Equations with Variables on Both Sides
I can solve an equation with variables on both sides by collecting the variable onto one side.
The problem this sheet solves
Students who combine across the equals sign are treating it as an instruction to compute rather than a statement that two sides are equal. Because the arithmetic they performed is correct, telling them to be careful changes nothing. What has to change is the meaning of the symbol, and that a variable term can be removed from a side exactly the way a number can. This sheet addresses the equals sign directly and treats subtracting a variable term as the same legal move as subtracting a constant, so nothing new has to be memorised. Once one side is clear the equation is the two-step form students already own, and the sheet says so, which keeps the method count from growing.
The key rule
Remove a variable term the same way you remove a number: subtract it from both sides. Once one side has no variable left, finish it as a two-step equation.
Terms do not travel across the equals sign. They are removed from both sides at once.
Watch out
The mistake: Writing 5x + 3 = 3x + 11 as 8x + 3 = 11.
The fix: The 3x was added, not removed. Subtract it from both sides: 2x + 3 = 11.
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.