Reading a worked example feels like learning, but it does not show whether you can do the skill alone. This template pairs each example with three practice questions, so the reading becomes doing.
What is the template?
Copy this onto a sheet of paper for each example you study.
- The example. Write the question, then the steps in your own words, with one line on why each step is taken.
- Practice 1, same pattern. A question with only the numbers changed. Do it without looking.
- Practice 2, new surface. The same skill in a different setting, such as a word problem.
- Practice 3, a twist. The skill combined with one other idea, close to an exam question.
- Notes. One line on where you slipped and what fixed it.
How does it look filled in?
Here is a worked example from Form 4 Mathematics on solving linear equations.
Example: Solve 4x − 7 = 2x + 9.
| Step | Why |
|---|---|
| 4x − 2x = 9 + 7 | Collect x terms on one side, numbers on the other |
| 2x = 16 | Simplify |
| x = 8 | Divide both sides by 2 |
Check: 4(8) − 7 = 25 and 2(8) + 9 = 25. ✓
Practice 1: Solve 5x − 3 = 2x + 12. (Answer: 3x = 15, so x = 5.)
Practice 2: Ali is twice as old as his sister minus 4. Their ages together are 38. Write and solve the equation.
(Let the sister be s. Then 2s − 4 + s = 38, so 3s = 42 and s = 14, so Ali is 24.)
Practice 3: Solve 3(x + 2) = 5x − 6. (3x + 6 = 5x − 6, so 12 = 2x and x = 6.)
Notes: “I forgot to multiply the 2 in the bracket on Practice 3. Expand brackets first.”
The notes line is the part that changes what you do next time.
How do you use it week to week?
Pick two examples from the chapter you are studying, and do one pairing on each, on separate days. Keep the sheets in one folder.
After a week, reread only the notes lines. Patterns appear quickly, such as always forgetting to expand, and they tell you what to drill. The mistake log and paper-error review keeps those patterns in one place.
What if Practice 2 always fails?
That usually means the student can follow the procedure when the question looks the same, but cannot yet recognise it when it is hidden in words. I understand examples but cannot answer new questions explains why and what to do.
The timed original practice session builder then lets you practise the skill under time.
Where does a teacher help?
A teacher watching Practice 2 can see exactly where the translation from words to equation breaks, and ask one question to fix it. You can bring your completed pairing sheets to a one-hour trial class (from RM50) with an experienced teacher assigned for the subject.
For other study methods, see the free resources page.