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Math feedback comments that give students a next step
“Check your signs” is true, and it rarely changes what a student does next. Below are common errors in algebra and functions, each with a vague comment and a better one: what went wrong, where, and one thing to do about it. Copy them, adapt them, and swap in your students’ own numbers.
By Oscar ONeill ·
Name what happened, using their numbers
A comment that quotes the student’s own line (“line 3”, “4(2)(6)”) shows you read their work and tells them exactly where to look.
Give one action
Redo a line, expand to check, substitute back. One clear action is easier to follow than a paragraph of advice.
Leave time to act on it
Comments are most useful when students get class time to respond to them. See the test corrections routine.
Solving equations
Clearing fractions but missing a term
Instead of
Careful with fractions.
Try
When you multiply by 6 to clear the fractions, every term gets multiplied, including the + 2. Redo your first line and check that each term changed.
Moving a term without changing its sign
Instead of
Check your signs.
Try
On line 3, + 3 moved across the equals sign as + 3. Moving it means subtracting 3 from both sides. Redo from line 3, then substitute your answer to check it.
Distributing a negative
Instead of
Watch the negative.
Try
−(x − 4) is −x + 4, not −x − 4. The negative multiplies both terms in the bracket. Rewrite that line and carry on from there.
No check when the question asks for one
Instead of
Check your answer.
Try
The question asked you to check. Substitute your answer into the original equation, work out each side, and show that they’re equal.
Factoring
Factors with the wrong signs
Instead of
Check your signs.
Try
Your factors (x + 1)(x + 3) expand to x2 + 4x + 3, but the question has −4x. Find two numbers that multiply to +3 and add to −4, then expand to check.
Factoring as if the leading coefficient were 1
Instead of
Factor this properly.
Try
For 2x2 + 7x + 3, look for two numbers that multiply to 2 × 3 = 6 and add to 7. Try 6 and 1, split the middle term, and group.
Not fully factored (if your rubric requires it)
Instead of
Not finished.
Try
(2x − 2)(x − 3) isn’t fully factored, because 2x − 2 still has a common factor of 2. Write it as 2(x − 1)(x − 3).
Solving each factor with the wrong sign
Instead of
Wrong answer.
Try
Your factors (x − 1)(x − 3) = 0 are right. Setting x − 1 = 0 gives x = 1, not −1. Substitute your answers to check that they make the expression zero.
The quadratic formula
Arithmetic slip in the discriminant
Instead of
Calculation error.
Try
4(2)(6) is 48, not 42. Work out b2 and 4ac on separate lines before you subtract.
Losing the sign of b
Instead of
Check the formula.
Try
With b = −8, −b is +8. Put b in brackets when you substitute, −(−8), so the sign isn’t lost.
Dividing only part of the numerator
Instead of
Formula used wrong.
Try
The whole numerator is divided by 2a. In (8 ± 4) / 4, work out 8 + 4 and 8 − 4 first, then divide each by 4.
Rounding too early
Instead of
Not accurate.
Try
You rounded on line 3 and kept going, so the error grew. Keep the exact value, or at least three decimal places, until the last line.
Functions and quadratic features
Missing ± when taking a square root
Instead of
Missing an answer.
Try
(x − 1)2 = 4 has two solutions, because 22 and (−2)2 both equal 4. Write ± whenever you take a square root to solve an equation.
Maximum or minimum reversed
Instead of
Wrong direction.
Try
The −2 in front means the parabola opens down, so the vertex is the highest point: a maximum, and the range is y ≤ 8. A quick sketch with your zeros shows it.
Vertex sign from vertex form
Instead of
Check the vertex.
Try
In y = a(x − h)2 + k, the vertex is (h, k). In y = 3(x + 2)2 − 5, x + 2 is x − (−2), so the vertex is (−2, −5).
Substituting a negative into a function
Instead of
Careful with negatives.
Try
f(−2) means replacing every x with (−2), in brackets. For f(x) = x2 − 3x: (−2)2 − 3(−2) = 4 + 6 = 10.
Domain and range swapped
Instead of
Domain and range mixed up.
Try
Domain is the set of x-values the function can take; range is the set of y-values it produces. For a parabola, the domain is all real numbers and the range starts at the vertex.
Showing work and communicating
Correct answer, no work shown
Instead of
Show your work.
Try
Your answer is right, and the question asks you to show how you got it. Write the steps so your method can earn its marks, and so you can find a slip if there is one.
Answer not stated
Instead of
Incomplete.
Try
You found x = 1 and x = 3. Finish with a line that answers the question that was asked: the x-intercepts are (1, 0) and (3, 0).
Using a tool to draft comments
The same rules apply
MarkScanner drafts per-question comments in this pattern: what went wrong, why, and one action. You read and edit them before anything is printed, because a draft can misread a line or name the wrong cause. If a comment sounds generic, rewrite it with the student’s own numbers.
See the pattern on whole papers in the worked examples, or read how to reuse comment patterns without the feedback feeling canned.
Try it free
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