Every algebra teacher and tutor sees the same mistakes cycle through every year. They're not signs of a student who "can't do math" — they're predictable gaps that compound fast if left uncorrected. Here are the five I see most often, and what to do about each one.

1. Distributing a negative sign incorrectly

When students see −(3x − 5), they often write −3x − 5 instead of −3x + 5. The negative sign distributes to every term inside the parentheses — including the subtraction, which flips to addition. Drilling this one pattern eliminates a huge category of errors across algebra and beyond.

2. Adding fractions by adding numerators and denominators separately

1/2 + 1/3 ≠ 2/5. This one feels intuitive to students but is completely wrong. Fractions require a common denominator before adding. Once a student internalizes why (you can't add different-sized pieces), the rule sticks. Until then, it keeps showing up on every test.

3. Misapplying the order of operations

PEMDAS is taught early, but students routinely rush through it. The most common version: solving left-to-right without handling exponents or parentheses first. A quick fix is to have students circle every operation before solving and label the order before writing a single number down.

4. Dropping the variable when solving equations

Students solve 2x = 10 correctly to get x = 5, then on the next step write just 5 and forget what they solved for. Small habit, big consequences on multi-step problems. Always write what the variable equals, not just the number.

5. Treating "simplify" and "solve" as the same thing

Simplifying an expression (3x + 2x → 5x) is not the same as solving an equation (5x = 20 → x = 4). Students who conflate these often try to "find x" when there's no equation — and get confused when there's no single answer. The distinction is worth teaching explicitly.

What to do about it

The good news: all five of these are fixable with targeted practice. The bad news: generic homework sets don't target them — they just give students more opportunities to repeat the same error. If your student is making these mistakes, focused review on each pattern (not more of the same problems) is what moves the needle.

If you'd like a free assessment to identify where your student is getting stuck, reach out here.

5 Algebra Mistakes Middle Schoolers Make Every Year