AMO common mistakes
AMO · Understand the traps and how to avoid them.
On a multi-step problem, the student answers the first quantity computed (e.g., total cost before the discount) and stops, submitting an intermediate value as the final answer.
Working memory gets anchored on the first 'answerable' number, and the student never re-reads the actual question sentence to confirm which quantity was requested.
What to do instead
Before writing the final answer, underline the question's demand word (how many more, total, remaining, per person) and check the last computation against it; train with problems where the intermediate result is deliberately a tempting distractor.
The student sets up an equation or number sentence with the quantities in the wrong order, e.g., writing 3 − 8 or dividing the smaller by the larger, producing a negative or fractional result for a counting problem.
Younger students match numbers to operations by keyword ('left' means subtract) without checking which quantity is larger or what the operation means in context.
What to do instead
Have the student restate the situation in words first ('8 apples, eat 3, so the answer is less than 8'), then write the sentence; require a plausibility check that the result is a whole number in a sensible range.
When a problem gives a pattern or table, the student extends it by one term and reports that term instead of the term actually asked for (e.g., asks for the 20th figure, student writes the 5th).
The student confuses 'continue the pattern' with 'answer the question' and lacks a strategy for jumping many steps at once.
What to do instead
Teach finding the rule (add 4 each time, start at 3) and writing it as 'start + (n − 1) × step', then substituting n = 20; verify with a small case like n = 3 before trusting the formula.
The student computes an area or perimeter using the wrong formula for the shape, or mixes units (cm with cm²) in the final answer.
Formulas are memorized as strings without attaching them to a picture, and unit labels are treated as decoration rather than meaning.
What to do instead
Require a quick labeled sketch with dimensions before computing, and mandate unit tracking in every line; discuss why perimeter is a length and area is squared.
On fraction problems, the student adds numerators and denominators (1/2 + 1/3 = 2/5) or compares fractions by comparing denominators alone.
The student overgeneralizes whole-number rules to fractions, where the same symbols behave differently.
What to do instead
Anchor with a same-whole diagram or benchmark comparison to 1/2; drill finding a common denominator and rewriting each fraction before adding, and check the sum is larger than each addend.
The student solves a rate or ratio problem by guessing which operation to apply, producing an answer that is off by a factor (e.g., 3 times too large) without noticing.
The student has no habit of estimating the answer's size before computing, so a unit-rate error passes undetected.
What to do instead
Require a one-line estimate ('about 4 hours, so 12 is wrong') before calculating, and set up rates as a labeled proportion with units canceling; check the answer's units match what was asked.
In a problem with two unknowns or a system of conditions, the student fixes one value arbitrarily and solves only the easy half of the constraints.
The student treats a constraint as optional, or cannot hold two conditions simultaneously and drops one.
What to do instead
List every given condition as a numbered fact, then after solving check each fact against the proposed answer; practice problems where a single guess satisfies one condition but fails the other.
The student computes a percentage change or discount by applying the percent to the already-discounted price, or adds percents that should be compounded.
Percent problems are read left to right as a sequence of independent operations, ignoring that each percent applies to a different base.
What to do instead
Label the base for every percent ('20% of the original price', '10% of the new price') and write each step as a separate line with its base named; test with a concrete number like $100.
On algebra and integer problems, the student drops negative signs or distributes a minus sign over only the first term, e.g., −(x − 3) becomes −x − 3.
Sign handling is treated as clerical rather than structural, and the student works too fast to notice the sign error propagating.
What to do instead
Require parentheses around every substituted negative value and a slow, explicit distribution step; substitute a test value (x = 1) into the original and simplified expressions to confirm they match.
On counting and probability problems, the student counts arrangements as if order matters when it does not (or vice versa), or adds probabilities of overlapping events.
The student has no decision rule for distinguishing ordered from unordered selections and no picture of the sample space.
What to do instead
Before computing, ask 'would swapping these two give a different outcome?' and list a small sample space by hand (e.g., all pairs from 4 items) to see the structure; for overlapping events, subtract the intersection or use a two-circle diagram.