How to Teach Solving Algebraic Equations Step by Step
Solving an algebraic equation is fundamentally a sequencing problem: identify what's been done to the variable, then undo those operations in reverse order, applying each move to both sides simultaneously. Students who struggle with algebra are often not confused about the math, they're losing track of the sequence. When each step is a physical object that gets placed beneath the equation it applies to, the sequence becomes visible and controllable rather than something to hold in working memory while also doing arithmetic.
Watch 2x + 3 = 9 resolve to x = 3 in two moves. Each operation placed as a block beneath both sides before the next line is written.
Switch-Its makes each move a physical placement
With Switch-Its magnetic dry-erase blocks, each term in the equation gets its own block, and each inverse operation snaps below both sides before the simplified line is built beneath it, so the structure of the solution is visible at every stage.
One equation, one block to start
The equation 2x + 3 = 9 sits on a single block at the top. Everything that follows will be built beneath it. Each step becomes a new row of blocks, each move made visible before the next line is written.
Apply the operation to both sides
The equation expands into separate term blocks. A −3 block snaps below the 3 on the left, and a matching −3 block goes below the 9 on the right. Both sides receive the operation simultaneously. The balance of the equation is something students place, not just declare.
Two moves, one variable isolated
Subtract 3 from both sides: 2x = 6. Divide both sides by 2: x = 3. The full solution sequence is readable from top to bottom. It is a record of every move, not just the answer.
Equation solving is one of the most procedure-heavy topics in middle school math, which makes it a strong candidate for a physical approach that keeps the structure visible at every step. It fits into the same argument for concrete manipulatives that applies across math and science, the case made in full in Holding Ideas in Your Hand.