Mixed practice requires pupils to identify a calculation’s structure and choose between familiar mental, written or calculator-supported methods. It should follow secure teaching of each method. Otherwise, the activity tests confusion rather than developing choice.

Use a small mixed set and require the pupil to state or annotate the method before calculating.

Confirm the methods are secure

Before mixing, check that the pupil can use each approach accurately in a focused set. Possible choices include:

• mental calculation using a known relationship;

• a standard written procedure;

• fraction or percentage methods;

• calculator-supported calculation;

• algebraic manipulation;

• estimation for checking.

Remove and reteach any method that remains unreliable.

Mix a small number of structures

Begin with two or three familiar demands.

For example:

• 25% of 80;

• 17% of 240;

• 0.25 × 80;

• an estimate of 17% of 240.

The pupil might use a benchmark percentage mentally for the first, a calculator or structured written method for the second and decimal multiplication for the third.

Another set might compare calculations suited to factorisation, expansion and numerical substitution.

Require a decision before calculation

Ask:

• “What does the question require?”

• “Which method would be dependable?”

• “Is there a useful relationship?”

• “Would a calculator improve access or remove the intended learning?”

• “What should the answer be roughly?”

The pupil may note M for mental, W for written or C for calculator, then justify the choice.

Discuss efficiency without rewarding novelty

An efficient method balances accuracy, effort and the values involved. A familiar written method may be better than an ingenious shortcut if it is more dependable for that pupil.

Compare methods after the pupil has a correct solution. Ask what feature of the numbers made one method useful.

For 398 + 205, adjustment may be efficient. For a long decimal calculation, a standard written or calculator-supported approach may be safer.

Give separate feedback on choice and execution

A pupil may choose an appropriate method but make an arithmetic slip. Another may obtain the correct answer through a method they cannot explain.

Review:

1. the chosen method;

2. how it was applied;

3. whether the answer is reasonable.

Correct the relevant part rather than replacing the entire approach.

Reteach insecure methods separately

If a procedure is repeatedly avoided or misused:

• remove it from the mixed set;

• model it with a worked example;

• practise it in a focused block;

• compare it with one clearly different approach;

• reintroduce it once accurate.

Do not leave it in the set merely to increase challenge.

Common mistakes to avoid

• Mixing methods before they are secure.

• Including too many structures at once.

• Treating the fastest method as automatically best.

• Rewarding novelty over dependability.

• Checking only the final answer.

• Leaving an insecure method in the mixed set.

• Using calculator choice without teaching estimation and checking.

Evidence and further reading

The Education Endowment Foundation’s Improving Mathematics in Key Stages 2 and 3 discusses strategy choice, practice and mathematical reasoning. The national curriculum mathematics programmes of study expect pupils to choose suitable operations and methods and check the reasonableness of results.