ISEE Math Achievement common mistakes
ISEE Math Achievement · Understand the traps and how to avoid them.
When a word problem gives a rate (miles per hour, cost per item, words per minute), the candidate multiplies the two numbers without checking whether the units cancel to the quantity asked for, then reports the product as the answer.
Rate problems look like multiplication problems, and candidates pattern-match on 'per' as a cue to multiply. They do not track units, so they cannot see when the product has units like miles·hours instead of miles, or when division is required to get a per-unit answer.
What to do instead
Before computing, write the target unit and the units of each given number. Set up the operation so unwanted units cancel, as in miles = (miles/hour) × hours. If the units do not cancel to the target, invert the operation. Practice by labeling every number in a problem with its unit and writing a one-line dimensional check before selecting an answer.
The candidate reads the first few words of a multi-step problem, identifies a familiar problem type, and solves that type instead of the question actually asked, for example finding the total cost when the question asks for the change from a payment.
Under time pressure, the brain completes a familiar pattern early and stops reading. Multi-step ISEE items deliberately embed a final question that differs from the intermediate quantity, so the most obvious computed number is often a distractor answer choice.
What to do instead
Read the last sentence of the problem first and underline the exact quantity requested. After computing, return to that sentence and confirm the computed value answers it, not a related quantity. When two answer choices correspond to intermediate and final values, that is a signal to re-read the question stem.
When a problem requires two operations in sequence (for example, a discount then tax, or a perimeter then a cost per foot), the candidate performs only the first operation and stops, or applies the second operation to the original number instead of the intermediate result.
Multi-step problems require holding an intermediate result in working memory while reading the next condition. Candidates who do not write down the intermediate value lose track of which step they are on, and answer choices often include the result of the first step alone.
What to do instead
Adopt a fixed routine: after each operation, write the intermediate result on its own line with a short label such as 'price after discount = 48'. Only then read the next condition. Never chain operations mentally; each step gets a written line and a label.
The candidate solves for a variable and submits that value as the answer, even though the question asks for a related quantity such as the larger of two numbers, the number of items of one type, or an angle's supplement.
Algebra instruction trains 'solve for x', so x becomes the goal. In problems where x was chosen for the smaller or first quantity, the requested value is a different expression, and the value of x itself is usually offered as a trap answer.
What to do instead
At the moment of defining the variable, write explicitly what x represents, for example 'x = number of child tickets'. When the equation is solved, write the requested quantity as an expression in x and substitute, rather than stopping at x. Circle the requested quantity in the question before starting.
On questions comparing fractions, decimals, and percents, the candidate orders or compares them by the visible digits rather than by value, for example judging 0.4 smaller than 1/5 because 4 is smaller than 5, or treating 3/8 as larger than 0.4 because 8 is larger than 4.
Different notations invite digit-level comparison. Candidates who do not convert to a common form compare numerators, denominators, or decimal digits directly, which is valid only within a single notation.
What to do instead
Convert every quantity in a comparison to the same form, usually decimals, before ordering. Memorize the common fraction-decimal-percent equivalences (1/8 = 0.125, 1/5 = 0.2, 3/8 = 0.375, 2/5 = 0.4, 5/8 = 0.625, 3/4 = 0.75) so conversion is fast and does not consume time.
When adding or subtracting fractions, the candidate adds the numerators and adds the denominators (1/2 + 1/3 = 2/5), or when multiplying fractions, finds a common denominator first.
The procedures for adding and multiplying fractions are learned close together and interfere with each other. The addition rule (common denominator, add numerators only) is the one most often corrupted, and the result often appears among the answer choices.
What to do instead
Anchor each operation to a reason. For addition, the denominator names the size of the pieces, so the piece size must match before counts can be combined; for multiplication, 'of' means scaling, so multiply straight across. Before computing, say the rule aloud or write it: add/subtract = common denominator, multiply = straight across, divide = multiply by the reciprocal.
The candidate computes a percentage of a number using the wrong base, for example applying a 20% discount and then a 10% discount as a single 30% discount, or computing percent increase from the new value rather than the original.
Percentages are relative quantities, and candidates treat the percent as an absolute amount that can simply be added. Successive percent changes compound on different bases, and percent change is defined relative to the original value, which is easy to forget.
What to do instead
Write the base next to every percent before computing, for example '20% of original' and '10% of the reduced price'. For successive changes, apply them one at a time to the running value. For percent change, always write (new − original) ÷ original and label the denominator as the original amount.
The candidate computes an average by adding the given values and dividing by the number of values listed, even when the problem supplies a count, a total, or a missing value, such as finding the score needed on a final test to reach a target average.
The candidate has one formula, sum ÷ count, and applies it mechanically. Problems that give the average and ask for a missing element require reversing the formula (total = average × count), which is a different operation that the mechanical approach skips.
What to do instead
Always write the average relationship as total = average × count before substituting. Identify which of the three quantities (total, average, count) is unknown, then solve for it. For 'what score is needed' problems, compute the required total first, then subtract the known values from it.
When a geometry question gives dimensions in different units, or asks for area while giving perimeter information (or the reverse), the candidate substitutes the numbers into whichever formula comes to mind without converting units or checking which quantity is given and which is asked.
Formulas for perimeter and area of rectangles, triangles, and circles are memorized as a cluster and retrieved by association rather than by matching the formula to the requested quantity. Mixed units add a second failure point that candidates overlook because the numbers look compatible.
What to do instead
Before computing, write two labels: 'given = ___' and 'asked = ___', then select the formula that produces the asked quantity. Convert all dimensions to a single unit first and note the conversion explicitly. For circles, check whether the problem gives radius or diameter, since the diameter is the most common trap.
The candidate works entirely in their head, does not write intermediate steps, and then cannot locate an arithmetic slip; or, having found an answer that matches a choice, stops without checking it against the original conditions.
Mental arithmetic hides errors and prevents backtracking, and answer choices are designed so that predictable errors produce a matching option. Matching a choice therefore feels like confirmation even when the work is wrong.
What to do instead
Write every step, including simple arithmetic, and keep the work organized in columns so it can be re-read. Use a final check: substitute the chosen answer back into the original condition, or estimate the answer first (for example 19 × 21 is about 400) and confirm the choice is in the expected range before marking it.