Study skills · Systems
A Worked-Example Practice Cycle for Maths and Science
Use this workflow for a procedure you are beginning to learn. It gives you a route from understanding a model to choosing and carrying out the steps yourself. The goal is to need less support as your understanding grows.
What supports this approach
This is a School Calendar example workflow, not a separately tested programme. It combines the worked-example recommendation with explanation, checking and later variation.
This is a School Calendar example routine combining established learning ideas, not a separately validated named programme.
Evidence and background: IES: Organizing Instruction and Study to Improve Student Learning; Dunlosky et al. (2013): Improving Students’ Learning; Wisniewski et al. (2020): The Power of Feedback Revisited.
Before you start
Use a teacher-approved model with every step visible. Prepare a completion question and an independent question at a similar level. Save a slightly different question for a later session.
A solved example and three related questions
Methods inside the system
Inspect the model
Identify the starting information, target and operation at each step. Explain why the operation is valid.
Complete then solve
Fill in a missing step before attempting a fully independent question. Use feedback to locate the earliest step that became uncertain.
Add selection practice later
Once the procedure is familiar, add another related type. This optional mixed stage practises choosing an approach as well as executing it.
Follow the system step by step
Read and explain a complete example.
Complete a partial solution.
Solve a related problem with the model covered.
Check the answer and correct the earliest error.
Return later to a mixed set when ready.
Example: from 2x + 3 = 11 to independent solving
Model: 2x + 3 = 11. Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Check: 2 × 4 + 3 = 11. Explain that each operation preserves equality.
Completion: 3x + 2 = 14 → 3x = __ → x = __. The blanks are 12 and 4. If you wrote 16, revisit why 2 is subtracted from both sides.
Independent: 4x + 1 = 21. With the model hidden, subtract 1 and divide by 4 to get x = 5. Check in the original equation. A later mixed question, x/2 + 1 = 6, gives x = 10; here the final operation is multiplication, so copying the earlier pattern without thinking would fail.
Try it in another subject
For science speed calculations, follow a model using distance ÷ time, complete a missing substitution, then solve with new values and check the units.
Common mistakes and adjustments
Do not introduce a harder independent question before the learner understands the model. Change one demand at a time.
If independent work is already reliable, move to varied applications rather than repeating the same fully worked solution.
An example week
This is an example week, not a prescribed review interval. Adjust the tasks, time and support to the learner’s course and recall results.
| Day | Task | Minutes |
|---|---|---|
| Monday | Explain one equation model and complete two solutions | 20 |
| Wednesday | Solve and check three equations independently | 20 |
| Friday | Choose methods in a mixed equation set | 20 |
Put the week in your calendar
Replace the bracketed date and time zone, then paste the prompt into Magic Generate in School Calendar. Review dates, durations and tasks before adding the events. See the Magic Generate guide.
Principles behind this system
Worked Examples: Move from Guidance to Independent Practice
Learn a procedure through worked solutions, missing-step problems and independent attempts, with a maths example and a plan for reducing support. Explore its methods and patterns.
Self-Explanation: Connect Ideas and Explain Why
Use why questions, worked-step explanations and concrete examples to check understanding, with an algebra demonstration and a short study pattern. Explore its methods and patterns.
Feedback and Error Correction: Turn Mistakes into Better Practice
Use feedback to diagnose mistakes and choose a useful next attempt. Includes a fraction correction, error categories and a delayed retry routine. Explore its methods and patterns.
Optional extensions
These additions can support the routine but are not defining steps of the system.
- Interleaving: Learn to Choose the Right Approach — methods to try
- Words and Visuals: Make Concepts Easier to Understand — methods to try
For a subject-specific plan, see Math study routines. Or return to all study principles and systems.
Sources and review
- IES: Organizing Instruction and Study to Improve Student Learning
- Dunlosky et al. (2013): Improving Students’ Learning
- Wisniewski et al. (2020): The Power of Feedback Revisited
Reviewed 2026-09-27. Examples and calendar schedules are editorial illustrations.