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Fractions and equivalence with models that make sense

Fraction resources are useful when they make the whole and its equal parts clear. This guide moves from folding and comparing to explaining equivalent fractions on a number line. It includes ways to adjust practical work and check whether pupils understand the quantity represented rather than memorising a visual pattern.

Schools Direct editorialUpdated 2 min read

Establish the whole

Give pupils equal-sized paper strips and agree that one complete strip represents one whole. Fold strips into halves, quarters and eighths, checking that the parts are equal. Discuss why a larger piece is not necessarily a larger fraction when the wholes differ. Keep examples with unequal wholes for a later, deliberate comparison.

Build equivalence physically

Place one half beside two quarters of an identical strip. Ask pupils to explain what is the same and what has changed. The length represented is equal, while the number and size of the parts differ. Repeat with another example and invite a prediction before arranging the pieces.

Connect to a number line

Mark zero and one, then locate the same quantities from the strip activity. Align one half and two quarters at the same point. This helps pupils see a fraction as a number as well as a shaded region. Include an incorrectly partitioned line and ask children to identify the problem rather than simply supplying another correct example.

Choose models and questions carefully

Use resources with consistent whole sizes and unambiguous boundaries. Colour can support organisation, but pupils should still explain an equivalence when colours change. Provide pre-folded strips, tactile markings or large magnetic pieces where needed. Extend the work to fractions greater than one only when the unit whole remains clear. Assess through a new representation: ask pupils to show the same fraction with a strip, a drawing and a position on a line, explaining the connection between all three.

Action checklist

  • Keep the unit whole explicit
  • Check that parts are equal
  • Align equivalent amounts on a number line
  • Change colours to test understanding

Common questions

Why use a number line as well as fraction circles?

A number line helps pupils treat fractions as numbers and see equivalent fractions occupying the same position, complementing part-of-a-whole models.

Sources and scope

Source titles are provided for reference. Check the current original guidance and your school's circumstances before making a policy or compliance decision.

  • Schools Direct editorial — Original teaching activity and resource planning notes. Checked 1 November 2026.

See how we prepare and maintain our guidance.

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