,MIP1502 Assignment 2 (COMPLETE ANSWERS) Semester
1 2025 - DUE 30 June 2025; 100% correct solutions and
explanations.
Question 1
1.1 Introducing Algebraic Thinking in the Foundation and
Intermediate Phases
1.1.1 Pedagogical Benefits of Early Algebra Exposure (4 marks)
1. Development of Generalisation Skills: Early exposure to algebra
helps learners recognise patterns and relationships in numbers,
fostering the ability to generalise mathematical ideas. This
supports logical thinking and helps students understand that
mathematics is not just about specific numbers but about structures
and relationships.
2. Bridging Arithmetic and Algebra: Introducing algebraic thinking
early enables learners to transition smoothly from concrete
arithmetic operations to abstract algebraic expressions. It
demystifies symbols and prepares learners for the symbolic
reasoning required in senior grades.
1.1.2 Common Misconception and Its Address (3 marks)
Misconception: Learners often believe that the equal sign (=)
means “the answer is” rather than a symbol representing
equivalence between two expressions.
Addressing It: Teachers can address this by using balance scales
or number sentences like 4 + 3 = 2 + 5 to illustrate that both sides
must be equal. Regular exposure to equations in different forms
(e.g., 7 = 3 + 4) helps reinforce the relational meaning of the equal
sign.
1.1.3 Justification for Early Algebra Supporting Progression (3
marks)
, Early algebra lays the foundation for more complex algebraic concepts
such as variables, expressions, and equations in later grades. By
engaging in pattern recognition, generalisations, and symbolic
reasoning, learners develop cognitive structures that facilitate deeper
understanding of functions and problem-solving strategies in formal
algebra.
1.2 Mini-Lesson on Multiplying Negative Numbers
Objective: Understand why multiplying two negative numbers results in
a positive number.
1.2.1 Real-World Context (2 marks)
Imagine a submarine diving below sea level. If it descends 5 meters
every minute for 3 minutes, the change in depth is 3 × (-5) = -15 meters.
But if we think about rewinding time by 3 minutes (negative time), we
get -3 × (-5) = +15—meaning the submarine goes up 15 meters.
1.2.2 Visual Model (2 marks)
Use a number line. Start at 0. Show repeated subtraction moving left for
3 × (-2) = -6. Then reverse direction for -3 × (-2) by changing direction
of multiplication—moving right 3 times by +2 to land on +6.
1.2.3 Pattern-Based Reasoning (2 marks)
Let’s look at this pattern:
CopyEdit
3 × -2 = -6
2 × -2 = -4
1 × -2 = -2
0 × -2 = 0
-1 × -2 = +2
1 2025 - DUE 30 June 2025; 100% correct solutions and
explanations.
Question 1
1.1 Introducing Algebraic Thinking in the Foundation and
Intermediate Phases
1.1.1 Pedagogical Benefits of Early Algebra Exposure (4 marks)
1. Development of Generalisation Skills: Early exposure to algebra
helps learners recognise patterns and relationships in numbers,
fostering the ability to generalise mathematical ideas. This
supports logical thinking and helps students understand that
mathematics is not just about specific numbers but about structures
and relationships.
2. Bridging Arithmetic and Algebra: Introducing algebraic thinking
early enables learners to transition smoothly from concrete
arithmetic operations to abstract algebraic expressions. It
demystifies symbols and prepares learners for the symbolic
reasoning required in senior grades.
1.1.2 Common Misconception and Its Address (3 marks)
Misconception: Learners often believe that the equal sign (=)
means “the answer is” rather than a symbol representing
equivalence between two expressions.
Addressing It: Teachers can address this by using balance scales
or number sentences like 4 + 3 = 2 + 5 to illustrate that both sides
must be equal. Regular exposure to equations in different forms
(e.g., 7 = 3 + 4) helps reinforce the relational meaning of the equal
sign.
1.1.3 Justification for Early Algebra Supporting Progression (3
marks)
, Early algebra lays the foundation for more complex algebraic concepts
such as variables, expressions, and equations in later grades. By
engaging in pattern recognition, generalisations, and symbolic
reasoning, learners develop cognitive structures that facilitate deeper
understanding of functions and problem-solving strategies in formal
algebra.
1.2 Mini-Lesson on Multiplying Negative Numbers
Objective: Understand why multiplying two negative numbers results in
a positive number.
1.2.1 Real-World Context (2 marks)
Imagine a submarine diving below sea level. If it descends 5 meters
every minute for 3 minutes, the change in depth is 3 × (-5) = -15 meters.
But if we think about rewinding time by 3 minutes (negative time), we
get -3 × (-5) = +15—meaning the submarine goes up 15 meters.
1.2.2 Visual Model (2 marks)
Use a number line. Start at 0. Show repeated subtraction moving left for
3 × (-2) = -6. Then reverse direction for -3 × (-2) by changing direction
of multiplication—moving right 3 times by +2 to land on +6.
1.2.3 Pattern-Based Reasoning (2 marks)
Let’s look at this pattern:
CopyEdit
3 × -2 = -6
2 × -2 = -4
1 × -2 = -2
0 × -2 = 0
-1 × -2 = +2
