A number talk is a brief discussion built around one carefully chosen mathematical question. When pupils compare and order numbers, their explanations can reveal whether they are using place value, partitioning, benchmarks or number-line reasoning, or relying on an unreliable rule.

Keep the discussion short and connected to the current lesson. The purpose is to expose and develop mathematical thinking before pupils use a formal method.

Select a small, revealing set

Choose two to four values that highlight the idea being taught or a misconception you need to check.

Primary examples include:

• 407 and 470;

• 3,506 and 3,560;

• 0.4 and 0.35;

• three quarters and two thirds;

• £2.05 and £2.50.

Secondary examples include:

• 0.6 and 0.56;

• minus 3 and minus 8;

• 0.4, two fifths and 38%;

• 0.03 and 3 × 10⁻²;

• square root of 50 and 7.

Do not use a random list. Each set should give pupils a reason to attend to structure, scale or equivalence.

Ask three useful questions

A concise routine is:

1. Which is larger or smaller?

2. How do you know?

3. Can you show it another way?

The third question might lead to partitioning, a number line, a place-value grid, a bar model or an equivalent form.

For 0.6 and 0.56, a pupil could rewrite 0.6 as 0.60, place both values between 0.5 and 0.7, or interpret them as hundredths. These are different representations of the same comparison.

Listen for the reasoning, not only the answer

A correct answer may be based on an insecure rule. A pupil who says 0.56 is larger because 56 is larger than 6 needs the misconception addressed even if another comparison happens to produce the right result.

Ask the pupil to make each place value explicit or represent the values. Conversely, do not assume a hesitant verbal explanation means weak number understanding. Allow the pupil to point, draw, annotate or demonstrate with equipment.

Useful things to notice include whether the pupil:

• attends to the whole value rather than digit length;

• aligns decimal places correctly;

• uses zero as a reference for negative numbers;

• recognises equivalent fractions, decimals or percentages;

• chooses an appropriate benchmark;

• can justify an order rather than guess it.

Use representations purposefully

A representation should reveal the relationship.

• Use a place-value chart when digit position is the issue.

• Use an open number line when relative size or distance matters.

• Use partitioning to expose the structure of a whole number or decimal.

• Use a bar model when comparing fractions of the same whole.

• Use equivalent notation when values look different but represent the same amount.

Do not ask for several representations simply to prolong the discussion. Once the pupil has demonstrated secure reasoning, move into the lesson.

Correct misconceptions explicitly

Acknowledge the reasoning, then show where it fails.

For example: “You compared 56 with 6 as whole numbers. In these decimals, the 6 represents six tenths, which is sixty hundredths. Let’s place 0.60 and 0.56 on the same line.”

Ask the pupil to restate the comparison and apply it to one nearby example. Avoid leaving competing explanations unresolved for the sake of open discussion.

Keep number talks brief

A focused talk may last three to five minutes. It can be used:

• before formal calculation;

• as a lesson starter;

• when introducing a new representation;

• after spotting a common misconception;

• before estimating or checking an answer.

The same pupil should not be expected to explain publicly every time. Use think time, mini whiteboards, paired discussion and selected responses.

Primary and Secondary emphasis

In Primary, build links between concrete quantities, representations and numerals. Include whole numbers, fractions, decimals, money and measures at the appropriate stage.

In Secondary, retain those representations but connect them with negative values, percentages, standard form, irrational numbers and algebraic expressions. Keep the materials age-respectful and tied to current curriculum content.

Common mistakes to avoid

• Treating the activity as mental speed practice.

• Choosing values that do not expose useful reasoning.

• Accepting a correct answer without checking the method.

• Allowing a misconception to remain uncorrected.

• Valuing confident speech over diagrams or written reasoning.

• Asking every pupil to produce several representations.

• Letting the discussion replace the main mathematical work.

Evidence and further reading

The national curriculum mathematics programmes of study emphasise representing, comparing and reasoning with number. The Department for Education’s Primary mathematics guidance sets out progression in core number concepts, while the NCETM provides Key Stage 3 guidance on mathematical representations.