Systems Word Problems and Modeling
I can write a system from a context, name what the letters mean, and solve it.
The problem this sheet solves
Systems word problems fail at the modeling, not the solving. If one side of an equation measures dollars, the other side must too, and a count of tickets written where a total cost belongs produces an equation about nothing. The negative answer is often the only signal, and students who expect algebra to be strange ignore it. This sheet requires students to say what each letter means and to organise the information in a table with one column per unit, so each column yields one equation and the units are visibly consistent. Answers are checked against the SITUATION, not just the equations, which is what catches a model that solves cleanly and means nothing.
The key rule
Say what each letter means. Make a table with one column per unit. Each column gives one equation, and both sides of each must measure the same thing.
Dollars equal dollars. Tickets equal tickets. Never mixed.
Watch out
The mistake: A student writes 8a + 5s = 15 for the money, and solving gives a = −20.
The fix: 8a + 5s = 96. The left side is DOLLARS, so the right side must be dollars too, and 15 is a number of tickets. The a = −20 was the only warning that the equation was not about anything.
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.