For Aaron & Family

Getting More Accurate
at Algebra

For Aaron to use daily, and for his family to follow along — what to practice, why it works, and how to make it stick

Prepared by Michael Cohen · May 2026

📌 First, the good news

For parents: Aaron has a solid grasp of the algebra. When we work through material together, things click fast — functions, composition, transformations, factoring, probability. He's put in real work this semester, and it shows.

What we're working on now is precision — not new concepts, but execution. Aaron knows what to do; the issue is that the small steps inside a problem can get less attention than they deserve. The habits in this guide target exactly those moments. None of them require relearning anything.

For Aaron: You're already aware of this. You'll often catch yourself mid-problem and say "I go too fast sometimes." That's the right diagnosis. The habits below are specific things you can do about it — not generic advice, but moves that target the exact mistakes that keep showing up.

The key pattern: Almost all of Aaron's errors happen on the steps that feel easy — not the ones that require real thought. Telling yourself to be "more careful" in general doesn't fix it. Specific habits that fire at specific moments do.

5 Habits That Build Accuracy

Each one targets a specific error pattern. Click any card to expand it.

1
Keep an Error Log
The most important habit: turns scattered mistakes into a short, fixable list
3 min / session
Why it works

Your brain can't fix a pattern it can't see. When mistakes feel like isolated bad luck, nothing changes. But when you can look at a log and see that the same two things have gone wrong ten times in the past two weeks, it's hard to ignore — and you know exactly where to pay attention, instead of trying to be careful about everything, everywhere.

How to do it
1
After every practice set or tutoring session, spend 3 minutes reviewing any mistakes.
2
For each mistake, write three things: what happened, what type of error it was (sign, middle term, arithmetic, etc.), and what the correct step should have been.
3
Once a week, re-read all the entries. Over 2–3 weeks, 2–3 error types will dominate the list. Those are the only moments that need extra attention — not everything else.
Example log (try clicking Add)
What happened Error type Correct step
(x+3)² → wrote x²+9
Middle term
Need 4 products: x²+6x+9
−(4x+5) → forgot minus on 5
Sign drop
Circle every term first: −4x−5
8×8 = 56 inside algebra
Arithmetic
Write it out: 64. Don't do it mentally.
2
Circle Every Destination Before You Compute
Gets the tracking off your brain and onto the paper, where it can't disappear
5 sec / problem
Why it works

Negative signs are easy to drop in algebra because you have to hold onto them while doing something else at the same time. That's a tough combination. What usually happens: the negative hits the first term or two, then disappears on the last one. Circling puts the tracking on paper before any computing starts — it can't be forgotten if it's written down.

How to do it
1
When you see a negative sign in front of parentheses — before writing any products — circle every single term inside the parentheses.
2
Each circle is a pre-committed reminder: "this term gets a negative." You don't have to hold it in your head anymore — it's written down.
3
Say quietly: "minus hits every term." The verbal reminder adds a second check alongside the visual one.
Example
Problem:   −(3x + 5y + 2)
Step 1:   Circle 3x, 5y, 2   (before computing anything)
Step 2:   Write products:   −3x − 5y − 2
3
Write Every Sub-Step — No Mental Shortcuts
Especially FOIL: all four products, every time, on separate lines
10 sec / step
Why it works

When you're tracking algebra structure and doing arithmetic in your head at the same time, one of them usually loses. Writing the arithmetic out doesn't slow things down — it frees up attention for the algebra. The paper does the remembering, so your brain doesn't have to.

The FOIL rule (most important)
1
When squaring a binomial like (x+3)², say quietly: "four products: first, outer, inner, last."
2
Write all four products on their own lines — x·x, x·3, 3·x, 3·3 — then combine. Don't skip ahead.
3
The middle term (6x here) is the one that most often gets dropped when steps are skipped. Writing it out makes it impossible to miss.
Example: (x + 3)²
x · x   = x²
x · 3   = 3x    ← outer
3 · x   = 3x    ← inner
3 · 3   = 9
Result:   x² + 6x + 9 ✓
Same rule for arithmetic
Any multiplication fact computed during algebra — especially inside a larger problem — should be written out, not done mentally. The 10 extra seconds are worth far more than the time savings.
4
10 Minutes of Daily Accuracy Drills
Make arithmetic automatic so it stops getting in the way of the algebra
10 min / day
Why it works

The 8×8=56 errors don't happen because you don't know your times tables. They happen because when you're focused on the algebra, arithmetic has less mental space to work with. Drilling builds automaticity — the fact just comes, without needing any attention, the same way reading a word doesn't require sounding it out anymore. Once that kicks in, it stops interfering with the algebra around it.

Important: accuracy first, not speed
The goal isn't to go faster — it's to get every answer right. Set the pace slow enough that errors are rare, then let speed build naturally. A wrong answer drilled quickly embeds the wrong answer.
Suggested routine (10 min)
1
5 min — Arithmetic facts (Zetamac). Set to multiplication, number range 1–12. Aim for zero errors, not max score.
2
5 min — Mixed algebra practice (Khan Academy). Use the College Algebra section. Mix problem types — don't do 10 of the same kind in a row.
Free tools
5
The 3-Point Scan After Every Problem
A targeted 20-second check: not a re-solve, just the three spots where Aaron's errors actually happen
20 sec / problem
Why it works

Generic "check your work" doesn't catch these errors because a wrong answer that's close to right looks fine on a quick re-read. You see x²+9 and think "looks like a quadratic, good enough." This scan skips the re-read entirely — it only checks the three specific spots where errors actually happen, which makes it faster than a general review and more likely to find something.

After completing any problem, check these three things:
Negative in a distribution? Go back and verify that every single term inside the parentheses received the negative sign — especially the last one.
Binomial squared? Count the terms in the result. There should be three (x², middle term, constant). If there are only two, the middle term got dropped.
Any arithmetic done mentally? Find it and redo it written out. This takes 5 seconds and catches the 8×8=56 class of error every time.
This checklist should also appear in the Check zone of Aaron's exam cheat sheet — not "check your work" generically, but these three specific questions, personalized to where his errors actually live.

A note on timeline — for Aaron and for parents

These habits take 2–4 weeks to feel natural. That's long enough for them to run without thinking, which is when they actually hold up under exam conditions.

For Aaron: The goal isn't new material — you already have the concepts. It's building routines that run on autopilot, so they're still going when the test is stressful and the clock is moving.

For parents: The most useful question isn't "did you study?" It's something more specific: "Did you add to the error log?" or "Did you run the scan?" Those questions reinforce exactly what we're working on. Aaron will know whether he did it — and that's usually enough.

Any questions, reach out anytime — michael@mrcohen.com