**Apr 13, 2016**at 10:48 PM

# Tips for the Math Section of the New SAT

### Writing a New Curriculum

When the College Board first announced its plans to overhaul the SAT, we predicted that market pressure would push the test closer to its increasingly popular rival, the ACT. Those predictions were confirmed with the first preview of the test, with one glaring exception: while the grammar and reading sections looked suspiciously similar to the ACT, the new math section was something entirely new. Indeed, despite already having hundreds of pages of math instruction for ACT and SAT topics, we decided that we’d need to write this new math curriculum from scratch. We commandeered one of our conference rooms and set to work, cutting out test problems, taping them to the wall, and rearranging them in carefully labeled groups as if on the verge of unmasking some grand conspiracy. Chaos was quickly replaced by order, and we emerged with a few hundred pages and a solid appreciation for the redesigned SAT. In particular, we were impressed with its ability to effectively test, for the first time, what we called math “fluency”: that is, a student’s understanding of how different math concepts connect and reinforce one another.

### Illustrating Math Fluency

To illustrate what we mean, let’s take a quick look at examples of four question types on the new SAT that, together, make up almost a *third* of all math questions. Each type tests the same, basic skill—manipulating linear equations—from a slightly different angle. As we’ll see, this has big implications for both teachers and students.

**Basic Algebra**

One of the most common question types, particularly on the No-Calculator section, is the Basic Algebra problem. These straightforward questions test your ability to manipulate a linear equation in a balanced fashion. These are the classic “solve for *x*” problems:

To solve such problems, students need to have a basic flexibility with algebra: identify a goal (e.g., “solve for *x*”) and make intentional, balanced changes to each side in order to achieve that goal.

Now, let’s hop on over to the Calculator section of the test to see how this same skill can be tested with a slight twist.

**Applied Algebra**

On the calculator section, students will run into a related question type that we call Applied Algebra, or “Alphabet Soup” if we’re feeling particularly charming. These questions feature a paragraph describing a given physics equation (or something equally intimidating), but their bark is far worse than their bite.

This question may look tough at first glance… but it’s not! If you glance at the answers you’ll notice that the problem is just giving an equation (*PV* = *nRT*) and asking students to “solve for *T*.” The skill required to solve this problem is the exact same as for Basic Algebra: rearrange an equation to reach a goal. The only real difference is that, this time, the equation comes with a backstory.

These first two problem types test a student’s *flexibility* with thinking about linear equations; the next type deepens the stretch.

**Equation of a Line**

Equation of a Line questions require students to understand the context behind an equation in the familiar slope-intercept form (*y* = *mx* + *b*). For example:

Students are expected to know that the “*m*” in “*y* = *mx* + *b”* represents the **slope** of a line and that “*b*” represents the ** y-intercept** of a line. Students often must then use that understanding to (once again) manipulate the equation to reach a goal. But whereas the science behind Applied Algebra problems was largely irrelevant, the graphing context actually matters here!

That leads us to one last question type where the focus is almost entirely on understanding the real-world context behind a linear equation.

**Modeling**

“Modeling” problems directly test how an equation can be used to represent, or “model”, a given context. These questions give a real-world context that is relatively straightforward and ask students to create an equation that models it:

Or they may ask students to interpret the meaning of one piece of the equation:

Either way, modeling questions reward students who have an understanding of algebra as a *language* with meaning rather than as a series of rules to memorize. By focusing on a single skill from different angles, from the highly mechanical Basic Algebra problems to the highly conceptual Modeling problems, these four question types effectively test a student’s fluency with linear equations. As we’ll see, this is great news for students and teachers alike.

**The Benefit for Students**

When the College Board’s president, David Coleman, announced the redesigned SAT, he predicted that the new test’s emphasis on fluency over “tricks” would make tutoring less important and less effective. After living, breathing, and teaching the new test for a year, we’ve found the exact opposite to be true.

Math “fluency” – the understanding of how different topics covered in school connect with one another – is precisely what a good math exam should test.