Following an example and solving a new question are different skills. The example shows you the path, while the new question asks you to find it.
This page explains why the two feel so different and gives a routine for the new question. It belongs to the students section, and the prerequisite gap finder helps if the stall comes from an older gap.
What the example hides
A textbook example starts with the right formula already chosen. You see the working but not the decision that led to it.
A new question hides the decision in words. You must read the situation, name the type, and choose the method before any working starts.
A worked example of the hidden decision
Here is an original Mathematics pair. The example: a rectangle has length 8 cm and width 5 cm. Find its perimeter, which is 2(8 + 5) = 26 cm.
The new question: a rectangular garden has perimeter 40 m and length 12 m. Find its width. A student who copied the example tries 2(12 + 5), because the example used a width.
The decision is that the perimeter formula now works backwards: 2(12 + w) = 40, so 12 + w = 20 and w = 8 m. Check: 2(12 + 8) = 40.
The steps are simple. The new part is seeing that the unknown has moved.
A four-step routine for a new question
- Underline what is given and write each value with its unit.
- Circle what is asked, including the unit wanted.
- Name the type in one phrase: “reverse perimeter”, “two-step force problem”, “ratio sharing”.
- Choose a method that connects given to asked, and write the first line.
If step 3 is hard, your gap is recognising question types. Sort ten past-style questions into types without solving them. That alone trains the decision.
Practise the decision, not the steps
After each worked example, write one sentence: “I use this method when…”. Then find a question that looks different but fits that sentence.
Mixed practice works better than ten identical questions. It forces the decision every time.
Self-check
Decide the type, then solve: a square has perimeter 36 cm. Find its area.
Answer
Type: reverse perimeter, then area. A square has four equal sides, so each side is 36 ÷ 4 = 9 cm. Area = 9 × 9 = 81 cm². If you tried 36 × 36 or 36 ÷ 2, the decision step was the gap.
When paid one-to-one tuition may be worth considering
If the routine does not get you started, a stall on new questions may come from an older gap, such as algebra rearrangement. A teacher watching you start a question sees the exact point where the decision stalls.
The teacher begins from what you can already do and gives you new questions until the decision is yours. Try it in the one-hour trial class (from RM50).