Out of the concepts you have studied in this course, choose one that you feel would be particularly difficult for students to understand. Provide a concrete real-world situation or example to help illustrate this concept.

Rational Numbers and Proportional Reasoning in the Real World

Two of the concepts that I feel would be particularly difficult for students to understand are rational numbers and proportional reasoning. To help illustrate this concept, let’s consider a concrete example. Suppose you are looking at two different cars. Car A is $20,000, and Car B is $30,000. Now, let’s say you have $24,000 to spend. Which car should you buy? Car A is clearly the better option here because it is cheaper and within the budget. But let’s say you want Car B. In this case, the buyer could try to negotiate with the seller. The buyer could reason that since Car A is only $20,000, and they are willing to pay $24,000 for Car B, then perhaps the seller would be willing to sell Car B for $22,000.

And what if we looked at it from a different perspective? Let’s say that Car A gets 30 miles per gallon, and Car B gets 20 miles per gallon. Now, let’s say that gas costs $0.50 per gallon. If we look at it from this perspective, it is clear that Car B is the better option. Even though it is more expensive upfront, one will save money in the long run because it is more fuel-efficient.

How about the other features? Car A has a sunroof, and Car B does not. From this perspective, it depends on what the buyer is looking for in a car. If the buyer wants a sunroof, then Car A is the better option. In contrast, if the buyer does not care so much about a sunroof, then Car B is the better option.

In summary, it’s all about perspective. Therefore, when dealing with rational numbers and proportional reasoning, it is essential to be able to see things from different perspectives to make the best decision. Using rational numbers, one can argue that Car A is a better deal because it is cheaper. But using proportional reasoning, one can see that Car B is actually the better deal because it will save the buyer money in the long run.

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References

Billstein, R., Libeskind, S., & Lott, J. (2013). Problem Solving Approach to Mathematics for Elementary School Teachers, A: Pearson New International Edition PDF eBook. Pearson Higher Ed.