SK SSA Math 5 common mistakes
SK SSA Math 5 · Understand the traps and how to avoid them.
When adding or subtracting fractions with unlike denominators, adding the numerators and the denominators straight across (e.g., 1/2 + 1/3 = 2/5) instead of building a common denominator.
The whole-number procedure for addition gets applied to the notation of fractions; the fraction bar is read as a separator rather than as a division that fixes the size of the parts, so the candidate never notices the answer is smaller than one of the addends.
What to do instead
Require a written estimate before computing: 1/2 + 1/3 must land between 1/2 and 1. Then force the routine of finding the least common denominator, rewriting both fractions with matching denominators, and checking the sum against the estimate. Practice with fraction strips or number lines until the size-of-parts idea is automatic.
Applying the standard division algorithm to decimals and placing the decimal point by counting digits in the divisor, producing answers like 4.8 ÷ 0.6 = 0.8.
The rule 'count decimal places and move the point' is remembered as a ritual without the underlying meaning that the quotient must be larger than the dividend when dividing by a number less than one.
What to do instead
Rewrite every decimal division as an equivalent whole-number division by multiplying both numbers by the same power of ten, and state the equivalence aloud. Then sanity-check with multiplication: 0.8 × 0.6 = 0.48, not 4.8, so the answer must be 8.
Treating a variable as a label for an object rather than as a number, so 3x + 2 is simplified to 5x or 5, and 2a + 3b is collapsed into 5ab.
Early exposure to letters as abbreviations (m for metres, x for 'a number I do not know yet') leaves the candidate without the idea that like terms must share the identical variable part before coefficients can be combined.
What to do instead
Have the candidate substitute test values (x = 4) into the original and the proposed simplification to show the results differ. Then drill the rule explicitly: combine coefficients only when the variable parts are identical, and keep unlike terms as separate terms.
Extending a numeric or shape pattern by guessing the next term from the last two terms instead of from the rule, so a pattern with a constant second difference is continued additively.
Candidates look for the simplest visible relationship, usually a constant difference between consecutive terms, and stop checking once one step fits; they rarely test whether the same rule reproduces all the given terms.
What to do instead
Impose a two-step check: find the difference between every consecutive pair, then find the differences of those differences. Write the rule as a sentence and verify it against all given terms before predicting the next one. For shape patterns, count elements per stage in a table first.
Confusing area and perimeter formulas, for example computing the area of a rectangle as 2(l + w) or the perimeter as l × w, and reporting area in linear units.
Both quantities are taught together and both use the two side lengths, so the procedures interfere; the candidate has not attached the distinct meaning of 'distance around the edge' versus 'space covered' to each formula.
What to do instead
Before any calculation, have the candidate state what is being measured and which unit applies (square units for area, linear units for perimeter). Pair each problem with a quick sketch, and use grid paper so counting squares and tracing the boundary become visibly different actions.
Converting between units by choosing the operation from the direction of the numbers (large to small means divide) rather than from the relative size of the units, producing errors such as 3.5 m = 350 cm being written as 0.035 cm.
The conversion factor is recalled as a bare number without the relationship 'a metre is 100 times a centimetre', so the candidate has no way to decide whether the answer should grow or shrink.
What to do instead
Always write the conversion as a fraction with units and cancel them (3.5 m × 100 cm/1 m), and require a magnitude check: converting to a smaller unit must give a larger number. Build a reference table of common equivalences and rehearse it weekly.
Reading a bar or line graph by comparing the heights of the drawn bars or the visual steepness of segments without checking the axis scale, which may start at a nonzero value or use unequal intervals.
The visual impression of the picture dominates, and candidates are rarely taught that a truncated or broken axis exaggerates differences; they treat the graph as a literal picture of the data.
What to do instead
Train a fixed reading routine: read the axis labels and the scale interval first, note whether the axis starts at zero, then read values off the scale rather than off the picture. Ask 'what would this look like if the axis started at zero?' for every graph encountered.
Reporting the probability of a compound or complementary event without accounting for all outcomes, for example saying the probability of not rolling a 6 on a die is 5/6 of the favourable cases only, or adding probabilities of overlapping events.
The candidate counts the outcomes they are interested in and divides by a denominator that was never explicitly enumerated, or treats 'or' as always additive without checking whether the events can happen together.
What to do instead
Require an explicit sample space listed or in a table before any probability is written, then mark the favourable outcomes on it. Teach the complement rule P(not A) = 1 − P(A) as a check, and test whether events overlap before adding.
Answering the quantity asked for in the problem rather than the quantity the question actually requests, for example giving the cost of one item when the total cost was asked, or stopping at an intermediate value in a multi-step word problem.
Working memory is consumed by the arithmetic, so the final sentence of the problem is not re-read; the candidate treats the last number computed as the answer by default.
What to do instead
Have the candidate underline the question sentence before starting and write a one-line answer plan naming the final quantity and its unit. After computing, re-read the underlined question and confirm the answer matches it, including units and reasonableness.
Accepting the first numerical result that 'looks right' without estimating, so an answer off by a factor of ten or with a misplaced decimal is submitted unchanged.
Candidates equate finishing the computation with solving the problem and have not built the habit of a separate verification step; under time pressure, checking feels like wasted effort.
What to do instead
Institutionalise a ten-second check: round the inputs to friendly numbers, recompute mentally, and compare the order of magnitude with the written answer. Practise this on worked examples until it becomes part of every solution, and treat a mismatch as a signal to redo the work rather than adjust the answer.