LANTITE Numeracy common mistakes
LANTITE Numeracy · Understand the traps and how to avoid them.
When asked for a pre-GST or pre-discount price, the candidate takes the stated percentage of the final amount and subtracts it (e.g. for a $110 total including 10% GST, they compute 10% of 110 = 11 and answer $99).
The percentage was applied to the original, unknown amount, not to the final amount, so the candidate is working backwards from the wrong base while feeling that the operation is obviously 'subtract the tax'.
What to do instead
Write the relationship as an equation before calculating: original x 1.10 = final. Then original = final / 1.10. Check by forward-applying the multiplier to your answer and confirming it returns the stated final amount.
The candidate rounds partway through a multi-step calculation (e.g. rounds a unit price to 2 decimal places, then multiplies by 40 items) and the final answer differs from the key.
Intermediate numbers are easier to hold in working memory when rounded, and candidates do not realise that the rounding error is then multiplied by the size of the final step.
What to do instead
Carry full calculator precision (or at least 4 decimal places) through every intermediate step and round only the final answer, to the precision the question asks for.
When comparing two rates or deals, the candidate compares the totals directly or subtracts one total from the other instead of converting both to a common per-unit or per-100g basis.
The totals are the most visible numbers on the page, and the candidate conflates 'cheaper total' with 'better value' without noticing the quantities differ.
What to do instead
Force every option onto the same denominator before comparing: divide price by quantity to get cost per unit (or per 100 g, per litre, per hour), then compare those figures and state the unit in the answer.
The candidate correctly calculates an intermediate quantity (the discount amount, the tax component, the number of remaining items) and submits that as the answer when the question asked for the final price or the original quantity.
The intermediate step is the last thing computed, so it is mentally 'the answer'; under time pressure the question's actual target is not re-checked.
What to do instead
Before calculating, underline what the question is asking for and write a one-line plan ending in that quantity; after calculating, re-read the final sentence of the question and confirm the number you have matches it.
The candidate converts a time expressed as hours and minutes into a decimal by placing the minutes after the decimal point (e.g. treating 1 hour 45 minutes as 1.45 hours).
The decimal notation for money (where $1.45 means one dollar forty-five cents) is heavily practised, and the base-60 structure of time is not visually signalled.
What to do instead
Convert minutes to a fraction of an hour by dividing by 60 (45/60 = 0.75), and convert back by multiplying the decimal part by 60. Sanity check that a decimal part above 0.6 corresponds to more than 36 minutes.
The candidate converts an area or volume by applying the linear conversion factor once (e.g. changing 3 m² to 300 cm², or 25 000 cm² to 2.5 m²).
The candidate treats the conversion factor as a property of the number rather than of the unit, forgetting that both dimensions were measured in the smaller unit.
What to do instead
Convert the linear dimensions before multiplying, or square the linear factor: 1 m = 100 cm so 1 m² = 10 000 cm², and 1 m³ = 1 000 000 cm³. Check with a rough picture - a square metre is about the size of a large door, not a sheet of paper.
The candidate uses a map or plan scale linearly to find an area, multiplying a measured area by the scale factor (e.g. a 1:100 plan, 4 cm² on the plan, answered as 400 cm²).
The scale statement looks like a single multiplier to apply to whatever number was measured, and the candidate does not distinguish between lengths and areas.
What to do instead
Convert the lengths first, or square the scale factor for areas: at 1:100, an area on the plan is multiplied by 100² = 10 000. Do the same with cubes and 100³ for volume.
The candidate reads a value off a graph by aligning to the nearest gridline rather than the marker's actual position, or compares bar heights on an axis whose origin is not zero as though the bars were proportional to the underlying quantities.
Graph reading is usually done by quick visual matching, and a truncated or broken axis silently exaggerates differences while still looking like a normal chart.
What to do instead
Before quoting any value, identify the axis scale, the direction of the minor gridlines and whether the axis starts at zero. For comparisons, read the labelled values or tick marks rather than judging length by eye, and note in the question whether the axis is truncated.
The candidate reports the mean as the typical or representative value for a data set that contains an outlier or a highly skewed distribution, or averages two group means without weighting them by group size.
The mean is the most practised average, and candidates apply it by default without checking the shape of the data or the sizes of the groups being combined.
What to do instead
Check the data for extreme values and skew first; if present and the question asks for a typical value, use the median and be ready to say why. When combining groups, multiply each mean by its group size, add, then divide by the total number of items.
For 'at least one' questions the candidate adds the individual probabilities of each event, and for multi-stage chance questions they treat events as independent when the items are drawn without replacement.
The word 'or' in the question suggests addition, and independence is the default assumption unless the candidate actively notices that the first item is removed.
What to do instead
For 'at least one', compute 1 minus the probability of none, multiplying along the branches. Before multiplying, ask whether the pool changed: if items are not replaced, update the denominator (and numerator) for the second draw.