CCSLC Mathematics common mistakes
CCSLC Mathematics · Understand the traps and how to avoid them.
Reading a word problem once and immediately computing with the first two numbers that appear, without first stating what quantity is asked for and what units the answer needs.
CCSLC-style items embed numbers in context (recipes, bills, timetables, wages). Candidates pattern-match to a familiar operation and skip the comprehension step, so they answer a different question than the one asked.
What to do instead
Before any arithmetic, write one line: 'They want ______ (quantity), in ______ (unit).' Then underline the data that feeds that quantity and cross out distractors. Do this for every structured-response item, even easy ones, until it becomes automatic.
Treating a percentage as a whole number and computing 15% of a price as 15 times the price, or subtracting a discount from the wrong base (e.g. taking 20% off an already-discounted price by adding the two percentages).
Percentage is taught procedurally as 'divide by 100' and candidates memorise the button sequence without the meaning of 'per hundred'. Successive percentage changes compound, which intuition does not flag.
What to do instead
Always convert to a multiplier first: 15% means ×0.85 for a discount, ×1.15 for an increase. For successive changes multiply the multipliers (0.85 × 0.90), never add the rates. Sanity-check: a discount must make the answer smaller than the original.
Writing a ratio in the order the numbers appear rather than the order the question names, or scaling a ratio by adding the same amount to each part instead of multiplying each part.
Ratio language ('for every', 'to', 'per') is direction-sensitive, and additive thinking is the default intuitive strategy for scaling; multiplicative reasoning must override it deliberately.
What to do instead
Label each ratio term with its object before using it (sugar:flour = 2:5). For scaling, find the multiplier from the known part (total parts, or one known quantity) and multiply every term. Test with a small case: 2:5 doubled is 4:10, not 4:7.
Mixing units within one calculation - minutes with hours in a speed or wage problem, cents with dollars in a bill, grams with kilograms in a recipe - and reporting the answer without a unit.
Realistic contexts present data in the units people naturally use, and candidates transcribe numbers without converting. Unit labels are treated as decoration rather than part of the value.
What to do instead
At the start of each item, convert every given quantity to one working unit and write the converted values beside the originals. Carry units through the calculation as if they were symbols, and require the final line to read 'answer + unit' before moving on.
Giving a bare numerical answer to an 'explain', 'justify', or 'comment on' part, or writing 'because it is cheaper' with no comparison of the actual figures.
Candidates read these parts as optional commentary and spend their effort on the calculation. They also confuse explanation with restating the result, since school feedback often rewards the right number alone.
What to do instead
Treat command words as a checklist: 'explain' needs a because-clause citing the computed values; 'compare' needs both figures named; 'comment' needs a judgement plus a reason. Draft the sentence with the numbers inserted, e.g. 'Plan B costs $12 less over 6 months because...'.
Accepting a plausible-looking answer without checking it against the context - a bus that travels 900 km in 2 hours, a person's weekly wage of $4,000 from a $10 hourly rate, a discount larger than the price.
Candidates trust the arithmetic and stop; estimation and reasonableness checks are rarely practised, and there is no habit of asking whether the magnitude fits the real world.
What to do instead
After computing, run a 10-second plausibility test: compare against a known anchor (walking 5 km/h, a bus ~80 km/h, a full-time week ~40 hours). If the answer is off by a factor of ten or more, re-read the setup before writing anything down.
Choosing the cheapest headline price or the highest advertised interest rate without computing total cost over the stated period, ignoring fees, deposit, or term length.
Decision items reward comparing totals, but candidates compare the single most visible number. Advertised rates and prices are designed to be the most salient figure, and compounding or fees are buried.
What to do instead
Build a small comparison table with columns for each option and rows for every cost component (upfront, per period, total over the term). Fill every cell before judging. State the decision in one sentence naming the criterion used and the totals that support it.
Misreading tables and timetables - taking a value from the wrong row or column, ignoring a 'per 1,000' or 'per person' header, or forgetting that a timetable crossing midnight restarts at 00:00.
Reading a grid is a separate skill from calculating, and candidates scan for a matching number rather than locating the intersection of the correct row and column. Header qualifiers are skipped as small print.
What to do instead
Trace with a finger or pencil: name the row label aloud, then the column label, then read the cell. Copy the header qualifier into your working ('cost per 1,000 units'). For time spans, convert to a 24-hour scale first and add 24 hours when the end time is earlier than the start.
Leaving answers unrounded or wrongly rounded - quoting $47.3333 for a cash amount, truncating instead of rounding, or rounding intermediate steps so the final figure drifts.
Candidates either keep calculator displays verbatim or round at every stage for tidiness. The convention that money is given to two decimal places and that rounding happens at the end is assumed rather than taught explicitly.
What to do instead
Keep full precision in working and round only the final answer. Match the unit: money to 2 decimal places, people and items to whole numbers (and never round a part-person up when the question asks how many can be served). Record the rounded answer separately from the working line.
Presenting working as an unlabelled string of numbers with no statement of method, so that a correct answer cannot earn method marks and an arithmetic slip loses everything.
Candidates equate showing work with copying calculator output. They have not internalised that structured-response marking awards credit for a valid stated method independent of the final figure.
What to do instead
Use a fixed three-line layout: (1) the formula or plan in words or symbols, (2) substitution with units, (3) the answer with unit and a one-line check. Even when using a calculator, write the substituted line so the method is visible and recoverable.