No Solution and Infinitely Many Solutions
I can decide whether an equation has one solution, no solution, or infinitely many.
The problem this sheet solves
Every equation since two-step work has ended in x equals a number, so an ending that is a statement about numbers reads as failure rather than an answer. Students start over, sometimes repeatedly. And when they do keep it, 0 = 0 gets written as x = 0, which says something quite different from every number works. This sheet makes the two odd endings recognisable and nameable, and it mixes all three outcomes on the practice page so students cannot tell from the instructions which one is coming. Reading what is left after the variable goes becomes the final step of solving rather than a signal to restart.
The key rule
Solve as usual. If the variable disappears, read what is left. A false number statement means no solution. A true one means every real number is a solution.
The variable vanishing is an answer, not a mistake. Read the line you have rather than starting over.
Watch out
The mistake: Reaching 0 = 0 and writing x = 0.
The fix: 0 = 0 says nothing about x. It is true no matter what x is, so every number is a solution, not just zero.
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.