If you're prepping for the new SAT, there’s one huge change you’re probably aware of (and if not, you need to be!): the No Calculator section. While this change has sent many students running straight into the arms of the ACT, you shouldn’t let a little math scare you.
You SHOULD, however, start to learn one of my favorite topics (yeah, I have favorite math topics) of all time: Math Etiquette.
What's Math Etiquette, you ask? It’s simple, really. Math Etiquette is how I refer to a series of basic math facts that you should know cold, or math ninja tricks that help you solve problems and evaluate arithmetic quickly, accurately, and elegantly—just like regular etiquette helps you understand and navigate social situations. When used in conjunction, these facts and tricks form something larger than the sum of their parts (math pun totally intended): they form a working knowledge of how numbers interact together, of number properties, of the be-all-and-end-all…number sense. (Imagine that ethereal choral “aaaah”ing from when the Little Mermaid started to walk. Have I mentioned that I really, really like math?)
I first heard of number sense because it was the name of a math competition I entered in elementary and middle school—one that focused, sensibly enough, on exactly that. The test consisted of 50 questions. You had 10 minutes to go in order, performing the arithmetic problems without scratchwork, erasing, or crossing out. If you skipped a questions or showed erasure marks or scratchwork, you got 4 points deducted from your score—for each question you screwed up. And these problems were along the lines of:
24 x 26 =
35 x 45 =
210 – 24 =
To tackle this test, I learned various math tricks, like how to multiply any 2-digit number by any 2-digit number in my head, perfect squares, and cube roots. Though I did quite well and won several of these competitions, the real win from the experience was developing a sense of how numbers worked, and an ease and confidence in working with them. To this day, I continue to perform all sorts of mental math and estimations—which won me tons of math competitions, got me top SAT and SAT II scores, guided my academic life through Brown, and has been a huge help every single day of my life as an adult in NYC (you really DO use math skills in daily life, I swear).
When you are well versed in Math Etiquette, you will possess superpowers like these:
1) Calculating basic arithmetic with quickness and ease.
Since you’ve mastered the list of stuff you just need to know, you don’t have to recreate the wheel every time you see one of those things in a problem. For example, if you memorize that 5-12-13 is a common Pythagorean triple, and you run into a question about a right triangle with a hypotenuse of 13 and a leg of 5, you don’t need to go through the arithmetic of
132 = 52 + b2 (oh wait, let me calculate by hand that 13x13=169 and 5x5=25...then subtract them to get 144...and now guess and check to see “what squared is 144?”...)
to figure out that the missing leg is 12. Instead of spending 3 minutes bashing your head (and my head!) against a wall to recreate a math fact you should already know, you will just know the answer. No sweat.
2) Flexibility with problem solving
Since you can translate between different forms of the same numbers, like fraction-decimal-percentage equivalents, you have options of how to solve the problem. You can make these choices based on how you think you’ll get there faster. You’ll have an idea that things might simplify more painlessly if you treat everything as a decimal as opposed to fraction for a particular problem. You’ll understand that a ratio can be written three ways, yet one of those ways will allow you to manipulate it more than the others.
3) Spotting shortcuts easily
You’ll know enough about how numbers and expressions work to see where numbers cancel out or simplify, leaving you with less arithmetic to calculate! For example, if you need to multiply 0.8 x 600, instead of doing long-form multiplication, you’ll remember that if you move the decimal to the right one place on the first number, you can compensate for it by moving the decimal to the LEFT one place on the second number. You’ll now have 8 x 60 = 480. (Which you hopefully could do in your head.)
4) Math intuition
Just like you get more socially assured if you master regular etiquette, mastering math etiquette means you’ll operate more smoothly in all your math endeavors. If you get to the point where you understand how the numbers work together, like individual instruments in a symphony, you will look at a problem and start to have hunches of what first step to take. And you’ll start to be right!
That’s because after working through tons of problems, you start to remember certain pathways to get to the answers. One problem will remind you of another problem you did, so you’ll instinctively start to go about the (new, unknown) problem like you did the old one. After lots of practice, you’ll get better and better at discerning which way will get you to the answer, even if you come across a problem you swear you’ve never seen before.
In other words, you’ll instinctively become a math problem solver, and a lot less reliant on a calculator! That’s very good news for the No Calculator Math on the SAT (and it’s no burden on the ACT, either!). So dive into Math Etiquette!