TABE Math common mistakes
TABE Math · Understand the traps and how to avoid them.
When adding or subtracting decimals such as 12.4 + 3.75, the candidate writes the numbers so the right-hand digits line up (12.40 over 3.75 becomes 12.40 over 37.5) and produces an answer off by a factor of ten.
Years of whole-number practice where the right edge is always the ones place; the decimal point is treated as a decoration rather than the anchor for place value.
What to do instead
Before computing, rewrite the problem vertically with the decimal points stacked in a single column and fill empty places with zeros (12.40 / 03.75). Then place the decimal point in the answer directly below the column before adding.
Adding fractions by adding across: writing 1/2 + 1/3 = 2/5, and similarly subtracting numerators and denominators separately.
The whole-number rule 'add the top, add the bottom' is overgeneralized; the candidate has no mental model of fractions as sizes, so the result never looks wrong.
What to do instead
Before computing, estimate each fraction as a decimal or compare to 1/2 - 1/2 is about 0.5 and 1/3 about 0.33, so the sum cannot be 2/5 (0.4). Then convert to a common denominator and add only the numerators.
Evaluating expressions strictly left to right, so 4 + 3 × 5 is worked as 7 × 5 = 35, and 2 + 3² is worked as 5² = 25.
Reading direction is left to right, and no written record of operation order is made before calculating, so the first two numbers encountered get combined.
What to do instead
Copy the expression and mark the operations with numbers showing the order (multiplication/exponent first, then addition/subtraction) before doing any arithmetic; do one marked step per line.
Every percent problem is solved the same way - '15 is 30% of what number?' is computed as 0.30 × 15 = 4.5 instead of 50.
The most frequently practised percent type ('find the percent of a number') becomes a reflex, and the candidate does not stop to identify which quantity is missing.
What to do instead
Write the relationship part = percent × whole and label which of the three quantities the question gives and which it asks for. If the whole is missing, divide instead of multiply, then substitute the answer back into the sentence to check.
When solving 3x + 4 = 19, the candidate subtracts 4 from the left side only, or divides by 3 before removing the +4, producing x = 19/3 − 4 or x = 5 with no verification.
The equation is seen as a list of instructions to 'undo' in the order written rather than as a balance that must stay equal on both sides.
What to do instead
Write every step on two lines - one for the left side and one for the right side - and never change one without the other. Undo addition/subtraction before multiplication/division, then substitute the answer into the original equation to confirm.
Distributing a negative coefficient incorrectly: −2(x − 5) is expanded as −2x − 10, and −(x + 3) as −x + 3.
The minus sign is attached only to the first term because the second sign is read as a separator rather than as part of the term being multiplied.
What to do instead
Rewrite each term with its sign in parentheses before multiplying: (−2)(x) + (−2)(−5), then simplify to −2x + 10. Check with a number, e.g. let x = 1 and confirm both forms give the same value.
Choosing the area formula when the question asks for distance around a shape (or the reverse), and labelling a perimeter answer in square units or an area answer in plain units.
Both tasks are filed mentally as 'measure the shape', and the formula sheet supplies several look-alike formulas that are selected by shape rather than by the quantity requested.
What to do instead
Before choosing a formula, decide which of two questions is being asked: 'Am I covering the surface (square units) or fencing the edge (linear units)?' Write the expected unit next to the answer line and discard any answer whose unit does not match.
Converting square or cubic units as if they were linear: treating 1 square metre as 100 square centimetres, or converting a rate given in square feet by multiplying once by 12.
The single conversion factor between the base units is applied once, ignoring that both dimensions change.
What to do instead
Convert one dimension at a time and let the units cancel: 1 m² = (100 cm)(100 cm) = 10 000 cm². As a rule, square the linear factor for area and cube it for volume, then sanity-check that the number got much larger or smaller.
Finding the median by taking the middle entry of the list as written (or averaging the first and last numbers) without first putting the values in order.
The word 'middle' is acted on immediately, and the sorting step is invisible in the definition so it is skipped under time pressure.
What to do instead
Always rewrite the data set in ascending order as a separate first step, cross out pairs from the outside in, and only then read or average the remaining middle value(s). Note in writing when the count is even so two values must be averaged.
Reading values off a bar graph, line graph, or number line using the wrong interval - e.g. treating a gridline labelled in steps of 5 as steps of 1, or counting tick marks instead of spaces between them.
The eye jumps to the nearest line and assumes each gridline means one unit, and the axis labels are scanned rather than read for their step size.
What to do instead
Before reading any point, state out loud or in writing the value of one gridline interval (label minus label, divided by the number of spaces between). Then count spaces, not marks, from a labelled line to the point.