ADF JOA Numerical common mistakes
ADF JOA Numerical · Understand the traps and how to avoid them.
When a series alternates between two interleaved rules (e.g., +3, ×2, +3, ×2), the candidate applies one rule to every consecutive pair and declares the series broken or picks a value that fits only the last step.
The eye locks onto the most recent gap and extrapolates from it; interleaved series look irregular at first glance, so the candidate abandons structure-seeking too early and guesses by feel.
What to do instead
Before computing anything, write the first differences under the series. If differences do not form a clean pattern, split the terms into odd-position and even-position rows and test each row separately. Practise 20 alternating-rule series until splitting is automatic.
On a series with growing gaps (e.g., +2, +4, +8, +16), the candidate computes the next gap correctly but then adds it to the wrong term, or stops one step short and reports the gap rather than the next term.
Working memory is loaded by the multi-step arithmetic, so the final operation (adding the gap to the last term) gets dropped or applied to the previous gap value.
What to do instead
Adopt a fixed two-line layout: line one lists the gaps, line two writes the running term. Circle the requested quantity (next term vs. next gap) before starting. Always finish by re-reading the question stem to confirm what is being asked.
In multi-step arithmetic, the candidate evaluates left to right and computes 8 + 4 × 3 as 36, or handles a bracketed subtraction of a negative incorrectly (e.g., 15 − (4 − 9) as 10 instead of 20).
Reading order competes with operation order; under time pressure the brain follows the visual left-to-right sequence rather than the precedence hierarchy.
What to do instead
Insert precedence marks before calculating: bracket each multiplication/division group with a pencil stroke, then work outward. For sign errors, rewrite every bracket as an explicit addition of a signed number before combining.
The candidate computes a percentage increase and a percentage decrease of the same rate as cancelling out (treating +20% then −20% as no change), or applies a discount to the already-discounted price instead of the original.
Percentages feel additive because the numbers look symmetric; the candidate anchors on the rate rather than on the changing base.
What to do instead
Force a base into every percentage step by writing the multiplier chain (e.g., 1.20 × 0.80 = 0.96). For successive discounts, label each base explicitly ('on original', 'on reduced price') before multiplying.
When a ratio is given as 3:5 and the candidate must split a total, they divide the total by the number of parts in the ratio (2) instead of the sum of the parts (8), or they assign the larger share to the smaller ratio term.
The ratio digits are read as quantities rather than as part-counts; the candidate skips the step of summing parts because it feels like an extra operation.
What to do instead
Use a rigid template: total parts = sum of ratio terms; one part = total ÷ total parts; then multiply by the required term. Write the ratio terms above the answer blanks so the mapping is visible before any division.
On a table question, the candidate reads the row total as the column value, or compares two categories using figures from different years because the row and column headers were only skimmed.
Tables present many numbers at once and the eye is drawn to bold or peripheral totals; time pressure discourages tracing headers back to the cell.
What to do instead
Before reading any number, trace the row header and column header with a finger or pencil to the target cell and say the label pair aloud (silently). Underline the exact cell used. Never quote a total unless the question asks for a total.
In a word problem, the candidate extracts the numbers but solves a different question - e.g., asked for the cost per item, they report the total cost; or they ignore a stated constraint such as 'the remainder is shared equally among 4 people'.
Numbers are salient and easy to grab, while the relational wording ('per', 'each', 'remaining') is processed shallowly, so the arithmetic drifts to the most obvious operation.
What to do instead
Before calculating, write a one-line 'given / required' note and box the required unit (per item, per person, total). After solving, check that the answer's unit matches the boxed unit.
The candidate mixes units within one calculation - adding minutes to hours, or multiplying a rate in km/h by a time given in minutes without converting - and reports an answer off by a factor of 60.
Units are treated as decoration rather than as quantities; the conversion step is invisible in the arithmetic so nothing flags the error.
What to do instead
Attach units to every number as you write it and carry them through the multiplication (km/h × h = km). If the units do not cancel to the required output unit, stop and convert before continuing.
The candidate spends several minutes on one stubborn question, then rushes the remaining questions and makes avoidable arithmetic slips on items they could have solved.
Sunk-cost pressure makes abandoning a question feel like losing progress; without a pre-set threshold, there is no cue to move on.
What to do instead
Set a hard per-question cap in advance (e.g., 60–75 seconds) and practise with a visible timer. When the cap hits, mark the question, enter a provisional answer, and move on; return only if time remains.
The candidate re-checks answers by re-reading their own working rather than recomputing, so a transcription slip (writing 84 for 48) survives verification and is submitted.
Re-reading confirms the reasoning felt right and skips the arithmetic; the brain recognises its own output as familiar and treats familiarity as correctness.
What to do instead
Verify by a different route: recompute from scratch on scrap paper, or check with an inverse operation (subtract to test an addition, divide to test a multiplication). Compare digit order explicitly on any number copied from the question.