6th Grade Equations with Variables on Both Sides Quizzes

It depends on where your students are in the progression. Common Core places one- and two-step equations as the core Grade 6 algebra standard, with variables on both sides typically introduced in Grade 7. That said, Grade 6 students who are confident with inverse operations and combining like terms are often ready for introductory problems — particularly simple cases like 2x + 3 = x + 7 where no distribution is needed. These quizzes work well as an extension for students who've mastered the Grade 6 standard and are ready for the next step.

Ground it in what they already know: if students can solve 2x + 3 = 11, they have the tools. The new move is recognizing that a variable term on the right side can be treated like any other term — subtract it from both sides to consolidate. Use a balance-scale visual to show that the equation stays equal as long as you do the same thing to both sides. Keep early problems simple (no distribution, small whole-number coefficients) so the new concept is the only challenge.

The most common error is treating the variable on the right side as if it doesn't exist — students solve for x using only the left side and ignore the right-side variable entirely. A close second is sign errors when subtracting a variable term: students write x − x correctly but then drop or mishandle the constant that was attached to it. Requiring students to write out every step explicitly (rather than doing steps mentally) catches both errors early.

The quizzes include full answer keys with step-by-step solutions, which makes them effective for independent practice or homework where students need to self-check. You can assign them digitally as a hosted quiz on Wayground, or print the PDF for paper practice — handy for schools managing screen time. Either way, the answer key lets students pinpoint exactly which step went wrong, not just whether the final answer was right.

Wayground's Read Aloud accommodation reads question text aloud for students who need it, which removes the reading barrier from what is fundamentally a math task. For students who find dense text on a page visually overwhelming, you can also adjust font size and line spacing at the quiz level — a small change that meaningfully reduces cognitive load when students are already working hard on the algebra itself.