Combining Like Terms and the Distributive Property
I can distribute, then combine like terms to fully simplify an expression.
The problem this sheet solves
After distributing, students combine everything in sight. The 12 gets folded into the x terms because the instruction they remember is combine like terms and nothing in that phrase tells them a constant is not like an x. The answer 17x is not careless; it is consistent, and it will repeat until like is defined by variable AND exponent rather than by proximity. This sheet defines like terms by what has to MATCH, then makes students simplify all the way rather than partway, which is the standard the rest of the course assumes. Algebra tiles show why an x tile and a unit tile cannot merge no matter how they are arranged, and the constant is deliberately left visible in the answer so students see that finished does not mean one term.
The key rule
Distribute first if there are parentheses, then combine like terms: add or subtract the coefficients of terms with the same variable and exponent. A constant only combines with another constant.
x and x² are not like terms, and neither are a constant and a variable term.
Watch out
The mistake: 3(x + 4) + 2x simplified as 17x — folding the 12 into the x terms.
The fix: 3x and 2x combine to 5x. The 12 has no variable, so it stays separate: 5x + 12.
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.