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Math Grammar: Unspoken Rules of Math

Let's start by acknowledging all of the following examples are equivalent to one another. Yet, there's this universal unspoken format in sharing mathematics. Yes, the format may arise during math classes discussions, but it's rarely explicitly and intentionally taught. While I believe the desire for students to recognize equivalent expressions trumps these formatting rules, I couldn't resist compiling a list of a few I regularly encounter. Why Math Grammar? Why not Math Punctuation? Simple, Math Grammar has a better ring to it.

I vividly imagine the line up of terms like team players lining up from strongest to weakest. Certainly adds an interesting take to negative exponent terms being represent in the denominator. The terms with the highest exponents are the strongest and lead the pack in descending order right down to the basic constants.

As much as we dish out the commutative property of multiplication, there's certainly a preference for the outside distributing multiplier to stand it's ground on the left side of the parentheses. Just looking at the 6 on the right hand side makes me squirm.

Okay, I'll admit it, maybe this one is just a me thing. But I swear leaving out that 0 place holder increases the odds of making careless mistakes or someone misinterpreting your values. Take the extra millisecond and write the 0 please!

Less is more here! Writing the 1 in front is generally a novice move, that's incorporated when initially learning strategies like combining like terms, etc. Simplifying expressions is about using the fewest amount of symbols to equate to the same value. Writing one is insignificant and adds no numeric value, but rather utilized as a teaching moment that these are equivalent. I joke with my students that mathematicians are lazy and thus, constantly looking for a way to use as few symbols as possible.

There's no way I captured all of them. Are there any others that come to mind?

Want your own printable set with all 12?!

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