FMT3701 Assignment 2
(CORRECT ANSWERS)
2025 - DUE 26 July 2025
ALL QUESTIONS ANSWERED.
QUESTION 1 (42 marks)
1.1 Explain the concept “number sense” and its development. (3)
Number sense refers to a person's ability to understand, interpret, and work with numbers. It
encompasses a range of skills and concepts that allow individuals to make sense of numerical
information and apply it in various contexts. This intuitive understanding of numbers
includes recognizing their size, relationships, and the ability to work flexibly with them in
problem situations, which is crucial for making sound decisions and reasonable judgments.1
Key Components of Number Sense
Number Recognition: The ability to identify and name numbers.
Understanding Quantity: Grasping the concept of how many items are in a set.
Estimation: Making reasonable guesses about quantities or calculations.
Number Relationships: Understanding how numbers relate to one another (e.g., greater than,
less than).
1.2 Distinguish between verbal and object counting giving, two (2) examples for each (10)
Counting can be categorized into two main types: verbal counting and object counting. Here’s a
breakdown of each type along with examples.
Verbal Counting
,Verbal counting, also known as rote counting, refers to the process of counting using spoken or
written words without the need for physical objects. It often involves reciting numbers in
sequence. This type of counting is closely related to language development and is typically
learned through repetition and memorization, often in the form of rhymes, songs, and games.1
Examples:
Counting from 1 to 10 aloud: "One, two, three, four, five, six, seven, eight, nine, ten." This is an
example of rote counting where the sequence of numbers is memorized and recited.
A teacher asking students to count the number of days in a week verbally: "How many days are
there in a week? One, two, three, four, five, six, seven." This helps students learn the sequence of
numbers and their corresponding days.2
Object Counting
Object counting involves counting tangible items or objects. This method helps in visualizing the
quantity being counted and involves the principles of correspondence and cardinality.
Correspondence means assigning one number to each object, while cardinality refers to
understanding that the last number counted represents the total quantity in a set.3
Examples:
Counting apples in a basket: "There are three apples in the basket." Here, each apple is counted
once, and the final number represents the total number of apples.
A child counting blocks: "I have five blocks stacked here." The child physically touches or
moves each block while counting to keep track of the number of items in the set.
1.3 Briefly contrast:
1.3.1) order irrelevance (3)
Definition: The principle of order irrelevance states that the outcome of a process or
operation does not depend on the sequence in which the elements are arranged. This
, concept is crucial in mathematics and logic, where the order of operations can often be
rearranged without affecting the final result.
Example: In addition, a + b is equal to b + a, demonstrating that the order of operands
does not affect the result. This principle is a fundamental aspect of commutative
operations, which are operations where the order of the operands does not change the
outcome.
1.3.2) movement is magnitude (3)
Definition: This concept suggests that movement can be quantified and is often
represented in terms of magnitude, which refers to the size or extent of the movement. In
physics, magnitude is a scalar quantity that represents the size of a vector, such as
displacement, velocity, or force, without regard to its direction.
Example: In physics, the distance traveled by an object can be measured in meters,
indicating the magnitude of its movement. This quantification allows for precise
calculations and predictions about the behavior of moving objects.
1.3.3) abstraction (3)
Definition: Abstraction involves simplifying complex systems by focusing on the
essential features while ignoring the irrelevant details. This process is fundamental in
various fields, including computer science, mathematics, and philosophy, where it helps
in managing complexity by creating models or representations that capture the core
aspects of a system.1
Example: In programming, an abstract class defines a template for other classes without
providing a complete implementation, allowing for flexibility and reuse. Abstraction
allows programmers to handle complexity by breaking down systems into more
manageable parts, focusing on the interactions and relationships between these parts
rather than the details of their implementation.
(CORRECT ANSWERS)
2025 - DUE 26 July 2025
ALL QUESTIONS ANSWERED.
QUESTION 1 (42 marks)
1.1 Explain the concept “number sense” and its development. (3)
Number sense refers to a person's ability to understand, interpret, and work with numbers. It
encompasses a range of skills and concepts that allow individuals to make sense of numerical
information and apply it in various contexts. This intuitive understanding of numbers
includes recognizing their size, relationships, and the ability to work flexibly with them in
problem situations, which is crucial for making sound decisions and reasonable judgments.1
Key Components of Number Sense
Number Recognition: The ability to identify and name numbers.
Understanding Quantity: Grasping the concept of how many items are in a set.
Estimation: Making reasonable guesses about quantities or calculations.
Number Relationships: Understanding how numbers relate to one another (e.g., greater than,
less than).
1.2 Distinguish between verbal and object counting giving, two (2) examples for each (10)
Counting can be categorized into two main types: verbal counting and object counting. Here’s a
breakdown of each type along with examples.
Verbal Counting
,Verbal counting, also known as rote counting, refers to the process of counting using spoken or
written words without the need for physical objects. It often involves reciting numbers in
sequence. This type of counting is closely related to language development and is typically
learned through repetition and memorization, often in the form of rhymes, songs, and games.1
Examples:
Counting from 1 to 10 aloud: "One, two, three, four, five, six, seven, eight, nine, ten." This is an
example of rote counting where the sequence of numbers is memorized and recited.
A teacher asking students to count the number of days in a week verbally: "How many days are
there in a week? One, two, three, four, five, six, seven." This helps students learn the sequence of
numbers and their corresponding days.2
Object Counting
Object counting involves counting tangible items or objects. This method helps in visualizing the
quantity being counted and involves the principles of correspondence and cardinality.
Correspondence means assigning one number to each object, while cardinality refers to
understanding that the last number counted represents the total quantity in a set.3
Examples:
Counting apples in a basket: "There are three apples in the basket." Here, each apple is counted
once, and the final number represents the total number of apples.
A child counting blocks: "I have five blocks stacked here." The child physically touches or
moves each block while counting to keep track of the number of items in the set.
1.3 Briefly contrast:
1.3.1) order irrelevance (3)
Definition: The principle of order irrelevance states that the outcome of a process or
operation does not depend on the sequence in which the elements are arranged. This
, concept is crucial in mathematics and logic, where the order of operations can often be
rearranged without affecting the final result.
Example: In addition, a + b is equal to b + a, demonstrating that the order of operands
does not affect the result. This principle is a fundamental aspect of commutative
operations, which are operations where the order of the operands does not change the
outcome.
1.3.2) movement is magnitude (3)
Definition: This concept suggests that movement can be quantified and is often
represented in terms of magnitude, which refers to the size or extent of the movement. In
physics, magnitude is a scalar quantity that represents the size of a vector, such as
displacement, velocity, or force, without regard to its direction.
Example: In physics, the distance traveled by an object can be measured in meters,
indicating the magnitude of its movement. This quantification allows for precise
calculations and predictions about the behavior of moving objects.
1.3.3) abstraction (3)
Definition: Abstraction involves simplifying complex systems by focusing on the
essential features while ignoring the irrelevant details. This process is fundamental in
various fields, including computer science, mathematics, and philosophy, where it helps
in managing complexity by creating models or representations that capture the core
aspects of a system.1
Example: In programming, an abstract class defines a template for other classes without
providing a complete implementation, allowing for flexibility and reuse. Abstraction
allows programmers to handle complexity by breaking down systems into more
manageable parts, focusing on the interactions and relationships between these parts
rather than the details of their implementation.
