Writing Equations from Word Problems
I can turn a word problem into an equation, solve it and check the answer in the story.
What students learn
Students learn to define a variable with its units, write one equation that says everything the story says, solve it and verify the answer in the story's words.
See inside
The key rule
Name the unknown and its units. Write one equation for the whole situation, solve it, then check the answer in the story, not only in the equation.
once + each × m = total
A fee paid one time is added once; a price paid each month multiplies m.
Watch out
Ana has 3 times Ben's cards. Together they have 48. How many has Ben?
The mistake: 3b = 48, so b = 163b is only Ana's cards. Together means Ben's plus Ana's.
The fix: b + 3b = 48, so 4b = 48 and b = 12Check in the story: 12 + 36 = 48 cards.
The mistakes it targets
- Writes an equation for only part of the story
- Swaps the one-time fee and the amount for each item
- Answers a different quantity from the one the question asks for
- Checks the answer only in the equation, not in the story
The interactive Teacher Deck (33 slides, PowerPoint)
- The Learn page taught on screen: 8 fill-in blanks, each filled on its own click as students write it
- The worked example one slide per step (five 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, four 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.