There’s one section of the SAT that strikes a particular lightning-bolt of fear into some students’ hearts: the No Calculator Math section. The prospect of handling a bunch of equations without any kind of device to lean on is enough to send some students running to the ACT. But as I routinely tell my private SAT/ACT tutoring clients: if you’ve determined that the SAT is otherwise the right test for your goals and needs, there’s no reason to let a bit of unassisted math scare you away from the SAT!
There *are* good reasons, however, to start studying one of my favorite topics (that’s right, I have favorite math topics) ever: Math Etiquette.
What's Math Etiquette? I’m so glad you asked. Math Etiquette is my term for a cluster of basic math facts and skills that you should have down pat if you plan to take the SAT by December 2023. And although the Digital SAT replaces the SAT for everyone in March 2024—and will not have a No-Calculator Section—Math Etiquette will continue to serve you in your college math classes, and in your everyday life! (It’s also helpful for the ACT!)
That’s because these math ninja moves will help you solve problems and evaluate arithmetic swiftly, accurately, and nimbly—the same way that “etiquette” in the traditional sense helps you understand and navigate tricky social situations. When used together, these math facts and hacks add up to something bigger than the sum of their parts (so to speak): they give you a big-picture sense of how numbers interact together, of number properties, and of the holy grail known as number sense. (Imagine a heavenly choir of “aaaahs” here. Have I mentioned that I really, really dig math?)
I first heard the term “number sense” because it was the name of a math contest I competed in during elementary and middle school. The test comprised of 50 arithmetic questions, which you had 10 minutes to solve. You had to proceed through the problems in order—AND 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 each time. The problems in question were along the lines of:
22 x 26 =
45 x 55 =
211 – 23 =
To prepare for this test, I learned a set of math tricks, such as: perfect squares; cube roots; and how to multiply any 2-digit number by any 2-digit number in my head. Though I was proud of my performance in these competitions—I even won several!—the real triumph I took away from the process was developing my intuitive 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, skills that have won me tons of math competitions, snagged me top SAT and SAT II scores, guided my academic life through Brown, and have been a huge help every single day of my life as a small business owner and adult living in New York City. (You’ve probably had adults tell you this before, but let me add my voice to the chorus: you really DO need mental math skills in daily life!).
What will Math Etiquette teach you for the SAT?
1) Calculating basic arithmetic with SPEED and ease.
Once you’ve mastered the list of facts/skills you just need to know, you won’t have to recreate the wheel every time you see one of those things in a problem. For example, let’s say you’re taking the SAT No-Calculator Math section and you encounter a question that presents you with a right triangle with a hypotenuse of 13 and a leg of 5. You’re asked to calculate the length of the second leg of the triangle. If you’ve put in your Math Etiquette reps beforehand, you’ll remember that 5-12-13 is a common Pythagorean triple…and thus WON’T need to waste time working through this arithmetic:
132 = 52 + b2 (hold up, 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?”...)
Instead of spending 3 minutes—a lifetime of wasted points, in SAT time!—to recreate a math fact you should already know, you will just know that the answer is 12. Bingo, bango—you’re free to move on to the next question/points trove!
2) Flexibility in problem solving.
Math Etiquette will empower you to translate between different forms of the same numbers, e.g., to just know off the top of your head how a common fraction can be alternatively expressed as a decimal and as a percentage. This gives you different options when it comes to how to solve the problem, and you can just pick the method that you think will be quickest. You’ll develop an intuition that a given problem might simplify more easily, for instance, if you treat everything as a percentage as opposed to a fraction. You’ll understand that a ratio can be written three ways—yet one of those ways will allow you to manipulate it more readily than the others.
3) Spotting shortcuts easily
Math Etiquette will help you perceive expressions in a way that you can more easily pick up on where numbers cancel out or simplify, leaving you with less arithmetic to calculate! For example, if you need to multiply 0.7 x 500, 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 7 x 50 = 350. (A multiplication you could likely do in your head.)
4) Math intuition
Just like you become more socially confident the more you practice social etiquette, practicing math etiquette will make you more self-assured—and thus faster—in all of your math endeavors. Once you gain a holistic understanding of how numbers all work together, like individual instruments in a rock band, you will look at a problem and start to have a sense of what first step to take. And those hunches will, more and more often, be correct!
That’s because after working through a bunch of problems, you start to remember certain choreographies that get you 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 intuiting which method will get you to the answer, even if you come across a problem you’ve technically never seen before.
In other words, you’ll become an instinctive math problem solver, and a lot less reliant on a calculator! That’s precisely what you need to succeed in the No Calculator Math on the SAT (and it’s a boon on the ACT, too!). So join me, in the coming weeks, for a journey into the beautiful world of Math Etiquette. Now that you’re familiar with the umbrella concept, this series will continue on to bring you the actual facts and tricks you should memorize/practice in order to sail to math-y triumph!
In the meantime, if you want an experienced and enthusiastic math nerd in your corner, learn more about studying with me solo, or check out the one-stop ebook guide I’ve written for both Math sections of the SAT.
