MFP1501 Assignment 3 2023 (ANSWERS)
QUESTIONS ASKED:
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 Z...
, 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. 1.1Summarise the process of mathematical modelling by first
drawing a diagram similar to Figure 3.2 in the study guide. N. B it should not be the
same. Be creative. (8) 1.2In each of the steps in your diagram make use of practical
examples that will translate into your scenario of using abstractions of mathematics
to solve problems in the real world. (15)
1.1 Diagram for the Process of Mathematical Modelling
You can create a diagram that illustrates the four-step process of mathematical modeling
by using four circles or any other shapes, each representing a different step in the
process. Connect them sequentially with arrows to show the flow of the process.
1. Step 1: Real-World Problem to Mathematical Expression (You could represent
this with a circle containing an image of a car and learners, connecting to a
mathematical expression)
2. Step 2: Mathematical Manipulation (A circle with mathematical symbols or a
calculator)
3. Step 3: Interpretation of the Mathematical Solution (A circle with both numbers
and real-world objects, like 3.5 cars)
4. Step 4: Check Against Original Constraints (A circle with a tick or cross symbol,
indicating the validation of the solution)
1.2 Practical Examples for Each Step
Here's a description of each step using the practical example in the question.
1. Step 1: Real-World Problem to Mathematical Expression
Example: You have 21 learners going to the Zoo Lake and one car can carry
a maximum of 6 learners. You express this problem mathematically as
21÷621÷6.
2. Step 2: Mathematical Manipulation
Example: Divide 21 by 6 using mathematical operations, which yields 3.5.
This tells you that 3 full cars will be needed, and a fourth car will be half full.
3. Step 3: Interpretation of the Mathematical Solution
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