Maths notes are most useful when they help you take the next step in a question. A page full of copied solutions can be difficult to use if it does not explain why each line follows from the last.
Try making a short method sheet for one skill. Include a worked example, the reason for each step, a check and one mistake to watch for. Leave space for a question you will attempt without looking.
Write the action beside the working
Consider this equation:
There are two sensible routes. You could expand the bracket first. Here, dividing both sides by 3 gives a shorter first line:
- Divide both sides by 3. The whole bracket is multiplied by 3, so undo that multiplication: 2x − 5 = 3.
- Add 5 to both sides. Undo the subtraction: 2x = 8.
- Divide both sides by 2. Undo the multiplication by 2: x = 4.
The important note is not just “divide, add, divide”. Write the principle: apply the same operation to both sides so the equality is preserved. That instruction also works when the numbers change.
Include a check you can repeat
Substitute 4 into the original left-hand side:
The result matches the right-hand side, so the solution checks. Keep this substitution beside the method. It gives you something specific to do when you are uncertain about a later answer.
You could also note the expansion route: 6x − 15 = 9, then 6x = 24 and x = 4. Comparing the two routes shows that a valid method can have more than one starting point.
Record the mistake, not the whole lesson
A compact error log can sit underneath your notes. Describe what went wrong precisely enough that you can act on it.
| What happened | What to check next time | Practice task |
|---|---|---|
| I expanded 3(2x − 5) as 6x − 5. | Multiply every term inside the bracket by 3. | Expand three brackets before solving another equation. |
| I changed only one side of the equation. | Write the operation on both sides. | Solve two equations with one operation per line. |
You do not need an entry for every slip. Choose the mistakes that recur or reveal a gap in your method.
Turn the notes into a question
Close the method sheet and try 4(3x − 2) = 28. Write each operation on its own line and check your result in the original equation.
Check your practice answer
Divide by 4 to get 3x − 2 = 7. Add 2 to get 3x = 9, then divide by 3: x = 3. Substitution gives 4(9 − 2) = 28.
If you need to reopen the notes, identify the exact step that required help. Practise that step, then try a different question later. A finished set of notes should lead you back to working independently, with a clearer method and a check you understand.