ACI2605
ASSIGNMENT 3 2025
UNIQUE NO. 891101
DUE DATE: 3 JULY 2025
,Teaching Numbers and Operations in the Intermediate Phase
QUESTION 1: The History of Numbers
1.1 Critical Analysis of Steen’s Definition
1.1.1 Binary Number System (10) Steen (1988) defines mathematics as the study of
patterns, and this aptly applies to the binary number system, which uses only two digits
(0 and 1). Binary patterns underpin the functionality of digital computers, where
sequences of 0s and 1s represent logical states. The binary system illustrates
mathematical structure through functions and operators in computing. For example, in
binary, the number 5 is represented as 101, which demonstrates pattern recognition in
powers of 2. Steen’s focus on maps and morphisms is observed in logic gates and
Boolean algebra that manipulate binary data to perform operations. Thus, the binary
number system exemplifies how mathematics explains and structures patterns that form
the foundation of digital technology.
1.1.2 Decimal Number System (10) The decimal system, based on base-10, is the
most commonly used number system in daily life. Steen’s notion of patterns aligns with
the place-value structure of decimal numbers, where each digit’s position represents a
power of 10. For instance, the number 345 consists of 3 hundreds, 4 tens, and 5 units.
Patterns emerge in operations such as multiplication tables and decimal expansions.
Additionally, functions such as addition and multiplication reveal consistent structural
patterns, reinforcing Steen’s idea of mathematics as a science of pattern. In teaching,
recognizing these patterns helps learners develop number sense and computational
fluency, aligning with Steen’s definition.
QUESTION 2: Unit - Rate
2.1 Scenario-Based Questions
, 2.1.1 Equation (5) Let m be the number of minutes in the morning drive. Since the
afternoon drive takes 1.5 times longer, it will be 1.5m. The total time t each day is:
t = m + 1.5m = 2.5m
2.1.2 Graph Explanation (5) When graphing the equation t = 2.5m on a coordinate
plane:
The x-axis represents morning drive time (m).
The y-axis represents total drive time (t).
The graph is a straight line through the origin (0,0). Yes, the points should be
connected because time is a continuous variable; the bus can take any number
of minutes (not just whole numbers), so the line represents all possible values.
2.1.3 Five Guidelines for Introducing Unit Rate (10)
1. Use relatable contexts: Scenarios such as price per item, speed, or cooking
measurements help learners grasp the concept.
2. Incorporate visual aids: Use tables, number lines, and graphs to show
relationships.
3. Encourage exploration: Let learners manipulate quantities to see how ratios
change.
4. Connect to real-life decisions: Compare unit prices to decide best buys.
5. Promote discussion: Ask learners to explain their reasoning and solutions.
QUESTION 3: Number Sense
3.1 Four Components of Number Sense (8)
1. Number meaning: Understanding what numbers represent (e.g., 5 as five
apples).
ASSIGNMENT 3 2025
UNIQUE NO. 891101
DUE DATE: 3 JULY 2025
,Teaching Numbers and Operations in the Intermediate Phase
QUESTION 1: The History of Numbers
1.1 Critical Analysis of Steen’s Definition
1.1.1 Binary Number System (10) Steen (1988) defines mathematics as the study of
patterns, and this aptly applies to the binary number system, which uses only two digits
(0 and 1). Binary patterns underpin the functionality of digital computers, where
sequences of 0s and 1s represent logical states. The binary system illustrates
mathematical structure through functions and operators in computing. For example, in
binary, the number 5 is represented as 101, which demonstrates pattern recognition in
powers of 2. Steen’s focus on maps and morphisms is observed in logic gates and
Boolean algebra that manipulate binary data to perform operations. Thus, the binary
number system exemplifies how mathematics explains and structures patterns that form
the foundation of digital technology.
1.1.2 Decimal Number System (10) The decimal system, based on base-10, is the
most commonly used number system in daily life. Steen’s notion of patterns aligns with
the place-value structure of decimal numbers, where each digit’s position represents a
power of 10. For instance, the number 345 consists of 3 hundreds, 4 tens, and 5 units.
Patterns emerge in operations such as multiplication tables and decimal expansions.
Additionally, functions such as addition and multiplication reveal consistent structural
patterns, reinforcing Steen’s idea of mathematics as a science of pattern. In teaching,
recognizing these patterns helps learners develop number sense and computational
fluency, aligning with Steen’s definition.
QUESTION 2: Unit - Rate
2.1 Scenario-Based Questions
, 2.1.1 Equation (5) Let m be the number of minutes in the morning drive. Since the
afternoon drive takes 1.5 times longer, it will be 1.5m. The total time t each day is:
t = m + 1.5m = 2.5m
2.1.2 Graph Explanation (5) When graphing the equation t = 2.5m on a coordinate
plane:
The x-axis represents morning drive time (m).
The y-axis represents total drive time (t).
The graph is a straight line through the origin (0,0). Yes, the points should be
connected because time is a continuous variable; the bus can take any number
of minutes (not just whole numbers), so the line represents all possible values.
2.1.3 Five Guidelines for Introducing Unit Rate (10)
1. Use relatable contexts: Scenarios such as price per item, speed, or cooking
measurements help learners grasp the concept.
2. Incorporate visual aids: Use tables, number lines, and graphs to show
relationships.
3. Encourage exploration: Let learners manipulate quantities to see how ratios
change.
4. Connect to real-life decisions: Compare unit prices to decide best buys.
5. Promote discussion: Ask learners to explain their reasoning and solutions.
QUESTION 3: Number Sense
3.1 Four Components of Number Sense (8)
1. Number meaning: Understanding what numbers represent (e.g., 5 as five
apples).
