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Parents and students, Years 7 and 8

Common Year 7 and 8 algebra mistakes Australian students make (and how to fix them)

30 October 2026

Algebra is where many students first decide they are "not a maths person". Usually what has actually happened is smaller and much more fixable: one or two specific habits keep going wrong, and every topic that uses them starts to feel hard.

This guide lists the algebra mistakes that come up most often in Years 7 and 8, shows what each one looks like on the page, and gives a fix your child can practise. The topics line up with the Number and Algebra content in the Australian Curriculum, including the Victorian Curriculum 2.0, though schools teach them in different orders and at slightly different times. If you want the bigger picture of why these years matter for later maths, our article on Year 8 algebra fundamentals covers that. This one is about the mistakes themselves.

How to use this guide

Grab your child's last algebra test or a page of homework with some red marks on it. As you read, try to match each wrong answer to one of the mistakes below. Most students have two or three favourites, and those are where practice pays off fastest.

1. Treating 3x as 3 + x

What it looks like: If x = 4, the student says 3x = 34 or 3x = 7.

Why it happens: In arithmetic, writing two numbers side by side means something different (34 is thirty-four). Algebra's convention that 3x means 3 × x is new and easy to forget.

The fix: For a week, have them write the multiplication sign every time they substitute: 3x becomes 3 × 4 = 12. Once it is automatic, they can drop it again.

2. Adding unlike terms

What it looks like: 2x + 3y = 5xy, or 4x + 2 = 6x.

Why it happens: Students know they are supposed to "simplify", so they combine whatever is in front of them.

The fix: Use a plain-language check: "Can I add 2 apples and 3 bananas and get 5 apple-bananas?" Then practise circling like terms in the same colour before combining anything. Only terms with exactly the same pronumeral part (x with x, x² with x², xy with xy) can be added.

3. Mixing up x² and 2x

What it looks like: Writing x × x = 2x, or x + x = x².

Why it happens: Both involve "two" and "x", and the difference between adding and multiplying is not yet secure.

The fix: Substitute a number to test it. If x = 5, then x + x = 10 and x × x = 25. Those are clearly different, so 2x and x² must be different. Encourage your child to use this "try a number" check whenever they are unsure if two expressions are equal.

4. Losing negative signs

What it looks like: -3 + 7 = -10, or 5 - (-2) = 3, or writing -x² when they meant (-x)².

Why it happens: Negative numbers are usually taught in Years 7 and 8, often just before algebra, and are not yet fluent when algebra arrives. Errors with negatives then spread into every topic that follows.

The fix: Go back to integers before going further with algebra. A number line drawn in the margin helps a lot. Fifteen minutes on our Year 7 integers and Year 8 integer operations worksheets is often the quickest way to unblock several algebra topics at once.

5. Only multiplying the first term when expanding

What it looks like: 3(x + 4) = 3x + 4.

Why it happens: The student multiplies the first term and forgets the bracket applies to everything inside.

The fix: Draw arrows from the number outside to every term inside the bracket before writing anything. Two arrows, two multiplications. With practice the arrows become unnecessary.

6. Expanding with a negative in front

What it looks like: -2(x - 5) = -2x - 10, when it should be -2x + 10.

Why it happens: This combines mistakes 4 and 5. The student remembers to multiply both terms but loses track of the sign on the second one.

The fix: Treat the sign as part of the number. Say "negative 2 times negative 5" out loud, and write the result in brackets first if needed: -2x + (+10). This is one of the most common errors we see in Year 8, and it comes back in Year 9 and 10 whenever students expand quadratics or subtract fractions.

7. "Moving" terms without doing the same to both sides

What it looks like: Solving x + 5 = 12 by writing x = 12 + 5, or solving 3x = 12 by writing x = 12 - 3.

Why it happens: Students learn shortcuts like "move it to the other side and change the sign" without understanding why it works. When the shortcut gets muddled, there is nothing to fall back on.

The fix: Return to the balance idea: whatever you do to one side, you do to the other. Write the step out in full: x + 5 - 5 = 12 - 5. It is slower for a week or two, then much more reliable. Our Year 7 linear equations and Year 8 linear equations worksheets are good places to practise this.

8. Not checking the answer

What it looks like: Solving 2x + 3 = 11 and getting x = 7, then moving on.

Why it happens: Checking feels optional, and students are keen to finish.

The fix: Make substitution a habit for every equation. Put x = 7 back in: 2 × 7 + 3 = 17, not 11, so something has gone wrong. This takes ten seconds and catches a surprising number of errors in tests. It is the single most useful algebra habit a Year 7 or 8 student can build.

9. Fraction mistakes inside algebra

What it looks like: x/3 + x/4 = 2x/7, or solving x/4 = 3 by writing x = 3/4.

Why it happens: Algebra with fractions depends on fraction skills from primary school and Year 7. If adding fractions with different denominators is shaky, algebraic fractions will be too.

The fix: Do the same calculation with numbers first. Would 1/3 + 1/4 equal 2/7? No, it equals 7/12, using a common denominator. The algebra follows the same rule. For equations like x/4 = 3, remind them that "x divided by 4" is undone by multiplying both sides by 4. If fractions are the root issue, the Year 7 fraction operations worksheets are the place to start.

10. Writing an equation the wrong way round from words

What it looks like: "Sam has 5 more marbles than Jo. Jo has j marbles." The student writes Sam = j - 5, or 5j.

Why it happens: Turning words into algebra means understanding the relationship, not just picking out numbers. Students often grab numbers in the order they appear.

The fix: Test it with a real number. If Jo has 10, Sam has 15. Does the expression give 15 when j = 10? j + 5 does. j - 5 and 5j do not. The Year 8 linear problems worksheets have plenty of these.

Why these mistakes stick around

Most of these errors are not about understanding a new idea. They are habits. A student can understand the distributive law perfectly well in a lesson and still write 3(x + 4) = 3x + 4 under test pressure two weeks later.

Habits change through repetition spread over time, not through one explanation. That means the fix is not more teaching. It is practising the exact type of question they get wrong, several times, across a couple of weeks, until the correct method becomes automatic. Our article on spaced practice and retrieval for secondary maths explains why spreading practice out works better than one long session.

Practise the exact mistake, not the whole topic

When a student gets one algebra question wrong, the usual response is to revise "algebra" in general, which means doing lots of questions they can already do. It is far more efficient to practise just the type that went wrong.

A simple routine:

  1. Take the question they got wrong and identify which of the ten mistakes above it was.
  2. Have them try it again without looking at the solution.
  3. Check it against a worked solution, and find the exact step that went wrong.
  4. Do two or three fresh questions of the same type, with different numbers.
  5. Come back to it a few days later and try another fresh one.

This is what Tuterly does for Years 7 to 10 maths. Your child snaps the algebra question they got wrong, has another go with the solution hidden, then gets fresh questions on the same idea until it is mastered. Because each new question is genuinely different, they are practising the skill, not memorising one answer.

What parents can do (even if algebra was a long time ago)

You do not need to remember algebra to help. The most useful things are habits you can encourage:

  • Ask "how could you check that?" after any equation. Substitution works for almost every Year 7 and 8 algebra question.
  • Ask them to try a number. For mistakes 2, 3, 9 and 10, substituting a simple number reveals the problem.
  • Look for patterns in the red marks. If the same mistake appears on three different pages, that is the thing to practise.
  • Keep sessions short. Ten to fifteen minutes on one mistake type is better than an hour on everything.

Our parent guide to helping with secondary maths homework has more on how to support without taking over.

Where to go next by year level

Frequently asked questions

Which algebra mistake is the most important to fix first?

Negative numbers (mistakes 4 and 6). They affect almost every algebra topic from Year 7 to Year 10, so fixing them early has the biggest flow-on effect.

My child understands it in class but gets it wrong in tests. Why?

Understanding a method when the teacher has just explained it is different from recalling it a week later under time pressure. Short, spaced practice on the exact mistake type closes that gap.

Should my child memorise rules like "change the side, change the sign"?

Shortcuts are fine once the reason behind them is secure. If your child is mixing up the shortcut, going back to the balance method (do the same to both sides) is usually the fastest fix.

Is it too late to fix Year 7 algebra in Year 9?

No. Older students often fix these habits quickly once the specific mistake is identified, because they already know the surrounding maths.

Your next steps

  1. Find two or three recent algebra mistakes and match them to the list above.
  2. Pick the most common one and practise just that type for 10 to 15 minutes.
  3. Build the substitution check into every equation.
  4. Revisit the same mistake type a few days later with fresh questions.
  5. Repeat with the next mistake on the list.