Two students can spend the same hours on SAT math and end up in very different places. Tom sees the same habits again and again in the students who improve most, and they help whatever score you’re aiming for, whether that’s a perfect score, 150 more points, or 50. The students who improve most use every practice question to learn something they will use on the next one.
None of the habits takes special talent. No one is born knowing how to rearrange an equation or when to reach for Desmos, and students who seem to have a knack for math have usually practiced more, and more thoughtfully. The walkthrough above follows one session that uses the habits. The sections below take them one at a time, and the last section puts them together into a session to run this week.
Consistent Practice
The mistake
Cramming a few long sessions, then stopping for weeks.
The fix
Choose practice times that fit an ordinary busy week, and keep returning to them.
Every other habit on this page depends on coming back to the work. Regular, focused sessions spread across the week give each skill several chances to stick, and a major review of study techniques rates spreading practice out over time among the most useful techniques it examined. A schedule that fits an ordinary busy week does more for you than an ambitious one you abandon.
Spend the sessions on the skills that are holding you back. If Desmos is new to you, it is often the quickest place to gain, because many questions get faster and safer once the calculator feels familiar.
Practice times that fit your week
Days you’ll practice
Minutes per session
3 sessions a week, 90 minutes in all
The longest stretch without practice is 2 days, so each session starts close to the last one.
Asking Why Each Time You Repeat a Problem
The mistake
Repeating a kind of problem until the steps are memorized, without asking why they work.
The fix
Each time, ask why the method works and why a different one would fail, and carry the answer into the next attempt.
Some ideas don’t make sense the first time, or the fifth. Tom tells students that sometimes you have to work a kind of problem a hundred times before the understanding clicks, and that it clicks only if you think about what you’re doing while you do it. Repetition builds understanding when each attempt asks why the method works and why something else wouldn’t.
What changes when you ask why a rule works
Following a memorized rule
I flipped the sign because the rule says to flip it when you divide by a negative. I'm not sure why.
Memorizing a rule helps with speed, and it is a poor substitute for knowing why the rule exists. A memorized rule breaks when a question looks different from the ones you practiced, while a rule you understand adapts to the new form, as the second inequality above shows.
Explaining Your Steps and Getting Feedback
The mistake
Reading the answer explanation, nodding, and moving on.
The fix
Explain how you reasoned, including why you believed each step, and let a tutor or an AI find the first assumption that went wrong.
An answer explanation shows a correct method, and it leaves out the belief of yours that produced the wrong one. That belief is still there, ready to produce the next wrong answer. Explaining why you believed each step brings the first wrong assumption into the open, where a tutor or an AI can correct it.
Research on “self-explanation,” where students explain material to themselves as they study, points the same way. In one small study, eighth graders prompted to explain a text line by line learned more than classmates who read it twice, and the major review of study techniques rates self-explanation as moderately useful. Below, a student explains a wrong answer out loud.
Which sentence shows the belief that produced the wrong answer to ?
Pick one of the sentences.
Here is a math question I got wrong: [paste the question]. Here is my work, and what I believed at each step: [your work and reasoning]. Find the first step where my thinking went wrong, and ask me a question that helps me see it myself. Don't give me the correct answer or redo the problem for me.
Use it after any miss, with your real work and what you believed at each step.
Solving Both by Hand and in Desmos
The mistake
Using the same method on every question out of habit.
The fix
During practice, solve each question with Desmos and with algebra wherever both work, and note which one worked better.
When both methods are possible, try both in practice and write down which one was quicker and which one you trusted more, the way Ben did in the walkthrough. Over a few weeks, the notes show you which kinds of questions belong in Desmos. Working each question twice also teaches the patterns the SAT repeats and how long each kind of question takes you. Solving both ways turns every practice question into a lesson about the test as well as the math.
Varied Practice on a Missed Pattern
The mistake
Redoing the exact question you missed, or ten copies of it.
The fix
While the mistake is fresh, practice a varied set on the same skill, including one question where the usual pattern doesn't apply.
Right after a miss, the skill behind it is fresh in your mind, which makes it the best time to practice. Copies of the missed question teach you to repeat one set of steps. A varied set changes the wording, the context, and the structure, and it includes a question where the familiar pattern fails, so each question makes you decide which idea applies. Practice that makes you choose the method prepares you for a test that never says which method a question needs.
What each question asks you to decide
- Distribute 3.
- Distribute 4.
- Distribute 2.
- Distribute 5.
- Distribute 6.
Every question asks the same thing, so by the third one you're repeating steps without deciding anything.
Research on “interleaved” practice, which mixes different kinds of problems in one set, points in the same direction. In one classroom study, 126 seventh graders practiced math either one kind of problem at a time or mixed together. A month after the review, the students whose practice was mixed scored far higher. Tom’s habit is narrower, a varied set on one missed skill, and it shares the ingredient that seems to matter: every question makes you decide what to do.
- One day later
- Thirty days later
Source: Rohrer, Dedrick, and Stershic, Journal of Educational Psychology, 2015
An AI can build the varied set for you in seconds. Ask for the answer letters to vary as well, because a set where every answer is B teaches you the letter.
I missed this question: [paste the question]. Make me five practice questions on the same skill. Change the wording, the context, and the structure, include one question where the usual shortcut doesn't work, and vary which answer letter is correct. Give me one question at a time, and don't tell me the answer until I've given mine and explained it.
Use it right after a miss, while the pattern is still fresh.
Warm-Ups on the Basic Skills Inside a Harder Question
The mistake
Going straight to hard questions while a basic step keeps slowing you down.
The fix
Start each session with a few quick problems on the basic skill underneath, until that step feels automatic.
Tom puts it this way: “Most of what seems like advanced mathematics is just basic mathematics that has been mastered.” A question that feels hard is often a stack of basic steps, and when one of them, such as clearing fractions or distributing a negative sign, still takes effort, the whole question feels heavier than it is. A few minutes of warm-up on the basic step underneath makes the harder questions lighter.
Warm-ups on the basic skills inside a harder question
What should you multiply both sides by to clear every fraction?
This question slowed me down: [paste the question]. List the basic skills it depends on, then give me a short warm-up on the one I'm weakest at, one quick problem at a time. Don't solve them for me, and wait for my answer each time.
Use it when a question felt slow because of a step inside it.
Checking Uncertain Answers With Spare Time
The mistake
Double-checking hard questions while easier ones are still unanswered.
The fix
Once every easier question has an answer, use the time left to solve your least certain answers a slightly different way.
On test day, the first job is to answer every question within reach, and the questions in each module run from easiest to hardest. If time remains after that, go back to the answers you were least sure about and solve each one a slightly different way, with Desmos if you used algebra, or with algebra if you used Desmos. A second method catches the sign errors and misplaced parentheses that rereading the same work tends to miss.
A Personal Reason to Get Better at Math
The last habit is about why you practice at all. Math feels overwhelming when it looks like a thousand separate rules to memorize. Tom felt that way in school, and he came to love math in his late twenties, when he found his own reason to care and saw that most of it comes down to a few simple ideas that return again and again in different forms. Find a reason of your own to get better at math, and look for the simple idea underneath each new topic.
Questions to ask yourself
- What would getting better at math let you do that you want to do?
- What does this topic have in common with something you already understand?
- How would you say what this rule does in one plain sentence?
- Where have you seen this idea before, in a different form?
A Complete Practice Session That Uses Every Habit
The checklist below puts six of these habits in order for a single practice session. The other two, consistent practice and a personal reason to get better at math, are what bring you back for the next session. A session that ends with a note and a varied set gives the next session its starting point. Check off each step as you finish it.
The steps of a complete practice session, in order
Sources
Research findings were checked on September 26, 2026. Each study describes specific students and conditions, so treat the results as evidence about practice in general.
- 01Psychological Science in the Public Interest, 2013Improving Students' Learning With Effective Learning TechniquesDunlosky and colleagues rate ten study techniques: practice testing and spaced practice highest, self-explanation and mixed practice moderate, rereading and highlighting low.
- 02Journal of Educational Psychology, 2015Interleaved Practice Improves Mathematics LearningRohrer, Dedrick, and Stershic's classroom study of 126 seventh graders, comparing mixed and one-kind-at-a-time math practice on tests one day and thirty days later.
- 03Cognitive Science, 1994Eliciting Self-Explanations Improves UnderstandingChi and colleagues found that eighth graders prompted to explain a text to themselves, line by line, learned more than students who read it twice, in a small study.
- 04College BoardMath Section OverviewThe order of questions in each SAT math module, from easiest to hardest.