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MFP1501 Assignment 3
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MFP1501Assignment 3
(ANSWERS) 2023 -
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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) 1.2 In 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) 4
1. Step 1: Translating the real-world problem into mathematical symbols.
Example: Given that there are 21 learners and each car can carry a
maximum of 6 learners, we represent this as a division problem: 21 ÷
6.
2. Step 2: Manipulating the mathematical symbols to find a solution.
Example: Solving the division problem, we find that 21 ÷ 6 = 3.5.
3. Step 3: Interpreting the mathematical solution back into the real world.
Example: Since we cannot have half a car, we interpret the solution as
needing 4 cars to carry all the learners.
4. Step 4: Checking the answer against the constraints of the original
problem. Example: By considering the constraint that each car can
carry a maximum of 6 learners, we verify that with 4 cars, all 21
learners can be transported.
Question 2 As a mathematics teacher, you are expected to help children
develop multiplicative thinking, which goes beyond repeated addition, as it
may not happen for many learners. It is the intention of MFP1501 learning unit
4 to support you to do so. Jacob and Willis (2003) outline hierarchical phases
through which multiplicative thinking develops, which include one-to-one
counting, additive composition, many-to-one counting, and multiplicative
relations. 2.1 Describe each phase through which multiplicative thinking
develops. (20) 2.2 Motivate your descriptions in 2.1 with practical examples.
(12)
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