Mixed practice places two or three familiar calculation types together so the pupil must identify the structure and select a method. It should begin only after each method can be used accurately on its own.

The purpose is deliberate choice, not surprise. Keep the set small and discuss both the selected method and the answer.

Check that each method is secure

Before mixing, confirm that the pupil can:

• recognise each calculation type in a blocked set;

• use the agreed method accurately;

• explain the main steps;

• retain the method after a short gap.

If one method remains insecure, reteach it separately. Mixing an uncertain method with others usually creates confusion rather than flexibility.

Begin with two familiar structures

A short activity might mix:

• addition bridging through 10 and subtraction crossing 10;

• multiplication and related division;

• mental addition and column addition;

• fraction-of-a-quantity and division;

• calculations suited to known facts and calculations requiring a written method.

Use clear examples and ask the pupil to state the method before calculating.

Ask why the method fits

Use prompts such as:

• “What is the calculation asking?”

• “Which relationship do you notice?”

• “Can this be done mentally?”

• “Would a written method be more dependable?”

• “Why does your method fit these values?”

For 99 + 36, compensation may be efficient. For 3,847 + 2,968, the agreed written method may be more dependable. Do not reward novelty when a simple method is appropriate.

Give feedback on choice and accuracy

A correct answer reached through an inefficient or misunderstood process still provides useful teaching information. An appropriate method with a minor arithmetic slip requires different feedback.

Discuss:

1. Was the method suitable?

2. Was it applied accurately?

3. Was the answer reasonable?

Ask for a corrected retry using the same method where the choice was sound.

Keep the mixed set manageable

Use perhaps six to eight items containing two or three structures. Do not mix every operation, representation and context at once.

Add variation gradually:

• change the values;

• include a short word problem;

• alter the order;

• include one calculation where a different method is clearly more efficient.

The pupil should learn to discriminate, not guess what the teacher wants.

Remove and reteach an insecure method

If the same method is repeatedly misidentified or applied incorrectly:

• take it out of the mixed set;

• model and practise it separately;

• compare it with one clearly different method;

• return it to mixed practice once secure.

Do not continue rehearsing the error in the name of challenge.

Common mistakes to avoid

• Mixing methods before they are taught securely.

• Including too many calculation types.

• Checking only answers, not method selection.

• Rewarding unusual strategies over dependable ones.

• Treating confusion as desirable difficulty.

• Leaving an insecure method in the set.

• Timing the activity before accurate choices are established.

Evidence and further reading

The Education Endowment Foundation’s Improving Mathematics in Key Stages 2 and 3 considers strategy choice, representations and practice. The national curriculum mathematics programmes of study expect pupils to decide which operations and methods to use and explain their reasoning.