A worked example shows the complete calculation and the reasoning behind each step. It can reduce unnecessary memory demands while a pupil learns a method, allowing attention to remain on the mathematical structure.

The example should not remain permanently visible. Move from a complete model to missing steps and then independent work, bringing support back briefly if the same error returns.

Match the example closely

The example and the pupil’s calculation should share the same mathematical structure without being identical.

If the model shows 47 + 36 using an agreed column method, a suitable next calculation might be 58 + 27. Changing the operation, place-value demand and layout at the same time makes it harder to apply the example.

In Secondary mathematics, if the worked example is 1/3 + 1/4 = 4/12 + 3/12 = 7/12, follow it with 2/5 + 1/3, which needs the same common-denominator step, before moving on to mixed numbers.

Talk through the example

Do not ask the pupil merely to copy it. Explain:

• what the calculation requires;

• why the method is suitable;

• what each step does;

• which notation or place value must remain aligned;

• how to check the result.

Ask the pupil to point to the relevant line and explain it back.

A useful prompt is: “What changed between these two lines, and why was that allowed?”

Use a fading sequence

Stage 1: Complete example

Present every step and annotate the reasoning.

Stage 2: Matched example with prompts

Give the pupil a similar calculation with step headings or a partially prepared layout.

Stage 3: Missing steps

Remove selected parts and ask the pupil to complete them.

Stage 4: Independent calculation

Provide only the question. Keep the worked example available nearby if the pupil needs to check one step.

Stage 5: Remove the model

Ask the pupil to complete a new example without referring to it, then explain or check the method.

Fade only after accurate guided practice. Removing support too early creates repeated errors; leaving it too long encourages copying.

Primary example

For 8 + 5 using make ten:

1. Show 8 + 5.

2. Partition 5 into 2 and 3.

3. Combine 8 and 2 to make 10.

4. Add the remaining 3.

5. Record 8 + 5 = 8 + 2 + 3 = 13.

The next example might show the first partition only. The following one asks the pupil to decide how to partition.

For a written method, align the example with the school calculation policy and link each digit with its place value.

Secondary example

For solving 3x + 5 = 20:

1. Subtract 5 from both sides: 3x = 15.

2. Divide both sides by 3: x = 5.

3. Substitute 5 into the original equation to check.

The faded example might provide the first transformation and leave the second blank. A later question removes the prompts.

For fractions, percentages or negative numbers, retain the same principle: show the procedure, ask why each step works and remove one support at a time.

Compare examples when useful

Once one method is secure, two completed examples can help pupils notice:

• where the same structure appears;

• why a step changes;

• which method is more efficient;

• where a common error occurs.

Do not introduce competing methods before the pupil has a dependable starting point.

Bring the example back temporarily

If an earlier error returns:

1. show the relevant worked example;

2. ask the pupil to locate the matching step;

3. complete one supported retry;

4. remove the example again.

This is a targeted response, not a reason to restart the entire sequence.

Check for understanding

Look for whether the pupil can:

• explain the steps;

• match the example with a new calculation;

• complete missing parts;

• detect an incorrect worked line;

• work independently after the model is removed;

• retain the method after a gap.

Accurate copying alone is not enough.

Common mistakes to avoid

• Using an example with a different structure from the task.

• Asking pupils to copy without explanation.

• Removing the example after one successful attempt.

• Leaving the complete model visible indefinitely.

• Showing several methods before one is secure.

• Increasing number complexity while the procedure is still new.

• Treating the worked example as the mathematics rather than a temporary scaffold.

Evidence and further reading

The Education Endowment Foundation explains how worked examples can support mathematical problem-solving and make strategies available for discussion. Its Improving Mathematics in Key Stages 2 and 3 report provides the broader evidence-informed framework.