01
Step one: state the goal and the worked problem
Begin with a single equation and say what finished looks like: x alone on one side. Take 3x + 5 = 20. Tell the learner the goal is to undo what was done to x, in reverse order. Beginners often stall because they do not know what they are aiming for, so naming the target first removes a hidden obstacle. Keep the first example small, with whole-number results, and write each line on its own row so the eye can follow the change from one line to the next without hunting.
02
Step two: undo operations and annotate each line
Subtract 5 from both sides to get 3x = 15, then divide both sides by 3 to get x = 5. Beside each line, write the action in plain words: subtract 5 from both sides, divide both sides by 3. These annotations are what turn an answer into a method. Learners can then copy the reasoning onto a new problem instead of memorizing a result. Emphasize that every move happens to both sides, because balance is the idea that makes the procedure valid. Resist adding shortcuts until the full version feels natural, since shortcuts hide the logic.
03
Step three: check by substitution, then vary the problem
Close the example by substituting the answer: 3 times 5 plus 5 equals 20, so the solution holds. Teach checking as a habit, not an extra. Then offer a similar problem with one change, such as a negative coefficient or variables on both sides, and provide a hint that reveals only the next move. Graduated variation shows whether the learner understood the method or only the example. Track which variation causes errors, and use that pattern to decide what the next lesson, hint or worksheet should address.