First off I admit that I was never particularly good at math once I reached calculus. But what bothered me all along was not understanding the real world examples. Yes, some math sets have word problems, but not nearly enough. Wouldn’t it be great if instead of just doing problem sets (yes I know these are necessary) each set included several real world examples as did exams.
For example, I asked ChatGPT to do just that for Algebra I and Calculus.
My prompt for Algebra I was:
Can you give me five examples of how I can connect an Algebra I class to real world examples. Include both the Virginial SOL that is being taught and the real world example.
One example I got for this was
Scenario: You’re budgeting for a party. You have $200, and decorations cost $50. Each guest will cost $15 for food. Write and solve an equation to find how many guests you can invite.
Equation: 15x+50=20015x + 50 = 20015x+50=200
Connection: Students learn to solve for xxx to figure out how many people they can host within their budget.
One example of Calculus is:
Topic: Solve optimization problems using derivatives.
Real-World Example:
Scenario: Maximizing profit for a business. A company sells a product for p(x)=100−2xp(x) = 100 - 2xp(x)=100−2x dollars per unit, where xxx is the number of units sold, and the cost to produce xxx units is C(x)=20x+200C(x) = 20x + 200C(x)=20x+200. Maximize the profit P(x)=R(x)−C(x)=(100−2x)x−(20x+200)P(x) = R(x) - C(x) = (100 - 2x)x - (20x + 200)P(x)=R(x)−C(x)=(100−2x)x−(20x+200).
Mathematical Concept: Differentiate P(x)P(x)P(x), find critical points by solving P′(x)=0P'(x) = 0P′(x)=0, and confirm maxima using the second derivative.
Connection: This gives businesses insight into how many units to sell to maximize profits.
Does this seem more understandable and something that we should institute in all classes that do not yet have it? The amazing thing is that the changes can be done so quickly by a teacher for an assignment. I would even hazard to guess that the largest learning management systems such as PowerSchool (Schoology) and Instructure (Canvas) are already working on integrating a button to allow for multiple assignments to be made instantaneously and in conjunction with universal design for learning principles (more on this in future posts).
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