Translating Words into Algebraic Expressions
I can translate a verbal phrase into an algebraic expression, watching for reversing phrases.
The problem this sheet solves
Most verbal phrases translate straight through, which is exactly what makes the reversing ones so costly. Less than, subtracted from and fewer than all put the second number FIRST, and a student who has learned to translate left to right has learned a rule that works often enough to feel reliable and fails on the phrases that matter most in word problems. This sheet sorts keywords into the ones that translate in order and the ones that REVERSE it, and it names the reversing group explicitly instead of leaving students to notice. Subtraction and division get the attention because they are the two operations where order changes the answer. The error analysis is built on the reversal, since it survives an otherwise fluent translation.
The key rule
Most phrases translate in the order you read them. But “less than,” “subtracted from,” and “fewer than” REVERSE the order — the number named first in the words comes SECOND in the expression.
Test it with a real number: “5 less than 20” is 15, not −15 — so it has to be x − 5, not 5 − x.
Watch out
The mistake: “5 less than x” translated as 5 − x — writing the words in the order they appear.
The fix: “5 less than x” means x − 5. The number comes first in the expression; “less than” reverses the words.
What is included
- Reference page — student-friendly definitions, a worked example, a Watch Out error pair, and the key rule
- Practice page — six problems, building from foundational to multi-step
- Apply page — a word problem, a reasoning prompt, and an error-analysis task
- Assess — a half-page exit ticket, two to a sheet, with a score box
- Full answer key — every item worked, plus a grading guide that says what each wrong answer tells you
- Ink-saver edition of all 7 pages
- 14-slide teacher deck (PowerPoint) with presenter notes on every slide
Standard codes refer to the Common Core State Standards for Mathematics. Math Class 678 is an independent publisher, not affiliated with, sponsored by, or endorsed by NGA Center or CCSSO. Every product is sold on Teachers Pay Teachers.