-to-one correspondence principle. In this case, learners
understand that each object must be counted once and that the last number said
represents the total quantity. This type of counting reflects deeper number sense, as
it involves understanding the concept of quantity. Examples include a learner placing
one block at a time while counting aloud “one, two, three…” and understanding that
three blocks are present. Another example is a child counting how many apples are
in a basket, saying one number for each apple, and concluding “five apples.”
In short, verbal counting demonstrates memorisation of the counting sequence, while
object counting shows understanding of quantity. For effective development of
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
, +27 67 171 1739
number sense, learners must move from verbal to object counting. Teachers should
provide hands-on activities using real items to help learners make this connection.
Both forms are essential in early numeracy but serve different developmental
purposes, with object counting being more accurate for evaluating number
understanding. The image provided shows how verbal counting involves memory
and rhythm, whereas object counting uses number names in meaningful and logical
ways to represent actual amounts.
1.3.1 Order Irrelevance
Order irrelevance is the understanding that the order in which objects are counted
does not affect the total quantity. This means a learner can count five blocks starting
from any point and in any direction, and the total will still be five, as long as each
object is counted once. Learners who have not grasped this concept may think
changing the order changes the answer. Developing order irrelevance helps learners
count flexibly and with confidence. Teachers can support this concept by
encouraging children to count the same set of items in different orders and still arrive
at the same total.
1.3.2 Movement is Magnitude
Movement is magnitude refers to the misconception that the physical position or
movement of an object changes its quantity. For instance, a learner may believe that
spreading objects out means there are more, or that pushing them together means
there are fewer. This misunderstanding often appears in early childhood when
learners focus on the visual layout rather than the actual count. To address this,
teachers should provide experiences where learners count sets before and after
rearranging them to show that quantity remains constant. This understanding is
important in building a strong foundation for conservation of number in mathematics.
1.3.3 Abstraction
Disclaimer
Great care has been taken in the preparation of this document; however, the contents are provided "as is"
without any express or implied representations or warranties. The author accepts no responsibility or
liability for any actions taken based on the information contained within this document. This document is
intended solely for comparison, research, and reference purposes. Reproduction, resale, or transmission
of any part of this document, in any form or by any means, is strictly prohibited.
