Worked example · Grade 9 math (MTH1W) style
Two students reach the right answer by different methods. Two get it wrong in different places. One of them checked her answer, and the check told her something was off. Here is how a rubric that rewards the check, a teacher’s review, and specific feedback turn four papers into four different next steps.
By Oscar ONeill ·
The question
Quiz question
Solve and check: (x + 1) / 2 = (x − 3) / 3 + 2
[4 marks]
Teacher's answer key
The rubric
MarkScanner drafts a rubric from the teacher’s test and answer key. The teacher edits it and approves it, and the final marks follow it. This is one reasonable rubric for this question, not the only one.
| Item | What earns the mark | Marks |
|---|---|---|
| A | Clears the fractions by multiplying every term by a common denominator, or works with the fractions correctly. | 1 |
| B | Reaches a correct equation without fractions, such as 3x + 3 = 2x + 6, or an equivalent one. | 1 |
| C | Solves for x. Follow-through applies: correct solving from the student’s own equation earns this mark. | 1 |
| D | Checks by substituting into the original equation and evaluating both sides. | 1 |
Another teacher could reasonably decide differently. What matters is deciding before marking, so every paper gets the same decision.
Four responses
Each response is transcribed line by line. Under it: the marks for each rubric item, and what happened when the teacher reviewed the draft. In MarkScanner, nothing is final until the teacher approves it.
Clears the fractions, then checks
Final mark: 4/4
Student working, line by line:
| A | Earned | 1/1 |
|---|---|---|
| B | Earned | 1/1 |
| C | Earned | 1/1 |
| D | Earned | 1/1 |
No flag. The teacher agreed with the draft.
Works with the fractions directly, no check
Final mark: 3/4
Student working, line by line:
| A | Valid method: works with the fractions correctly. | 1/1 |
|---|---|---|
| B | x/6 = 1/2 is an equivalent equation. | 1/1 |
| C | Earned | 1/1 |
| D | No check, and the question asked for one. | 0/1 |
Flagged because the method isn’t the one in the answer key. The teacher confirmed it’s valid and kept items A and B.
Clears the fractions, misses one term
Final mark: 2/4
Student working, line by line:
| A | The + 2 wasn’t multiplied by 6. | 0/1 |
|---|---|---|
| B | Not earned | 0/1 |
| C | Follow-through: x = −7 is correct from 3x + 3 = 2x − 4. | 1/1 |
| D | A correct check that shows a mismatch. | 1/1 |
No flag. The teacher agreed with the draft, including item D: Chloe’s check is done correctly, and it shows her answer doesn’t work.
Clears the fractions, sign slip, no check
Final mark: 2/4
Student working, line by line:
| A | Earned | 1/1 |
|---|---|---|
| B | Earned | 1/1 |
| C | Moving + 3 across should give 6 − 3. | 0/1 |
| D | No check. | 0/1 |
No flag. The teacher agreed with the draft.
Chloe and Dev both scored 2/4. Chloe’s problem is in the first line: she didn’t multiply every term. Dev’s first two lines are correct, and his problem is moving a term across the equals sign. A gradebook shows two identical marks. The written steps show two different lessons.
Chloe’s check caught her error. Dev skipped the check, and it would have caught his. Rewarding the check, even when it reveals a wrong answer, tells students it’s a tool for finding mistakes rather than a box to tick.
Feedback
A mark says how much. Feedback should say what worked, where to look again, and one thing to try next. MarkScanner drafts comments in this pattern; the teacher edits them before anything is printed. These are written for this example.
4/4
3/4
2/4
2/4
After the quiz
A corrected answer shows a student can fix this question. A new question with different numbers shows whether the idea has landed. The teacher gives this one in class after the papers go back.
Solve and check: (x − 2) / 4 = (x + 1) / 2 − 3
x − 2 = 2(x + 1) − 12, so x = 8. Check: LS = 6/4 = 3/2, RS = 9/2 − 3 = 3/2 ✓
A constant term again sits outside the fractions (the − 3), so Chloe has to multiply it too, and Dev has to move terms carefully and check.
More on this routine: math test corrections that give you new evidence.
What this doesn't show
A marked question shows what a student wrote on one day. It doesn’t show everything they understand, and two students with the same mark can need very different help. The conversation in class and the next piece of work still matter.
Real student work is also messier than these transcriptions. When MarkScanner can’t read something clearly, or its draft looks doubtful, it flags the answer for you. An answer without a flag can still be wrong, so the teacher’s review is part of the workflow, not an extra.
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