Praxis Middle School Math common mistakes
Praxis Middle School Math · Understand the traps and how to avoid them.
When adding or subtracting fractions, the candidate operates across the numerators and across the denominators (e.g., writes 2/3 + 1/4 = 3/7) instead of rewriting the fractions with a common denominator.
Whole-number arithmetic is deeply overlearned, and the fraction bar is read as a separator between two independent whole-number problems rather than as a single value. Candidates who have memorized 'add the tops, add the bottoms' from a misread rule rarely stop to estimate.
What to do instead
Before computing, force a magnitude estimate (2/3 + 1/4 is close to 1), then build the common denominator by listing multiples of the larger denominator. Drill a self-check: the sum of two positive fractions must be larger than either addend - 3/7 fails that test instantly.
The candidate evaluates a negative base raised to a power without parentheses as if the base were negative (treats -3^2 as 9), and evaluates subtraction of a negative as addition of a negative (treats -2 - (-5) as -7).
The minus sign carries three different jobs (subtraction operator, negative sign, opposite-of sign) and candidates collapse them into one. Textbook typesetting makes the distinction visually subtle, so the rule never gets encoded as a rule.
What to do instead
Adopt a spoken convention: read -3^2 aloud as 'the opposite of three squared' and (-3)^2 as 'negative three, squared.' Write the expansion longhand ( - (3·3) versus (-3)·(-3) ) every time for one week of practice, then require the same longhand on missed problems.
On percent change problems the candidate divides by the new value instead of the original value, or assumes a 20% increase followed by a 20% decrease returns to the starting amount.
Percent is treated as an absolute quantity that can be added and subtracted like a number, rather than as a ratio whose base shifts with each step. Word problems that supply three numbers encourage grabbing two of them without identifying which is the base.
What to do instead
Anchor every percent problem with the sentence 'percent of ___', filling the blank explicitly before setting up the proportion. For successive changes, compute with multipliers (1.20 × 0.80 = 0.96) rather than adding percents, and test with a concrete $100 starting value.
When simplifying 5 - 2(x - 3), the candidate distributes only the 2 and keeps the leading minus untouched, producing 5 - 2x - 6 instead of 5 - 2x + 6.
The distributive property is learned as 'multiply the number in front,' and a minus sign does not look like a number in front. The invisible coefficient of -1 is never made visible, so the sign change on the second term is simply missed.
What to do instead
Rewrite every subtraction of a parenthetical as addition of a negative before distributing: 5 + (-2)(x - 3). Then draw arrows from the -2 to both terms. Verify by substituting x = 1 into the original and the simplified forms and confirming equal values.
The candidate solves a linear inequality correctly but keeps the inequality symbol unchanged after multiplying or dividing both sides by a negative number, e.g., reporting -2x > 6 as x > -3.
Inequalities are practiced far less than equations, so the solving procedure runs on autopilot and the one asymmetric rule never gets triggered. The rule is often memorized as a phrase without a reason attached, so it does not surface under time pressure.
What to do instead
Attach a numeric test to the rule: -2x > 6 must have the same solution set as 2x < -6. Also graph the solution on a number line and test one point from the claimed interval (x = 0 fails -2x > 6), which catches the error in seconds.
The candidate substitutes the diameter for the radius in circle formulas, computing area as πd² or circumference as 2πd, often because the given figure labels the full width.
The two formulas look nearly identical, and when a problem supplies the diameter the candidate reaches for the first circle formula that surfaces. The relationship d = 2r is known but not applied as a mandatory first step.
What to do instead
Make 'find r first' a written step: on every circle problem, write r = ___ before touching any formula, and if the diameter is given, halve it on that line. Pair each answer with a units check - area in square units, circumference in linear units - so the two formulas stay distinct.
When converting between square or cubic units, the candidate applies the linear conversion factor once, e.g., converting 3 m² to 300 cm² instead of 30,000 cm².
The conversion factor is learned for lengths and then applied mechanically to any unit conversion. Area and volume are two- and three-dimensional, and the squaring or cubing of the factor is a step that has no visible cue in the problem.
What to do instead
Convert by expanding the unit itself: write 1 m² = (100 cm)(100 cm) = 10,000 cm² and 1 m³ = (100 cm)³ = 1,000,000 cm³. Keep a reference card for the common metric and customary area/volume factors and check that the numeric answer grows by the square or cube of the linear factor.
Given subgroup means and subgroup sizes, the candidate averages the means directly instead of weighting by group size, producing the wrong overall mean.
The arithmetic mean is learned as 'add and divide by how many,' and the number of groups looks like 'how many.' The candidate does not notice that the groups contribute unequal numbers of data points.
What to do instead
Before averaging anything, restate the question as 'mean of how many individual values?' and reconstruct the total by multiplying each group mean by its size. If group sizes differ, the simple average of means is always wrong; if they are equal, both methods agree - a quick test the candidate can apply.
For 'at least one' probability questions, the candidate adds the individual event probabilities (or multiplies them) rather than using the complement, and often reports a value above 1.
The phrase 'at least one' maps loosely onto 'one or more events happen,' which sounds additive. The complement structure P(at least one) = 1 - P(none) requires a deliberate reframing that the candidate skips under time pressure.
What to do instead
Build a reflex: any time the words 'at least one' appear, immediately write 1 - P(none) and compute the probability that the event never occurs. As a guardrail, any probability answer outside 0 to 1 signals an error - check it before moving on.
The candidate rounds intermediate results (e.g., rounding 3.666... to 3.7 and then multiplying) and gives a final answer that differs from the exact one, or solves for x when the question asked for 2x + 5.
Under time pressure, candidates chain calculator output into the next step and treat the last number computed as the answer. The final sentence of a multi-step problem is read once, quickly, and the requested quantity is not isolated from the quantity found.
What to do instead
Underline the requested quantity in the prompt before starting and write a one-line plan ending in that quantity. Carry full precision through intermediate steps, rounding only the final answer, and back-substitute the result into the original conditions to confirm it satisfies them.