Evaluating Algebraic Expressions
I can substitute given values into an algebraic expression and simplify with order of operations.
The problem this sheet solves
Evaluating looks like the easiest skill in the unit, and it quietly produces some of the most durable errors, because −3² and (−3)² are different numbers and only one of them is what substitution means. A student who drops the parentheses is not confused about exponents; they are confused about what replacing a variable actually does. This sheet makes substitution a two-part move: put the value in PARENTHESES first, then simplify. That single habit removes the negative-base error, the coefficient error and most order of operations slips at once, so it is worth more than any of the three taught separately. The error analysis is built on the negative-squared case specifically, because it survives otherwise correct work.
The key rule
Substitute every variable with its given value, in parentheses, then simplify with order of operations: parentheses, exponents, multiplication and division, addition and subtraction.
Parentheses around a substituted value protect its sign — drop them before an exponent and the sign can flip.
Watch out
The mistake: Writing −3² = −9 for x² at x=−3.
The fix: (−3)² = 9 — parentheses square the whole −3.
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.