Translating Words into Algebraic Expressions
I can translate a verbal phrase into an algebraic expression, watching for phrases that reverse the order.
What students learn
Students learn to write an expression from words: they keep the order they read, reverse it after less than, fewer than and subtracted from, and put a whole sum or difference in parentheses.
See inside
The key rule
Keep the order you read, except after less than, fewer than and subtracted from: they reverse it. A sum or difference multiplied, divided or squared as a whole goes in parentheses.
7 fewer than 2n → 2n − 7
Test it: 8 less than 20 is 12, which is 20 − 8, not 8 − 20.
Watch out
Write an expression for “5 less than a number x.”
The mistake: 5 − xThe words were written in the order they were read.
The fix: x − 5Less than reverses the order: start with x, then take 5 away.
The mistakes it targets
- Writes less than, fewer than or subtracted from in reading order
- Leaves out the parentheses around a sum that is multiplied
- Squares only the letter instead of the whole difference
- Takes a monthly discount off once instead of every month
- Halves only the last number instead of the whole amount
The interactive Teacher Deck (32 slides, PowerPoint)
- The Learn page taught on screen: 9 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (four steps), each with the reason for the step
- Six practice and three apply problems: a your-turn slide with a think-time bar, then the solution one line per click
- Jump buttons on every slide: go straight to any problem, the answer bank or the exit ticket
- Speaker notes on each problem: the question to ask, the worked answer and the common error to listen for
- A completed deck PDF (19 pages) with every slide fully built, to print or post
The student packet (9 pages)
- Learn: guided notes with four definitions, the key rule, a worked example and a Watch Out error pair
- Practice: two warm-up, two standard and two stretch problems, with an answer bank for self-checking that hides three common-mistake decoys
- Apply: two word problems and one error analysis
- Assess: an exit ticket of four items, two per page, with an I-can self-rating
- Homework (page 5): eight new problems, two warm-up, four standard and two stretch
- Answer key (pages 6–7): every problem worked step by step, five common mistakes with what to do about each, and a grading guide, plus the homework key (page 8)
- Color and ink-saver editions of the whole packet
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.