Justifying Each Step in a Solution
I can name the property that justifies each step when I solve an equation.
The problem this sheet solves
Justification asks for something students have not been asked for before: the NAME of the property that makes a step legal for every equation, not a restatement of what was done to this one. A student who can solve fluently can still leave that column empty or fill it with arithmetic, because nothing so far has separated the move from the reason. This sheet lays the vocabulary of justification over solving moves students already own, so nothing about solving is retaught and all the new load is on naming. Two-column proofs are built up from steps rather than presented finished, which is what makes the reason column feel answerable instead of decorative.
The key rule
Every step in solving is legal for a reason. Do the same thing to both sides, distribute, or combine like terms, and name which one in the reason column.
The reason names the PROPERTY, not the numbers. Subtraction Property, not minus 6.
Watch out
The mistake: Writing subtract 10 in the reason column.
The fix: Name the property that makes the step legal: Subtraction Property of Equality, not numbers.
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.