Worked example · Grade 10 academic math (MPM2D) style
Four students answer the same question. Two get it right by different routes. One makes a single arithmetic slip. One makes a sign error that carries through everything after it. A final-answer check would put the last two in the same pile. Here is how an approved rubric, a teacher’s review, and specific feedback tell them apart.
By Oscar ONeill ·
The question
Quiz question
Find the x-intercepts of y = 2x2 − 8x + 6. Show your work.
[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 |
|---|---|---|
| 1 | Uses a valid method: sets y = 0 and factors, or applies the quadratic formula. | 1 |
| 2 | Correct factors, or correct values substituted into the formula and the discriminant evaluated correctly. | 1 |
| 3 | Solves for both x-values. Follow-through applies: correct solving from the student’s own factors or discriminant earns this mark. | 1 |
| 4 | States the x-intercepts. | 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.
Common factor, then factoring
Final mark: 4/4
Student working, line by line:
| 1 | Earned | 1/1 |
|---|---|---|
| 2 | Earned | 1/1 |
| 3 | Earned | 1/1 |
| 4 | Earned | 1/1 |
No flag. The teacher agreed with the draft.
Factoring without the common factor
Final mark: 4/4
Student working, line by line:
| 1 | Earned | 1/1 |
|---|---|---|
| 2 | Restored by the teacher. (2x − 2)(x − 3) is a correct factorization. | 1/1 |
| 3 | Earned | 1/1 |
| 4 | Earned | 1/1 |
In this example, the draft took a mark off item 2 because Marcus didn’t take out the common factor. The teacher’s rubric doesn’t require that, so the teacher restored the mark. This is why every draft mark is editable.
Quadratic formula, with an arithmetic slip
Final mark: 3/4
Student working, line by line:
| 1 | Earned | 1/1 |
|---|---|---|
| 2 | Discriminant miscalculated: 4(2)(6) is 48, not 42. | 0/1 |
| 3 | Follow-through: both values are correct from √22. | 1/1 |
| 4 | Earned | 1/1 |
Flagged because follow-through decided item 3. The teacher checked that both decimals follow from Jo’s own discriminant and kept the mark.
Factoring, with a sign error
Final mark: 3/4
Student working, line by line:
| 1 | Earned | 1/1 |
|---|---|---|
| 2 | (x + 1)(x + 3) expands to x2 + 4x + 3. | 0/1 |
| 3 | Follow-through: correct solving from Sam’s factors. | 1/1 |
| 4 | Earned | 1/1 |
No flag. The teacher agreed with the draft.
Jo and Sam both scored 3/4, and a gradebook would show them as identical. Their written steps show two different problems: Jo made a multiplication slip in a correct method, and Sam chose factors with the wrong signs. The mark is the same; the feedback, and what each student practises next, is not.
Sam’s answer, x = −1 and −3, could also come from a student who factored correctly as (x − 1)(x − 3) = 0 and then solved each factor with the wrong sign. Same final answer, different misunderstanding. Only the written steps tell you which one happened, and they need different next steps.
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
4/4
3/4
3/4
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.
Find the x-intercepts of y = 2x2 − 10x + 12.
2(x2 − 5x + 6) = 2(x − 2)(x − 3), so x = 2 and x = 3.
The same structure with new numbers. Sam has to find two negative numbers again (product +6, sum −5), and Jo can check a formula answer by factoring.
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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