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Choosing Variables Wisely

Lesson Plans > Mathematics > Algebra
 

Choosing Variables Wisely

After discussing with my Algebra students what a variable is (recommended, read Variables as Pronouns), I spend some time talking about what letters we use as variables. I usually begin by pointing out that we can use either upper case or lower case letters as variables, but it's important to remember that a lower case a and an upper case A are not the same thing, and they cannot use them interchangeably. I tell them, if the problem has a lower case m and your answer is M = 12, I'll mark it wrong, even if 12 is the right answer!

I tell them that, especially in science classes, they may run into equations that include both upper and lower case of the same letter. If they haven't trained themselves to never switch between the two, they'll never be able to solve correctly.

Once I've gone over that, I ask, "Do you think there are any letters you shouldn't use as variables?" Often they'll give me a blank look that says, "Why are you asking us? We don't know anything about variables!"

So then I say, "For example, I definitely would avoid using the letter O as a variable." Usually someone will be quick to say, "Because it looks like a zero!" Then the fun begins, as I let the students try to identify which letters it would be a bad idea to use. Sometimes they'll make a suggestion of a letter to avoid, and I'll tell them, "Well, you can use that letter, as long as you write it a certain way." Below is the list that my class usually comes up with, and my comments are listed in parentheses.

b ⇒ looks like a six. (this letter gets used a lot in text books, so you won't be able to avoid it. Just make sure you put a good tail or square corner on the upright, and don't curl the top at all).

g ⇒ looks like a nine. (in Physics you'll have to use g, so make sure you put a nice curl on it, that goes below the line, and make sure your nine doesn't have a curl!)

l ⇒ looks like a one. (unless you write a script l, or switch to upper case)

o ⇒ looks like a zero

q ⇒ looks like a nine (put a backwards curl on the bottom of the q)

s ⇒ looks like a five (if you have to use it, make sure it's all curves, and make sure you always make fives with square corners)

t ⇒ looks like a plus sign (unless you put a curl on the bottom.)

z ⇒ looks like a two (recommendation: put a slash through the z, so it's clearly not a two)

After going through the alphabet, I share a few more things with them:

  • There are a couple letters I want them to avoid because they have a special meaning in math. Those letters are and e.
  • Sometimes they don't have a choice; if the textbook specifies the variable, you have to use the variable they stated. In that case, you just have to be very careful in your writing!
  • At the end of the alphabet, when we talk about putting a slash through the letter z, I also mention that I usually put a slash through my sevens as well. I give them an opportunity to try to guess why. Usually they don't guess it. I do it out of habit, mainly, but I encourage students to do the same because I've seen students whose handwriting is messy enough that they can't distinguish between a seven and a greater-than symbol!
  • Eventually, I tell them, mathematics and science get so complex that we don't have enough letters in our alphabet, so we start borrowing letters from the Greek alphabet to use as variables. So when they take geometry and start seeing things like α and β, they shouldn't freak out; those are just variables, and they work just like a and b.
Lesson by Mr. Twitchell

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