Use a worked example without copying the solution
Turn a completed solution into a sequence of decisions you can explain and repeat independently.
A solution can look obvious when every line is already on the page. The useful question is whether you could choose the next line yourself. Treat a worked example as a set of decisions to investigate: what was modelled, which principle applied, and how the result was checked.
1. Reconstruct the situation before the algebra
Read the question and leave the solution covered. Draw a small diagram, list the quantities supplied and identify what you need to find. Include directions when they matter. A useful diagram need not look realistic; it needs to identify the object or system being analysed.
Then inspect the solution's starting assumptions. Was friction neglected? Was acceleration treated as constant? Were two objects included in one system? An equation is useful because its conditions match the model. Recognising a familiar arrangement of letters is not enough to justify it.
2. Pause where a decision is made
Reveal the first step, then predict the next one. Say why that step is appropriate before doing the arithmetic. For a force problem, the important decision may be to find the resultant force before using Newton's second law. The division at the end is usually the easier part.
If your prediction differs, locate the first difference in reasoning. You may have selected a different system, missed a force or chosen the opposite positive direction. A different sign convention can still be valid if it is used consistently; a missing force cannot be fixed by rearranging the algebra.
3. Change one condition and predict the effect
Once you can explain the original, make a small variation. In the force example, hold both forces fixed and double the mass. Predict that the acceleration will halve, then calculate it. Next, keep the mass fixed and reverse the larger force. That changes the resultant and tests whether you understand the directions.
Choose variations that change the reasoning as well as the numbers. Ask what would happen if a previously neglected effect mattered. Do not silently keep using a constant-acceleration equation after changing the situation so that acceleration varies.
4. Close the example and solve a neighbouring problem
Use a fresh question on the same principle. Write a complete attempt without looking across at the original. If you get stuck, record the decision you cannot make: identifying the forces, choosing an equation or rearranging it. This makes your next look at the example specific.
Finally, annotate your own solution with a short reason beside each major step. Keep the reasons portable: ‘apply the principle to this system’ is more useful than ‘use the formula on line three’. Check the units, direction and whether the size of the answer fits the situation.
Before you move on
Check your thinking
In the example above, the mass becomes 4 kg while both forces stay unchanged. What changes, and what stays the same?
Show the explanation
The resultant force stays +6 N. Acceleration becomes +1.5 m/s² because the same resultant acts on twice the mass. The direction stays to the right. This assumes the two stated forces remain unchanged when the mass changes.