TMS3725
ASSIGNMENT 3 2025
DUE: 28 JULY 2025 (MEMO)
,TMS3725
ASSIGNMENT 3
Due date: 28 July 2025
Unique assignment number: 226392
QUESTION 1 [14 marks]
1.1.1 What is mathematical modelling? (
Mathematical modelling is the process of representing real-world phenomena or
problems using mathematical concepts, symbols, and structures. It involves translating
a contextual or everyday situation into a mathematical form such as equations, graphs,
or tables to understand, analyze, and solve it (DBE, 2003). According to the teaching
notes, it often begins by understanding the context, setting up a model (e.g., through a
table), solving the equation, and then interpreting the results back in the real-world
context. This approach allows learners to see the relevance and application of
mathematics in daily life (NCTM, 1989).
Using the formula distance = speed × time to solve a travel-related problem is a form of
modelling.
1.1.2 What are the advantages of mathematical modelling? (5)
Real-life application: It helps learners connect abstract mathematical concepts with real-
world problems, enhancing their understanding (DBE, 2003).
Conceptual development - Modelling supports conceptual understanding by linking
various mathematical representations and showing their interconnections (Presmeg,
2006).
, Critical thinking - Learners engage in higher-order thinking and problem-solving as
they analyze and interpret contextual data (NCTM, 1989).
Engagement and motivation - Using familiar, practical scenarios, modelling fosters
interest and makes mathematics more meaningful (DBE, 2003).
Supports mathematical literacy - Modelling prepares learners to describe and
analyze situations mathematically, contributing to their development as
mathematically literate citizens (DBE, 2003, p. 10).
1.1.3 What are the limitations of mathematical modelling? (5)
Complexity of real-world problems -Not all real-life situations can be accurately
simplified or represented mathematically, leading to oversimplified or unrealistic
models (DBE, 2003).
Misinterpretation of results - Learners may misapply mathematical solutions if they do
not critically interpret the results in context (Presmeg, 2006).
Requires foundational knowledge- Effective modelling relies on learners already
having strong mathematical skills and conceptual understanding.
Time-consuming - Developing and solving real-world models can take significant
classroom time, which may limit curriculum coverage.
ASSIGNMENT 3 2025
DUE: 28 JULY 2025 (MEMO)
,TMS3725
ASSIGNMENT 3
Due date: 28 July 2025
Unique assignment number: 226392
QUESTION 1 [14 marks]
1.1.1 What is mathematical modelling? (
Mathematical modelling is the process of representing real-world phenomena or
problems using mathematical concepts, symbols, and structures. It involves translating
a contextual or everyday situation into a mathematical form such as equations, graphs,
or tables to understand, analyze, and solve it (DBE, 2003). According to the teaching
notes, it often begins by understanding the context, setting up a model (e.g., through a
table), solving the equation, and then interpreting the results back in the real-world
context. This approach allows learners to see the relevance and application of
mathematics in daily life (NCTM, 1989).
Using the formula distance = speed × time to solve a travel-related problem is a form of
modelling.
1.1.2 What are the advantages of mathematical modelling? (5)
Real-life application: It helps learners connect abstract mathematical concepts with real-
world problems, enhancing their understanding (DBE, 2003).
Conceptual development - Modelling supports conceptual understanding by linking
various mathematical representations and showing their interconnections (Presmeg,
2006).
, Critical thinking - Learners engage in higher-order thinking and problem-solving as
they analyze and interpret contextual data (NCTM, 1989).
Engagement and motivation - Using familiar, practical scenarios, modelling fosters
interest and makes mathematics more meaningful (DBE, 2003).
Supports mathematical literacy - Modelling prepares learners to describe and
analyze situations mathematically, contributing to their development as
mathematically literate citizens (DBE, 2003, p. 10).
1.1.3 What are the limitations of mathematical modelling? (5)
Complexity of real-world problems -Not all real-life situations can be accurately
simplified or represented mathematically, leading to oversimplified or unrealistic
models (DBE, 2003).
Misinterpretation of results - Learners may misapply mathematical solutions if they do
not critically interpret the results in context (Presmeg, 2006).
Requires foundational knowledge- Effective modelling relies on learners already
having strong mathematical skills and conceptual understanding.
Time-consuming - Developing and solving real-world models can take significant
classroom time, which may limit curriculum coverage.
