Number sense is the understanding of how quantities, number symbols and number relationships fit together. A pupil may be able to recite a procedure but still struggle to judge which number is larger, estimate a sensible answer, partition a number or connect a written numeral to a quantity.

An intervention should identify the specific relationship that is insecure and teach from that point. It should not become a general repeat of the pupil's current maths lessons.

Before starting

Use a short assessment interview rather than relying only on a total score. Ask the pupil to explain and show their thinking while they:

• compare and order quantities;

• connect objects, spoken numbers and written numerals;

• partition and recombine numbers;

• place numbers on an empty number line;

• estimate quantities and check whether an answer is reasonable;

• recall and derive simple number facts.

Record the strategies and errors, not just correct answers. This establishes whether the main difficulty concerns quantity, symbols, place value or the relationships between numbers.

What effective teaching looks like

Teach one connected idea at a time using concrete, pictorial and symbolic representations. For example, compare two quantities with counters, show the same relationship on a number line, then write the matching number sentence. For an older pupil, place 0.3, 0.25 and ⅓ on the same 0 to 1 line and ask which is largest and how they know.

Ask the pupil to explain what each representation shows. Vary the examples while keeping the mathematical structure stable, then gradually remove materials once the pupil can explain and use the relationship without them.

Build frequent opportunities to retrieve previously taught ideas. Include deliberate comparison, estimation and reasoning rather than pages of near-identical calculations.

Choosing an intervention

Check the intended age, starting point, training requirements, group size and teaching time against the pupil's profile. Two UK options to investigate are:

• Success@Arithmetic Number Sense (paid) is described by Edge Hill University for pupils in Year 3 and above. It starts with an assessment interview, then selects a tailored sequence of up to 24 sessions, delivered by a trained teaching assistant to no more than three pupils.

• 1stClass@Number 2 (paid) is a structured small-group programme for primary pupils who need further support with the Year 2 mathematics curriculum. It is delivered by a trained teaching assistant in three 30-minute sessions each week over 10–15 weeks. Check that the pupil’s assessed starting point matches the programme before selecting it. The strongest evidence in this family is for 1stClass@Number 1 (paid), the Year 2 version: EEF-funded trials found about two months' additional progress, and the EEF lists it as a Promising Programme. That result is for @Number 1, so it doesn't show how well 1stClass@Number 2 works. Both programmes need staff trained through Edge Hill or one of its training partners; check dates and costs.

Do not select a programme because its name contains “number sense”. Confirm that its teaching sequence addresses the pupil's identified gaps and is suitable for their age.

Both programmes are written for Primary pupils. For Secondary pupils, use the same sequence with a double number line, bar models and place-value charts, and link each idea to current lessons on fractions, decimals, percentages or ratio. A free route for any age is to build the sequence from the DfE guidance at the end of this article, which sets out ready-to-progress criteria for each primary year group.

Monitoring progress

Set a small number of precise outcomes, such as placing two-digit numbers accurately on an empty number line or deriving an unknown fact from a known one. Check these every few sessions using unfamiliar examples. A typical pattern is three or four sessions a week of 20 to 30 minutes, one to one or in a group of two to four. The length of the block depends on how much support the pupil needs, and the school decides where it fits in the timetable and when to hold a fuller review; many schools review after six to eight weeks. Also check whether the pupil uses the new understanding in ordinary maths lessons.

If progress is limited, review the starting point, representation, teaching pace and delivery fidelity before simply extending the intervention.

Useful guidance

• DfE mathematics guidance for primary schools

• EEF: Improving Mathematics in Key Stages 2 and 3

Provider descriptions should be considered alongside independent evidence, cost, training requirements and local fit.

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.