Section Three of the redesigned SAT, also known as the No-Calculator Section, is striking fear in the hearts of Juniors all over the country this year.
After the redesigned PSAT, we heard that some questions in this section had grueling calculations. We heard that other questions had extraneous information. We mostly heard that students just plain didn’t feel comfortable without their trusty math-class appendage, Mr. TI-84.
There are several strategies that we are advocating to prepare students for this uncomfortable-but-manageable experience. Think of it as calculator detox: there will be withdrawal symptoms, there may even be some kicking and screaming, but in the end students will be stronger both with and without their calculators.
First, students need to reacquaint themselves with some of the basic arithmetic skills that have likely atrophied since the calculator became a permanent math-homework fixture. They also have to reacquaint themselves with their pencil. That doesn’t mean students need to become masters of long division overnight (help us all if it did), but it is important for them to revisit simpler arithmetic relics like reducing fractions, multi-digit multiplication, common rules of divisibility, and taking simple percentages.
Like riding a bicycle, the muscle memory is still there and most students just need to jump back on and start pedaling. Once they do, they’ll see that the steering mechanism is, without a doubt, the pencil. “Write out your work,” “underline key words,” “circle what the question is asking for” – these have always been the mantras that lead to standardized test enlightenment, and each one begins with picking up your pencil.
Second, a foundation of algebraic vision needs to be built. Many students already have this lurking in the back of their brains, waiting for a teacher to ask them to factor, to cross-multiply, or to use an exponent rule. These are examples of algebraic changes of form, not simplification steps, so they don’t always make their presence obvious. That’s where algebraic vision is needed. Students have to realize that many SAT questions expect you to make such form changes to see the question in a different light, a light under which the problem is much easier to solve. They won’t tell you to make them; you just have to be looking for opportunities to apply them properly.
Next, the ability to make approximate calculations and to rough-sketch graphs can be extremely valuable on the No-Calculator Section of the SAT. These employ the oft-overlooked skill of modeling for simplicity. For example, if part of your work on a problem involves multiplying 37 by 104, it may be enough to make the simpler calculation 40 times 100 because there may only be one choice in the same ballpark as the product 4000. When, in the absence of a calculator, you sketch the graph of a function to better understand its behavior, you need not make several hash marks or count out every single coordinate. Really all you need is a couple of axes and a good eye for approximation.
Lastly, students need to be on high alert when in ZONE F. This is a wild and frightening place where numbers don’t behave as they should. ZONE F stands for: Zero, One, Negatives, Exponents, and Fractions. These numbers and number types have properties that will not always follow the normal patterns, and so they should be treated with suspicion. When a ZONE F number is referenced in a question, take note and take an extra second to consider its peculiarities. If you are plugging in numbers for variables, either avoid ZONE F numbers altogether to circumvent special case scenarios, or, if the question has words like could or must or not or except, consider whether a ZONE F number creates a different threshold for what is possible in the expression you are plugging into.
Ultimately, the No-Calculator Section of the SAT does not have to be the nightmare that a student awakens from in a cold sweat. It can become the lucid dream that one controls with greater and greater aptitude by applying a few subtle strategies and revisiting old friends from a more innocent, pre-calculator past. And like any section of a standardized test, it should be thought of as a puzzle worth solving, rather than a monster to avoid.