After almost two decades of taking standardized tests, I still don’t understand why the questions are so ridiculous. Why does Alice need 47 watermelons? Who put two trains on the same track in opposite directions? Does everyone in the room really need to shake hands?
The questions are weird, but I can’t really complain. My test-taking skills got me into college, through college, and even made me some money along the way through tutoring. I’m not half bad at figuring out the probability you pick a red marble out of the bag, which came in handy a little while back.
I was in the passenger seat of a car in a different country, and the time came to fill the tank. When we got to the station, we clicked the button to pay for gas, and the screen instantly lit up with seven different payment amounts for pre-approval. Admittedly, we just kinda stared blankly at it for a minute. You see, as bald-eagle-loving Americans, we were used to the ability to let the pump just fill the tank and just hope it didn’t run over budget, but that wasn’t an option here. Instead, we were forced to select just how much we would approve. I started putting all the details together, and I came up with the following problem:
You are at a gas pump, and you need to fill your tank. Your tank size is roughly 20 gallons, and it is 3/4 empty. There are 3.8 liters in a gallon. The price of gas per liter isn’t listed anywhere, but you see on the screen that the previous customer paid 91 dollars for 54 liters. The options for pre-approval are 20, 30, 50, 70, 90, 100, and 110 dollars. What is the smallest amount you can pre-approve such that your tank will be completely full?
Before I give you the answer, try it yourself with a calculator. To be clear, when I solved it, I didn’t write out the problem; those details are just what was swirling in my head at that moment. I pulled out the calculator app on my phone, pressed a few buttons, and in about 30 seconds, I had my final answer of 100 dollars. We hit the button, started filling the tank, and the actual amount of gas needed to fill the car was worth 97 dollars, which meant my calculations were spot-on.
Solving the problem was fun, but it required a lot more processing than the short paragraph I wrote out. I had to know the unit conversion from gallons to liters. I had to assume the previous customer purchased low-octane fuel because it’s the most common choice. I had to understand how much rounding was just enough. I had to make assumptions about the gas tank. I had to package up all that real-world data into a pretty, little math problem.
To the credit of all the people in math class that said, “we can use a calculator in the real world,” yes, yes we can. They’re in our pockets constantly. However, we still need to understand which numbers are important. Synthesizing that information efficiently is the first step to making math useful in the real world. We can use it whenever, but it only makes sense when we have a real problem to solve. Being able to gather the relevant information from a situation is a useful skill I’m grateful to have practiced through standardized tests, and I’m beginning to appreciate those problems more now.
I still think the problems could be a bit more realistic though. I mean, 47 watermelons? Really?