Math Etiquette VI: Math...Vocabulary?

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What’s the #1 issue students tend to have when answering questions on the Math sections of the SAT or the Math section of the ACT? Is it functions? Ratios? Systems of Linear Equations?

You can guess different math topics until you’re blue in the face and you probably still won’t get it.

Give up?

It’s READING.

Yes, that’s right. Reading. The biggest issue I see with the students who come to me everyday is not a particular type of math that they didn’t learn extensively, it’s their ability to READ the question and extract every single bit of data from each and every word. Believe it or not, a single word can make a TON of difference to your approach of the problem, and ultimately, the correct answer. And we’re all in the game of snagging as many correct answers as possible, yes?

So, I’ve compiled a short list of the hidden clues that can most drastically increase your ability to solve a math question correctly. Think of it like a math-to-English translation guide. You’re welcome!

 

1) “Of” = multiplication

Yes, that two-letter preposition is a goldmine of math lingo. And what’s beautiful about it is how consistent it is. In every single case: “Of” = multiply!

Here’s how simple it is: “A third of the students like kale.” So how many students like kale? Translating "of" into multiplication, we can set up the equation this way: 1/3 x # of students = # of students who like kale.

 

2) “Per” = division; “cent” = 100; “percent” = /100

A percentage is a fraction with a denominator of 100, and you can multiply with it just like any other fraction. So, translating like we just did above, "45% of the Junior class likes squid” turns into this equation: 45/100 x # of juniors = # of squid eaters. 

 

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3) “Percent of “percent more/less than.

Here's a place where paying attention to the vocabulary doesn't just save you time—it can save you important errors. Many students fail to pay attention to the important differences in the wording in these kinds of questions! “Percent of” means you take the % and multiply it.

“Percent more than” or “percent less than” means you find out how much something has changed… and then find what percent THAT CHANGE is of the original!

In other words: 

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If I am 66 inches tall now, but I was only 60 inches tall a few years ago, I am 10% taller than (i.e. 10% more than) I was a few years ago.

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However, if the question asked “Kristina’s current height, in inches, is what percent of her original height?” THAT’s a different question entirely! Translating that sentence word-for-word, in order, the question is telling me to do this:

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If I plug the known numbers in, I get this:

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If I now solve for x, I get: 

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So, my current height is 110% “of”—but only 10% “more than”—my original height!

See how big a difference a preposition or adjective can make?

 

4) “Integer” = a number that does NOT have a fractional or decimal component.

You probably knew that one, right? But where most students get stuck is in realizing that an integer can be negative, 0, or positive! You have options! Test them all!

 

5) “Origin” = the point (0,0)

I know you intellectually know this, but in a word problem, if they say “line m goes through the origin to point (2,3),” most students just draw out the point (2,3) and feel like they don’t have any other information! Soooo not true!

In actually, they just GAVE you a second point… (0,0). NOW, you can find your slope and y-intercept and have a full equation for the line!

 

 No calculator? No problem—as long as you have math etiquette in your corner, that is!

No calculator? No problem—as long as you have math etiquette in your corner, that is!

6) "Intercepts" give you free points, too!

These are more pieces of hidden coordinate geometry treasure! If a problem says something “has an x-intercept of 4”—they just gave you a point! That’d be (4,0). Because remember: the x-intercept has a y-value of zero. Similarly, "y-intercept" means that the x-value is zero. So if a problem says something “has a y-intercept of -2”—you can immediately plot out the point (0,-2).

That also means that if a problem asks you for an “x-intercept,” you know that directly means that y=0… so PLUG IN Y=0 into whatever equation you have and solve! And—you guessed it!—if a problem asks you for a “y-intercept,” immediately PLUG IN “0” FOR X and solve away!

 

See how much you can get out of paying attention to the word parts of word problems?

This is just the tip of the iceberg of tricky math vocab that can be a goldmine of information, if you correctly know how to decipher it. I may be back with another round of math-to-English translation...especially if you tell me what you're having trouble with! Hit me up here—I'm looking forward to hearing from you. And until then, enjoy the confidence boost that mastering math vocab brings you, whether it's on No Calculator Math or just in daily life.