ISEE Math Vocabulary: Word Problem Terms and Traps

Why the words matter

This section explains why wording, and not only arithmetic, decides many answers on the Mathematics Achievement section and in word problems elsewhere on the ISEE.

A word problem is a short piece of writing that hides a calculation. Students who can add, subtract, multiply and divide without difficulty still lose points when they translate the sentence into the wrong operation. The error is easy to miss, because the calculation itself is correct and the final number looks reasonable.

Two features of the test make the language more important. First, the questions are written in compact, formal wording that many students rarely read in everyday life. Second, the answer choices usually include the result of the most common misreading. A student who reads “fewer than” backward will often find that backward answer waiting among the choices, which makes the wrong option feel confirmed.

The practical response is to treat math vocabulary as a skill of its own. A student who knows the phrases, and who checks each one against the story, removes a whole category of avoidable errors. The groups below are a teaching recommendation from the ISEEPrep teaching team and are not a list from E3n (formerly ERB).

The word groups

This section sorts the phrases students meet most often into five families, so that each phrase is learned together with the operation it usually signals.

The first table covers the four basic operations. The word “usually” is deliberate: a phrase signals an operation, but the story must still confirm it.

Operation	Common phrases	What the phrase usually asks	Watch for
Addition	altogether, in all, total, sum, combined, increased by	Join two or more amounts	“Total” can also mean a given final amount, so read what is known
Subtraction	fewer than, less than, how many more, difference, remain, decreased by	Take away, or find the gap between two amounts	The order of the numbers changes with the sentence
Multiplication	product, times, each, double, triple, groups of	Repeat an amount a set number of times	“Each” can also appear in a division problem
Division	per, shared equally, quotient, split among, ratio of	Share an amount into equal parts or find a rate	“Per” attaches to the amount that follows it

The second table covers comparison phrases, which describe a boundary rather than a single result. These are the phrases most likely to cause a wrong answer, because the two ends of a boundary look alike. The examples below use the number 10.

Phrase	Meaning	Does 10 count?	Whole numbers that fit
at least 10	10 or greater	Yes	10, 11, 12 and up
at most 10	10 or smaller	Yes	10, 9, 8 and down
no more than 10	10 or smaller	Yes	10, 9, 8 and down
no fewer than 10	10 or greater	Yes	10, 11, 12 and up
more than 10	greater than 10	No	11, 12 and up
fewer than 10	smaller than 10	No	9, 8 and down

Phrases such as “at most” and “no more than” mean the same thing, and so do “at least” and “no fewer than.” Students who learn the pairs together need to memorize fewer separate rules.

Two traps worth practicing

The direction of “fewer than” is the first trap. In the sentence “Ben has 6 fewer stickers than Lila,” the amount after “than” is the starting point. Ben’s count equals Lila’s count minus 6. Students often subtract in the order the numbers appear in a different sentence, or they take the phrase to mean that Lila has fewer. A quick check is to ask which person should have the larger amount. In this sentence, Lila should.

The boundary in “at least” is the second trap. A statement such as “a team needs at least 12 points to qualify” allows exactly 12. A student who writes “more than 12” has excluded a score that qualifies. When a question asks for the smallest possible value, this single boundary often decides whether the answer is 12 or 13.

Try the example

The practice question on this page uses two phrases that point in different directions, one that subtracts and one that adds. Students should work it in two stages, writing down what each phrase asks before calculating, and then choose an answer before opening the explanation.

Why each answer works or does not

This section reviews the four choices, because the wrong options each match a specific misreading that students can learn to recognize.

Choice (B), 47, is correct. The phrase “fewer than” turns the art club’s 28 members into 19 for the chess club, and the phrase “altogether” asks for both clubs, so the two amounts are added.

Choice (A), 19, is the number the first phrase produces. A student who stops here has done the first step correctly and has not finished the question. The remedy is to underline the final question and confirm that the number found answers it.

Choice (C), 65, comes from reading “9 fewer than” as “9 more than.” The student adds 9 to 28 and then adds again. This is the classic direction error, and it is the reason a quick reasonableness check is useful: a club described as having fewer members should have a count below 28.

Choice (D), 56, comes from setting the phrase aside and doubling the art club. It often appears when a student skims the problem and grabs the first number.

A self-test habit

This section describes a short routine that separates language errors from math errors, so that practice time goes to the right skill.

After any missed word problem, the student completes three prompts before looking at a solution:

1. State what the problem asks for, in the student’s own words.
2. Name the phrase that sets the operation and say which direction it points.
3. Check that the answer fits the story, for example a count that is smaller when the sentence says “fewer.”

If the student can complete the first two prompts clearly and still miscalculates, the missed point is a math error, and practice should focus on the computation. If the student cannot restate the problem, the missed point is a language error, and practice should focus on the phrases above, including rewriting the sentence in simpler words. Many problems contain both, and the routine makes that visible.

For students who are learning English alongside the test, this diagnosis matters even more, because a language gap can look like a weak grasp of math. The guide for English language learners describes how to tag each error and plan around it.

Your next step

Families can continue with the Mathematics Achievement overview to see how this skill fits with the rest of the section, then rewrite five word problems from school homework as one-sentence questions in the student’s own words. The free trial is a low-pressure way to try a timed question set and sort each miss into wording or calculation.