Calculation fluency is more than answering quickly. It combines secure number facts, efficient strategies, accurate procedures and enough understanding to choose and check a method.

Begin by identifying the first missing fact, relationship or procedure. Teaching should rebuild from that point rather than giving the pupil a larger volume of mixed calculations.

Find the point of difficulty

Use a short sample across the relevant operations and ask the pupil to show or explain their method. Check whether difficulty arises from:

• insecure additive or multiplicative facts;

• weak understanding of place value;

• inefficient counting strategies;

• confusion about the operation;

• loss of accuracy within a written method;

• difficulty checking whether an answer is reasonable.

Separate conceptual understanding from recall and transcription. A pupil may understand a method but calculate inaccurately, or recall facts without understanding when to use them.

Teach in a connected sequence

Model one efficient strategy and connect it to known facts and representations. For example, derive 7 + 8 from 7 + 7, or connect 6 × 8 to six groups of eight, an array and a related division fact.

Use worked examples, guided practice and a short amount of carefully chosen independent practice. Include cumulative retrieval so secure facts remain available while new ones are added. Accuracy and explanation come before pressure for speed.

For written calculation, make place value explicit, compare correct and incorrect examples, and ask the pupil to explain why each step is needed. Fade prompts only after the pupil can reproduce and check the method reliably.

Choosing a programme

The programme must match the assessed gap and the pupil's age.

• Number Sense Maths (paid): Number Facts Fluency (addition and subtraction facts, from age 5) and Times Tables Fluency (multiplication and division facts, from age 7). The provider says the programmes are modelled on the structure of phonics programmes. Schools subscribe; introductory training is free and in-depth courses are charged per person. The provider describes a decade of trialling; check for independent evaluation before buying. It fits a gap in recalling facts better than a difficulty with a written method.

• Success@Arithmetic (paid): an Edge Hill University programme delivered by trained teaching assistants to small groups. The Number Sense strand starts at Year 3 and the Calculation strand at Year 5. Use only the strand that matches the pupil's assessed difficulty, and check training dates and costs with Edge Hill.

• Free route: the DfE mathematics guidance at the end of this article sets out ready-to-progress criteria for each primary year group, which help you choose and order the target facts. For Secondary pupils, teach the same facts with age-appropriate examples, such as deriving 0.7 + 0.8 from 7 + 8.

Do not combine several commercial programmes in the same intervention. Consistent teaching, adequate practice and faithful delivery matter more than the number of resources used.

A typical plan

A typical pattern is a trained teaching assistant or teacher working with two to four pupils who share the same gap, three or four times a week for 10 to 20 minutes, linked to the current class topic. Set one or two targets, such as “recalls number bonds to 10 without counting and uses them to work out bonds to 20”. The size of the pupils' gaps decides how long it runs. The school chooses where it sits in the timetable and when to check progress, often after six to eight weeks. Check progress on unfamiliar examples and class work. Move on when the target holds on two separate checks, and change the approach if there is little progress.

Monitor what matters

Track a small set of target facts or methods, then test unfamiliar examples and application in lessons. Review accuracy, strategy choice, independence and retention after a gap. If progress stalls, check the teaching match and the pupil's underlying number understanding before increasing practice time.

Useful guidance

• EEF: Improving Mathematics in Key Stages 2 and 3

• DfE mathematics guidance for primary schools

Check current age ranges, training requirements, costs and independent evidence.

Talamo has no commercial relationship with any of the organisations named here. We suggest them only because we think they could be useful to schools.