NLN NEX Math common mistakes
NLN NEX Math · Understand the traps and how to avoid them.
When adding or subtracting fractions with unlike denominators, the candidate adds the numerators together and the denominators together (writes 1/2 + 1/3 = 2/5) instead of finding a common denominator first.
The candidate memorised 'add the tops, add the bottoms' from early whole-number work with fractions of the same denominator and never separated the two procedures. The rule feels symmetrical and plausible, so nothing triggers a check.
What to do instead
Before any fraction addition/subtraction, force one written step: rename both fractions with the least common denominator and write the new pair on the page. Then add only the numerators and copy the denominator unchanged. Do a sanity check by estimating with benchmark fractions (1/2 + 1/3 should be a bit under 1, not 2/5).
In decimal multiplication and division, the candidate drops or adds a decimal place - e.g., computing 0.4 × 0.25 as 1.00 instead of 0.100 - or moves the decimal in the divisor without moving it the same number of places in the dividend.
The candidate treats the decimal point as decoration applied at the end rather than as part of the quantity, and has no reliable procedure for counting decimal places in the product or for shifting both numbers in a division.
What to do instead
Use a fixed written routine: multiply as whole numbers, then count the total decimal places in both factors and place that many in the answer. For division, write the shift explicitly (0.6 ÷ 0.15 becomes 60 ÷ 15) and mark the arrows before dividing. Always finish with a magnitude estimate (0.4 × 0.25 is about 0.5 × 0.25 = 0.125, so 1.00 is impossible).
On percent problems the candidate applies the percent to the wrong quantity or uses the percent number as the divisor - e.g., answering '15% of 60' with 60 ÷ 15 = 4, or computing a percent increase by dividing the change by the new value instead of the original.
The candidate has a single vague formula ('percent = part over whole') but no method for deciding which number is the whole, so under time pressure the percent itself gets treated as the base. Percent increase/decrease is especially fragile because two plausible denominators exist.
What to do instead
Before calculating, write the sentence: 'The original/whole amount is ____, the part is ____.' For percent change, always divide by the original value and label it in writing. Convert the percent to a decimal in a separate step and cross out the percent sign so the number cannot be reused as a divisor.
When solving a linear equation, the candidate distributes a negative coefficient to only the first term in parentheses, or moves a term across the equals sign without changing its sign (writes 3x + 5 = 20 as 3x = 20 + 5).
The candidate is executing a memorised sequence of moves quickly rather than tracking equality as a balance operation; the negative sign in front of a parenthesis is visually absorbed into the first term only, and the inverse operation is applied inconsistently.
What to do instead
Force one line per operation, and when distributing write every product out ( −2(x − 4) becomes −2x + 8, showing both multiplications). For transposition, write the inverse operation on both sides of the line rather than sliding terms across, and substitute the final answer back into the original equation as a mandatory last step.
When solving an inequality, the candidate multiplies or divides both sides by a negative number and keeps the inequality symbol pointing the same way (turns −2x > 8 into x > −4).
Inequalities are practised far less than equations, so the flip rule is remembered as a trivia item rather than as part of the procedure, and it is easily skipped when the candidate is focused on the arithmetic.
What to do instead
Adopt a written checkpoint: whenever the working line has a division or multiplication by a negative, draw an arrow under the symbol and reverse it on the next line. Verify by testing one number from the resulting solution set in the original inequality - a single test value catches the error immediately.
The candidate reverses the order in subtraction and division phrases when translating word problems into algebra - writing 5 − x for '5 less than a number' or 12 ÷ x for '12 divided by a number' - producing an equation that cannot match the stated relationship.
English word order does not match algebraic order for 'less than', 'fewer than' and 'divided by', and the candidate translates left-to-right word by word instead of identifying the operation and its operands.
What to do instead
Circle the comparison phrase, then reorder it into 'operation (second quantity, first quantity)' in speech before writing symbols: '5 less than x' is spoken as 'x minus 5'. For division, rewrite 'divided by' as 'per' and state which quantity is being split. Test with a concrete number (let x = 10) to confirm the expression gives the sensible value.
In circle problems the candidate substitutes the diameter for the radius in A = πr² and C = 2πr, or uses the circumference formula when the question asks for area, producing answers that are off by a factor of 2 or 4.
Everyday language ('the distance across the circle') gets recorded as the value in hand, and the formulas are recalled as undifferentiated strings of letters rather than as descriptions of a picture. The half-diameter computation is a step the candidate skips entirely.
What to do instead
Draw the circle and label the given segment before choosing a formula; if the labelled segment passes fully through the centre, write r = d ÷ 2 as an explicit first line. Attach a unit check to each formula (area in square units, circumference in linear units) so a wrong formula is caught by the units alone.
The candidate converts units in the wrong direction (multiplies when the answer should be smaller), applies only one step of a multi-step conversion, or converts a volume by the linear factor instead of its cube - e.g., turning cubic inches into cubic feet by dividing by 12 rather than 1,728.
The candidate picks multiply or divide by pattern-matching 'big unit to small unit' without a reliable anchor, and treats volume as if it had one dimension. Chained conversions collapse into a single guessed operation under time pressure.
What to do instead
Write conversions as a fraction setup with units that cancel, so the direction is decided by the units rather than by intuition. For volume or area, cube or square the conversion factor explicitly and write it out (1 ft³ = 12³ in³ = 1,728 in³). Finish with a plausibility check: converting to a smaller unit must give a larger number.
In statistics items the candidate averages without counting every data value (dropping zeros or blanks), or reports the median of a data list without first sorting it, so a middle value is taken from the original order of the table.
Tables of data invite quick scanning, and zeros and empty entries are visually 'nothing' rather than a value of zero. The median definition ('middle number') is remembered without its precondition that the list be ordered, which is invisible when the data already looks roughly sorted.
What to do instead
Recount the set out loud and write n before dividing, explicitly marking each value as it is used, including zeros. For the median, always rewrite the list in ascending order as a separate line, then apply the odd/even rule. If the mean and median disagree sharply, check whether an outlier is distorting the mean.
On rate problems the candidate averages two speeds or rates by adding them and dividing by 2, and on graph items reads values off the axis by counting gridlines rather than using the stated scale interval.
The mean of two numbers feels like the natural 'average', and the candidate does not connect the rate to total distance over total time. Similarly, axis labels are skimmed, so a gridline worth 5 units is read as 1.
What to do instead
For combined-trip problems, always build a small table of distance and time for each leg, total them, and divide total distance by total time; note in writing that a simple average only works when the times are equal. For graphs, state the scale value of one grid interval in words before reading any point.