Literal Equations and Rearranging Formulas
I can solve a formula for any one of its variables.
The problem this sheet solves
Students divide before they subtract, and the bar stops reaching every term. P = 2l + 2w becomes l = P/2 − 2w, which is a different formula, and because it LOOKS rearranged nothing about it signals an error. The deeper block is that the answer is an expression rather than a number, so students do not trust that they have finished. This sheet treats every other letter as a number you happen not to know, which is the sentence that makes the whole topic ordinary. Removing what is added comes before dividing out what multiplies, and the worked example shows the fraction bar running under the WHOLE side, since that is precisely where the common version goes wrong. Useful for science formulas as well as algebra.
The key rule
Solving for a letter uses the same moves as solving for x. Treat every other letter as a number. Remove what is added or subtracted first, then divide out what multiplies the target.
Undo the sum before the coefficient. Strip 2w off P = 2l + 2w before dividing by 2.
Watch out
The mistake: Writing l = P/2 − 2w by dividing before subtracting.
The fix: Remove 2w first, then divide the whole side by 2: l = P − 2w/2. The bar must reach every term.
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.