ACI2605
ASSIGNMENT 3 2025
UNIQUE NO. 891101
DUE DATE: 3 JULY 2025
,ACI2605 ASSIGNMENT 3 ANSWERS (891101) Due Date: 3 July 2025
QUESTION 1: The History of Numbers
1.1 Critical Analysis of Steen’s Definition
1.1.1 Binary Number System (10 marks)
Steen (1988) describes mathematics as the study of patterns, and the binary number
system perfectly illustrates this. Binary is a base-2 system using only 0 and 1. Every
binary number represents a pattern of powers of 2. For example, 1011₂ = 1×8 + 0×4 +
1×2 + 1×1 = 11₁₀. In digital technology, binary patterns are essential for storing and
processing data. Binary patterns help define logical operations (e.g., AND, OR, NOT)
used in programming and circuit design. Steen’s emphasis on functions and morphisms
reflects how binary systems use specific operations to transform and manipulate these
patterns, creating consistent and predictable systems, aligning well with his concept of
mathematical structures.
1.1.2 Decimal Number System (10 marks)
The decimal system, or base-10, is the most widely used number system, reflecting
patterns through place value (e.g., units, tens, hundreds). Steen’s idea of finding
patterns aligns with the way we calculate, represent, and manipulate numbers in this
system. For example, the number 534 = 5×100 + 3×10 + 4×1 shows a pattern of powers
of 10. Arithmetic operations (like long division and carrying in addition) also follow
structured, repeatable steps that form mathematical patterns. These patterns are
foundational for developing number sense and for advanced algebraic thinking,
reinforcing Steen’s perspective that mathematics is about identifying and applying
patterns.
QUESTION 2: Unit - Rate
, 2.1 Scenario-Based
2.1.1 Equation (5 marks)
Let m = morning drive time in minutes
Afternoon drive = 1.5 * m
Total time t = m + 1.5m = 2.5m
2.1.2 Graphing Explanation (5 marks)
To graph t = 2.5m:
X-axis = m (morning minutes)
Y-axis = t (total time)
It’s a straight line through the origin (0,0) with slope 2.5
Yes, the points should be connected, as both time values (morning and total)
are continuous variables and not limited to whole numbers.
2.1.3 Five Guidelines for Teaching Unit Rate (10 marks)
1. Use real-life examples: like speed (km/h), price per kg, etc.
2. Visual aids: Use double number lines and tables.
3. Interactive learning: Let learners experiment with different quantities.
4. Focus on reasoning: Encourage learners to explain how they found unit rates.
5. Gradual complexity: Start simple and build up to more complex ratios.
QUESTION 3: Number Sense
3.1 Four Components (8 marks)
1. Understanding number meaning – Knowing what numbers represent.
2. Number relationships – Knowing doubles, halves, and patterns.
3. Number magnitude – Ability to estimate or compare values.
4. Operations understanding – Predicting outcomes of addition, subtraction, etc.
ASSIGNMENT 3 2025
UNIQUE NO. 891101
DUE DATE: 3 JULY 2025
,ACI2605 ASSIGNMENT 3 ANSWERS (891101) Due Date: 3 July 2025
QUESTION 1: The History of Numbers
1.1 Critical Analysis of Steen’s Definition
1.1.1 Binary Number System (10 marks)
Steen (1988) describes mathematics as the study of patterns, and the binary number
system perfectly illustrates this. Binary is a base-2 system using only 0 and 1. Every
binary number represents a pattern of powers of 2. For example, 1011₂ = 1×8 + 0×4 +
1×2 + 1×1 = 11₁₀. In digital technology, binary patterns are essential for storing and
processing data. Binary patterns help define logical operations (e.g., AND, OR, NOT)
used in programming and circuit design. Steen’s emphasis on functions and morphisms
reflects how binary systems use specific operations to transform and manipulate these
patterns, creating consistent and predictable systems, aligning well with his concept of
mathematical structures.
1.1.2 Decimal Number System (10 marks)
The decimal system, or base-10, is the most widely used number system, reflecting
patterns through place value (e.g., units, tens, hundreds). Steen’s idea of finding
patterns aligns with the way we calculate, represent, and manipulate numbers in this
system. For example, the number 534 = 5×100 + 3×10 + 4×1 shows a pattern of powers
of 10. Arithmetic operations (like long division and carrying in addition) also follow
structured, repeatable steps that form mathematical patterns. These patterns are
foundational for developing number sense and for advanced algebraic thinking,
reinforcing Steen’s perspective that mathematics is about identifying and applying
patterns.
QUESTION 2: Unit - Rate
, 2.1 Scenario-Based
2.1.1 Equation (5 marks)
Let m = morning drive time in minutes
Afternoon drive = 1.5 * m
Total time t = m + 1.5m = 2.5m
2.1.2 Graphing Explanation (5 marks)
To graph t = 2.5m:
X-axis = m (morning minutes)
Y-axis = t (total time)
It’s a straight line through the origin (0,0) with slope 2.5
Yes, the points should be connected, as both time values (morning and total)
are continuous variables and not limited to whole numbers.
2.1.3 Five Guidelines for Teaching Unit Rate (10 marks)
1. Use real-life examples: like speed (km/h), price per kg, etc.
2. Visual aids: Use double number lines and tables.
3. Interactive learning: Let learners experiment with different quantities.
4. Focus on reasoning: Encourage learners to explain how they found unit rates.
5. Gradual complexity: Start simple and build up to more complex ratios.
QUESTION 3: Number Sense
3.1 Four Components (8 marks)
1. Understanding number meaning – Knowing what numbers represent.
2. Number relationships – Knowing doubles, halves, and patterns.
3. Number magnitude – Ability to estimate or compare values.
4. Operations understanding – Predicting outcomes of addition, subtraction, etc.
