Did you know that removing one faulty question from a class test can make one pupil’s percentage go up and another pupil’s percentage go down? That sounds unfair until you examine what was removed from both the mark earned and the mark available. A percentage is a ratio. Change the numerator or denominator and the result changes, sometimes in surprising directions.
Recalculating a test percentage after withdrawing a question means applying the assessment’s approved correction rule consistently to every affected script and recomputing the earned marks divided by the new available marks. If the rule is to exclude a four-mark item from a 40-mark additive test, remove the marks each pupil earned on that item and remove its four available marks. The new maximum is 36, not 40. But item exclusion is only one possible correction rule; use the actual school’s or assessment body’s decision, not an improvised one.
Start with the exact marking decision, not the student’s old percentage
A child may ask, “My score was 28 out of 40. If the school deletes a four-mark question, does my new result become 28 out of 36?” The answer is not automatically yes. If the child received two marks on the withdrawn item and the adopted correction is full item exclusion, the revised numerator is 28 − 2 = 26, and the revised denominator is 40 − 4 = 36. Leaving two invalid marks inside the numerator would mix incompatible totals.
The essential diagnostic is whether the pupil tracks which marks are retained. Ask them to identify three things before doing arithmetic: the original total, the original mark on the withdrawn item, and the precise correction policy. If any one is unknown, the new percentage is not established. A percentage alone cannot tell you what the pupil scored on a particular question.
Why a question may be reconsidered
In a hypothetical classroom assessment, an item may contain a missing condition, an unreadable diagram, two defensible answers or a printing error. A teacher might review the mark scheme, allow valid alternative answers, award full credit under a chosen rule, exclude the item or use another documented approach. Those choices are not equivalent. A question that is hard is not necessarily faulty; and a question that a student dislikes is not automatically invalid.
Real examination bodies establish their own processes, sometimes involving much more than simple percentage recalculation. For broad context, Cambridge International explains its marking-and-grading approach and the importance of a consistent standard. The worked classroom calculations below are invented demonstrations of arithmetic, not claims about Cambridge, Singapore MOE or SEAB correction procedures.
Complete invented worked example: an excluded four-mark question
Pupil A: a percentage rises
Fictional class exercise, not an actual school policy or result: a test originally contains 40 possible marks. Question 8 is worth four, and the teacher has formally decided to exclude Question 8 from every script. Pupil A earned 28 marks in total, including two on Question 8.
- Original result: 28 ÷ 40 × 100 = 70%.
- Remove earned marks on excluded item: 28 − 2 = 26 marks retained.
- Remove available marks on excluded item: 40 − 4 = 36 marks available.
- Revised result: 26 ÷ 36 × 100 = 72.222…%, approximately 72.2% to one decimal place.
- Difference: approximately 72.2% − 70.0% = +2.2 percentage points.
Verify independently: 26/36 simplifies to 13/18; 13 ÷ 18 is 0.72222…, so 72.222…% is right. Reversing the computation, 26 retained marks plus two excluded marks equals the original 28. The maximum 36 plus the four-mark item returns 40. Both balances are useful audit checks.
Pupil B: a percentage falls even under the same fair rule
Now suppose Pupil B earned 34 out of 40, including all four marks on Question 8. The original result is 34 ÷ 40 = 85%. Under the identical exclusion rule, the retained score becomes 34 − 4 = 30 out of 36; 30 ÷ 36 × 100 = 83.333…%, or about 83.3%. The change is −1.7 percentage points to one decimal place.
Nothing about this result proves a teacher favoured one pupil. The excluded question accounted for a different share of each pupil’s original earned marks. Removing it changes both scores according to the same rule. A policy’s fairness must be considered in the whole assessment context; equal application of the arithmetic is necessary but not by itself a complete judgement about the policy.
The opposite policy produces a different answer
Imagine instead that an authorised teacher chooses to award all pupils the full four marks on that item while retaining the original 40-mark maximum. Pupil A, who originally received two, would gain the other two and receive 30 out of 40, or 75%. Pupil B already had four and would remain 34 out of 40, or 85%. This is a different policy, not another way of calculating the exclusion policy. Never switch between methods halfway through marking.
How to record the change so parents can understand it
An informative correction note should show the item identifier, its maximum marks, the reason the item was reconsidered, the authorised adjustment rule, and the before-and-after score for a pupil, subject to privacy. It should not disclose classmates’ identifiable marks. The note might say: “Question 8, four marks, was excluded from the class assessment after review. Your score on that item was two. Your adjusted total is 26 of 36, approximately 72.2%.”
It also helps to distinguish a raw percentage from a grade. A raw percentage follows arithmetic. A grade may depend on a grade boundary, grading policy, other components or moderated evidence. A teacher should not make a new grade claim simply by seeing a changed percentage. If the assessment has published correction and grading rules, those rules control.
An error-checking algorithm for a spreadsheet or calculator
- Step 1: write the original earned total T and original maximum M, with M greater than zero.
- Step 2: for an excluded item, record its earned marks q and maximum m, with 0 ≤ q ≤ m and m less than M.
- Step 3: calculate revised earned total T − q and revised maximum M − m.
- Step 4: compute revised percentage (T − q) ÷ (M − m) × 100, keeping enough digits until the final display.
- Step 5: check that retained earned marks do not exceed retained maximum and that all scripts follow the same approved rule.
Here the symbols are bookkeeping aids, not a required school convention. If marks come from non-additive rubrics, scaled results, weighted components or penalties, a simple subtract-and-divide formula may be inappropriate. Keep the original rubric and seek the responsible teacher’s official instructions. A spreadsheet that produces a neat number cannot repair a mistaken policy.
The misconception that a removed question always helps everyone
A denominator shrinks when marks are removed, but the numerator can also shrink. Students often notice only the smaller denominator and expect a higher percentage. A useful counterexample is a pupil who earned full marks on the excluded question: the retained percentage may be lower because the pupil performed especially well on that item. Conversely, a pupil who earned zero may see a larger percentage because the numerator stays unchanged while the maximum falls.
Other recurring mistakes include treating percentage points as relative percentages, rounding each intermediate mark calculation, applying exclusion to only the pupils who complained, and forgetting to save the original mark breakdown. An ethical correction remains traceable: original record, rule, revised record and reason. Nothing requires erasing the initial score from the internal audit trail.
Progressive practice: from arithmetic to fair explanation
Guided: one pupil, one excluded mark
A fictional pupil receives 17/25 including one mark on a two-mark item later excluded. Ask for the revised fraction: (17 − 1)/(25 − 2) = 16/23. The revised percentage is 16 ÷ 23 × 100 = about 69.6%; the original 17 ÷ 25 × 100 = 68%. The new percentage is higher by about 1.6 percentage points. The student must explain why 17/23 is wrong under the exclusion rule.
Paired: two pupils under one rule
The same two-mark item is excluded from another 25-mark test. Pupil C had 21 marks including two on the item; Pupil D had 14 marks including zero. C changes from 21/25 = 84% to 19/23 ≈ 82.6%. D changes from 14/25 = 56% to 14/23 ≈ 60.9%. Ask partners to explain the differing direction without claiming that one pupil was favoured. This also checks that the new denominator is used consistently.
Independent: spot the wrong policy
Give a report that reads: “Original 32/40; Question 5 worth four marks excluded; student had earned three on it; adjusted percentage 32/36 = 88.9%.” The pupil must flag the mistake: under the stated exclusion rule, the retained total is 29/36 ≈ 80.6%. Original 32/40 was 80%. The wrong calculation failed to remove three earned marks, manufacturing an exaggerated increase.
How this lesson transfers beyond tests
The same numerator-and-denominator discipline applies to surveys with nonrespondents, an experiment that excludes an invalid trial, an attendance rate that removes an ineligible day and a graph where the reference total changes. However, the decision to exclude data is a methodological judgement made before the calculation, not an excuse to discard inconvenient results. A correct formula cannot validate a bad exclusion reason.
A four-week teaching sequence
- Week 1: practise percentages and mark totals with whole-number examples; distinguish marks earned from maximum available.
- Week 2: compare full-credit and exclusion policies on identical invented scripts, explaining why they produce different answers.
- Week 3: audit a small fictional class table with three students, one excluded item and no identifying information.
- Week 4: write a clear parent-facing explanation with before/after percentages, correction rule, units and limitations.
What parents and teachers should look for
A parent can ask: “What did the school decide to do with the disputed question, and is my child’s revised total calculated under that rule?” The teacher can provide a clear explanation without turning a normal correction into a contest among students. Observable progress in the pupil’s mathematical understanding includes keeping the two totals straight, handling the units, checking the arithmetic and recognising a policy question separately from a calculation question.
For pupils whose test result is upsetting, focus also on what was learnt and which skills need another opportunity. The adjusted percentage is one report of performance, not a complete measure of ability or potential. Respect the school’s published procedures and communication channels for a real dispute.
Important limits
This is an educational calculation, not advice to change an official mark. Real external examinations may use equating, standardisation, moderated grade boundaries and confidential review processes. Even school-based assessments may have multiple components and assessment objectives that make simple reweighting unsuitable. Never promise a student’s final grade will rise because a question is withdrawn.
When a disputed item has multiple parts, first confirm whether the entire item or only a defined subpart has been removed. If the remaining score is based on a banded rubric or an assessment objective, do not assume the arithmetic example applies. Ask for the actual approved adjustment method.
Frequently asked questions
Why not keep the old earned marks and just lower the maximum?
That would count earned marks from a question whose possible marks no longer belong to the assessment. Under full exclusion, both the earned and possible parts of the excluded item must leave the total.
Should everyone be given full marks instead?
That is a separate policy option, not a universal rule. The authorised assessor must determine the treatment, document the rationale and apply it consistently under applicable requirements.
Will my grade change if the percentage changes?
Possibly, but not necessarily. Grade rules may depend on thresholds, components or other procedures. Ask the responsible assessment body rather than inferring the grade from one arithmetic adjustment.
Can a pupil’s percentage fall after a question is removed?
Yes. The worked Pupil B example shows a decrease from 85% to approximately 83.3% because the removed question was answered particularly well.
Is 72.2% the same as an increase of 2.2%?
No. From 70.0% to approximately 72.2% is an increase of about 2.2 percentage points. Relative percentage change uses a different denominator.
Related eduKate explanations
For other assessment fairness problems, explore how to show progress when a rubric changes and how to interpret retests using only previously missed questions. The Clementi Secondary 1 Mathematics learning model demonstrates the value of diagnosing a mistake before practising a correction, while the eduKate Education Hub connects the wider learning questions.
The core aim of this lesson is bigger than a percentage. A learner who can distinguish an assessment rule from the calculation, preserve the original evidence, explain the new denominator and check the final number has learnt a form of mathematical integrity. That skill remains useful long after this particular test is forgotten.