How do I learn from a worked example without copying it line by line?

Treat the example as a demonstration of decisions, not a finished answer to preserve. First read it all the way through to identify the task and the general approach. Then go back step by step. At each step, ask: “What is this doing?”, “Why is it needed here?”, and “What information from the question makes this step reasonable?” Say the answer in your own words before moving on. Your notes can be brief: record the purpose of a step, a condition that makes it useful, or a question you still have—not a duplicate of every line. For instance, instead of copying a calculation, note, “Rewrite the quantities in a common form before comparing them.” That note reminds you of the choice being made without pretending the procedure fits every problem.

After studying the example, close the book, cover the worked solution, or switch to a blank page. Keep the original question visible if you need it, but hide the steps and answer. Before writing calculations, write a short plan from memory: what the problem asks, what approach might fit, and what you will check at the end. If you cannot remember a step, pause and make a genuine attempt to explain what you need next. Then uncover only enough of the example to resolve that gap, cover it again, and continue yourself. Mark any peek so you can tell which parts you completed independently. The aim is not to forbid all help; it is to notice where your own reasoning stops and use the example deliberately.

Here is a small illustrative example. Suppose the worked example is 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2. While studying, explain the choices: the fractions need a shared denominator to combine their parts; 1/3 is rewritten as 2/6; then the numerators are added, and the result is simplified. Cover that solution and try a related problem, such as 1/4 + 1/8. First write your plan in words: “Make the denominators match, add the numerators, then simplify if possible.” Work it out without looking. Afterward, compare the reasoning: 1/4 becomes 2/8, so the sum is 3/8. The example’s specific numbers changed, but the useful decision—express both fractions in eighths—transferred. If your course uses a different method or notation, follow that instruction; this is only a simple practice illustration.

Compare one decision at a time rather than immediately copying the example’s answer. Check whether you understood what the problem asks, chose a suitable first step, and carried it out consistently. A different route may still be reasonable; ask whether it answers the question and whether you can explain why it works. If you find a mistake, label the kind of gap—such as “I didn’t make the units match” or “I lost track of what the question asked”—then correct that step in your own work. If stuck, look back only at the relevant part of the example, explain that step in your own words, cover it again, and continue. Finish by trying a second related problem if available. That last attempt checks whether you learned a reusable idea rather than memorized one solution.