Dear Reader,

Perhaps you belong to the group of people I have just mentioned in the title of this post. Perhaps you know someone who fits the title. If so, I have written this letter just for you or your friend. Enjoy! 

Hello, Reader. I have an understanding that you have some sort of hatred towards using units in word problems, not only in your math classes but also your science classes. Maybe, you’re just too lazy to add an extra word after your final answer that took you so many steps to arrive at. You’re more proud of the fact that you got the answer than the fact that you can identify what that number represents in the context of the problem. Well, let me tell you something. Good job! Good job in arriving at the correct numerical value. Good job at having confidence in your answer. But, here’s the thing: you’re still wrong. But I’ll get to that later.

For now, let’s talk about today. Today is a very special day. It is my day! You know what I mean. I’m turning 536,457,600! What? You don’t believe me? You’re saying that humans haven’t even been around that long? Well, I beg to differ. Let me rephrase my statement: at some moment today, I will have existed on the earth for 536,457,600 seconds. It’s true. Who said age had to be measured in years? 

Did you get my little joke? (I mean everything I said is true, but I said it all for a reason) Did you laugh at it? Did it annoy you… just like it annoys your teacher when you refuse to put the units in your final answer? If my teacher’s question was my age, then I could have said 536,457,600 and claimed that my answer is correct. That’s what some students do on tests and quizzes. They write a number and then circle it, marking it as their final answer. If the correct answer to a question is 10 feet, but you simply write 10, the teacher could just assume you meant 10 hands because there is no evidence to prove him/her otherwise. Similarly, when I first mentioned my age, you probably assumed I was talking in years, because that is the conventional way to express age. However, “conventional” does not mean “required” or “as the law dictates.” So I am completely allowed to express my age as I wish. 

Let’s look at this in a different light. Four apples plus four apples equal? Let’s assume you say eight. Then, I say that’s wrong. Your answer is incomplete. Four shoes plus four shoes equal? Again, you say eight. And again, I say you’re wrong. Now I ask, four thousand plus four thousand equals? Did you say eight thousand? Why not just say eight like the previous times? Then you say, before we were talking about items and now we’re talking about numbers. Plus, how could four thousand plus four thousand equal eight? Well… that’s what I’m saying! How could four apples plus four apples equal eight? In the “thousand” case, the thousands are used as units of counting. Similarly, apples are units of counting. If you read my post about complex numbers (click here), you learned about the imaginary number line and how it works sort of like the real number line. There, you can add one i and one i to get two i, not two. If you plot 2 and 2i on the complex plane you get two entirely different points. 

My point is that eight stays eight and two stays two as a numerical value. But word problems or real world scenarios (or any context for that matter) involve more than just numerical values. Eight in one context can be entirely different from eight in another context. A number may not have much meaning on its own. 

Here’s what this all boils down to. If your teacher takes off points for not including units where needed, he/she has a valid reason to do so. If you still want to complain, then I haven’t done a good job with my explanation. But here’s what I say: don’t complain, stay mathemagical 🙂

-Yours Truly