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MFP1501 Assignment 3 2023 - DISTINCTION
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MFP1501 Assignment 32023
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, Question 1
In this MFP1501, we refer to mathematical modelling as the process whereby we use abstractions of
mathematics to solve problems in the real world. For example, there are 21 learners in Grade 5 that will
go on an excursion to Zoo Lake. If one car will take a maximum of 6 learners, how many cars do we need
to carry everyone? You may use one car to work out 21 divided by 6. This will give you 3,5. So, you
would need 4 cars. Haylock (2014) argues that there are four steps involved in this reasoning.
In step 1, a problem in the real world is translated into a problem expressed in mathematical symbols
(21÷6, in this case).
In step 2, the mathematical symbol is manipulated to obtain a mathematical solution (3,5).
Step 3 is to interpret the mathematical solution back in the real world (3 cars, and a half). The final step
is to check the answer against the constraints of the original solution. In this case, since you cannot have
half of a car, the appropriate conclusion is that you need 4 cars.
1.1 Summarise the process of mathematical modelling by first drawing a diagram similar to Figure 3.1 in
the study guide. N. B it should not be the same. Be creative. (8)
The process of mathematical modeling involves several steps:
1. Problem Identification: Identify a real-world problem that can be solved using
mathematical concepts and techniques. This could be any situation where you need to
make predictions, optimize a system, or understand a phenomenon.
2. Mathematical Formulation: Translate the real-world problem into a mathematical model
by representing the relevant variables, parameters, and relationships using mathematical
symbols and equations. This step involves defining the problem in terms of
mathematical operations and functions.
3. Solution Techniques: Apply mathematical methods and techniques to manipulate and
solve the mathematical model. This may involve algebraic manipulation, calculus,
optimization methods, or statistical analysis, depending on the nature of the problem.
4. Interpretation: Interpret the mathematical solution in the context of the real-world
problem. This step involves translating the mathematical results back into meaningful
terms that can be understood and applied in the original problem domain. It requires
making connections between the mathematical quantities and the real-world quantities
they represent.
5. Validation and Evaluation: Validate the mathematical solution by comparing it to real-
world data or using other means of evaluation. Check if the solution satisfies the
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