UNISA TMN3704 & TMN3705 Exam Bundle | Complete
Practice Questions, Answers & Detailed Solutions
Question 1
What is the primary purpose of the Mathematics curriculum in the
Intermediate Phase (Grades 4–6) according to CAPS?
• A. To train professional theoretical mathematicians and calculus
researchers exclusively
• B. To develop a deep conceptual understanding, computational
fluency, and problem-solving skills applicable in real-life contexts
• C. To replace all language and literacy instruction in primary
schools
• D. To focus entirely on memorizing multiplication tables without
understanding underlying principles
• Correct Answer: B
• Detailed Rationale: The Intermediate Phase mathematics
curriculum aims to build foundational mathematical literacy,
logical reasoning, and problem-solving abilities that learners can
use in everyday life.
Question 2
According to Polya’s four-step problem-solving model, what is the very
first step a learner must undertake when faced with a mathematical
word problem?
, • A. Carry out the calculation immediately without reading the full
text
• B. Understand the problem by identifying what is given, what is
unknown, and the required conditions
• C. Write a formal research paper on number theory
• D. Guess the final answer randomly
• Correct Answer: B
• Detailed Rationale: Polya’s first step is understanding the
problem, ensuring learners comprehend the given data and goals
before attempting any mathematical strategy.
Question 3
What distinguishes conceptual knowledge from procedural knowledge
in mathematics education?
• A. Conceptual knowledge is knowing mathematical algorithms;
procedural knowledge is understanding underlying principles.
• B. Conceptual knowledge involves an understanding of
mathematical relationships, principles, and foundational ideas,
whereas procedural knowledge involves familiarity with rules,
algorithms, and step-by-step methods.
• C. There is no difference between the two forms of knowledge.
• D. Procedural knowledge is only used in secondary school algebra.
• Correct Answer: B
, • Detailed Rationale: Conceptual knowledge focuses on the "why"
behind mathematics, while procedural knowledge focuses on the
"how" (algorithms and computation steps).
Question 4
Which of the following best describes the Van Hiele Level 0
(Visualization) stage of geometric thinking?
• A. Learners analyze properties of shapes and formulate formal
mathematical proofs.
• B. Learners recognize shapes by their holistic appearance or visual
gestalt (e.g., identifying a rectangle because it "looks like a door")
rather than by their formal attributes.
• C. Learners use deductive axiomatic systems.
• D. Learners perform complex coordinate geometry
transformations.
• Correct Answer: B
• Detailed Rationale: At Level 0 (Visualization), children judge
shapes based on their overall visual appearance rather than
analyzing individual properties like parallel sides or equal angles.
Question 5
In the context of teaching whole numbers in Grade 4, what is the
pedagogical value of utilizing base-ten blocks (Dienes blocks)?
• A. They serve as decorative classroom items with no mathematical
purpose.
, • B. They provide a concrete manipulative representation of place
value, grouping, regrouping, and base-ten exchange principles.
• C. They are used exclusively for advanced high school calculus.
• D. They replace all written calculations permanently.
• Correct Answer: B
• Detailed Rationale: Base-ten blocks offer tangible tactile models
that help learners visualize abstract place value concepts (units,
rods, flats, cubes).
Question 6
What is a common misconception learners hold when comparing
1 1
fractions, such as believing that is larger than ?
8 4
• A. They understand that denominators represent equal
partitioning of a whole.
• B. They misapply whole-number thinking, assuming that because
1
8 is larger than 4, the fraction must also be larger.
8
• C. They confuse numerators with exponents.
• D. They correctly convert fractions to percentages every time.
• Correct Answer: B
• Detailed Rationale: Whole-number interference causes learners
to judge fraction magnitude by the size of the denominator alone,
ignoring inverse proportional relationships.
Question 7
Practice Questions, Answers & Detailed Solutions
Question 1
What is the primary purpose of the Mathematics curriculum in the
Intermediate Phase (Grades 4–6) according to CAPS?
• A. To train professional theoretical mathematicians and calculus
researchers exclusively
• B. To develop a deep conceptual understanding, computational
fluency, and problem-solving skills applicable in real-life contexts
• C. To replace all language and literacy instruction in primary
schools
• D. To focus entirely on memorizing multiplication tables without
understanding underlying principles
• Correct Answer: B
• Detailed Rationale: The Intermediate Phase mathematics
curriculum aims to build foundational mathematical literacy,
logical reasoning, and problem-solving abilities that learners can
use in everyday life.
Question 2
According to Polya’s four-step problem-solving model, what is the very
first step a learner must undertake when faced with a mathematical
word problem?
, • A. Carry out the calculation immediately without reading the full
text
• B. Understand the problem by identifying what is given, what is
unknown, and the required conditions
• C. Write a formal research paper on number theory
• D. Guess the final answer randomly
• Correct Answer: B
• Detailed Rationale: Polya’s first step is understanding the
problem, ensuring learners comprehend the given data and goals
before attempting any mathematical strategy.
Question 3
What distinguishes conceptual knowledge from procedural knowledge
in mathematics education?
• A. Conceptual knowledge is knowing mathematical algorithms;
procedural knowledge is understanding underlying principles.
• B. Conceptual knowledge involves an understanding of
mathematical relationships, principles, and foundational ideas,
whereas procedural knowledge involves familiarity with rules,
algorithms, and step-by-step methods.
• C. There is no difference between the two forms of knowledge.
• D. Procedural knowledge is only used in secondary school algebra.
• Correct Answer: B
, • Detailed Rationale: Conceptual knowledge focuses on the "why"
behind mathematics, while procedural knowledge focuses on the
"how" (algorithms and computation steps).
Question 4
Which of the following best describes the Van Hiele Level 0
(Visualization) stage of geometric thinking?
• A. Learners analyze properties of shapes and formulate formal
mathematical proofs.
• B. Learners recognize shapes by their holistic appearance or visual
gestalt (e.g., identifying a rectangle because it "looks like a door")
rather than by their formal attributes.
• C. Learners use deductive axiomatic systems.
• D. Learners perform complex coordinate geometry
transformations.
• Correct Answer: B
• Detailed Rationale: At Level 0 (Visualization), children judge
shapes based on their overall visual appearance rather than
analyzing individual properties like parallel sides or equal angles.
Question 5
In the context of teaching whole numbers in Grade 4, what is the
pedagogical value of utilizing base-ten blocks (Dienes blocks)?
• A. They serve as decorative classroom items with no mathematical
purpose.
, • B. They provide a concrete manipulative representation of place
value, grouping, regrouping, and base-ten exchange principles.
• C. They are used exclusively for advanced high school calculus.
• D. They replace all written calculations permanently.
• Correct Answer: B
• Detailed Rationale: Base-ten blocks offer tangible tactile models
that help learners visualize abstract place value concepts (units,
rods, flats, cubes).
Question 6
What is a common misconception learners hold when comparing
1 1
fractions, such as believing that is larger than ?
8 4
• A. They understand that denominators represent equal
partitioning of a whole.
• B. They misapply whole-number thinking, assuming that because
1
8 is larger than 4, the fraction must also be larger.
8
• C. They confuse numerators with exponents.
• D. They correctly convert fractions to percentages every time.
• Correct Answer: B
• Detailed Rationale: Whole-number interference causes learners
to judge fraction magnitude by the size of the denominator alone,
ignoring inverse proportional relationships.
Question 7
