Math // Fractions

Finding halves and quarters (age 5+)

Recognise, find, and name a quarter as one of four equal parts of an object, shape, or quantity

Ages
5 to 6
Type
Concept
Builds on
1 topic
Leads to
2 topics
Standards
1 code

Quick check

If you fold a square piece of paper into four equal parts, can the learner tell you that each part is a quarter — and point to just one quarter?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Fold a shape into four equal parts and identify each as 'a quarter'
  • Find a quarter of 12 objects by sharing into 4 equal groups
  • Identify whether a shape has been divided into quarters (four equal parts)

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

Before this

1 topic
  • What Is a Half?Required

    Fractions // Ages 5 to 6

    Understanding quarters extends from understanding halves — both are equal parts but quarters requires dividing into 4

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Finding halves and quarters (age 5+)

Ages 5 to 6 // Concept

Leads to

2 topics
  • Fractions of amountsRequired

    Fractions // Ages 6 to 7

    Working with 1/4, 2/4, 3/4 extends from Y1 understanding of quarters

  • Halves & Quarters of ShapesRequired

    Fractions // Ages 6 to 7

    Partitioning into fourths/quarters extends from Y1 understanding of quarters

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

A quarter is one of FOUR EQUAL parts of a whole. Reach quarters by repeated halving (fold in half, then halve each half, giving four matching parts in total), work them on single objects, lengths, and sets (a quarter of 12 = share into four equal groups and take one), and show that four quarters recompose the whole while two quarters make a half — seeding equivalence. The core learner actions are partitioning/folding to make equal parts and sharing a set into four equal groups, with naming and counting attached to the number of equal parts.

Common misconceptions

  • Any four pieces count as quarters regardless of size (equal-parts missing)
  • Muddling the names — calling a quarter 'a half', or vice versa
  • A quarter of a set found by making groups OF four rather than four equal groups
  • Thinking a quarter is bigger than a half because 'four is more than two' (whole-number bias, developing here)

Useful representations

  • A shape folded in half then half again into four matching parts
  • A strip/length marked into four equal parts
  • 12 counters shared into four equal groups
  • Four quarters reassembling into the whole; two quarters overlaying a half

Teaching practices

  • Reach quarters by repeated halving (halve, then halve each half) before free four-way partitioning — IES powers-of-two progression
  • Insist on four EQUAL parts; check by matching/overlaying
  • Work quarters of sets by sharing into four equal groups (not making groups of four)
  • Name and count: 'four quarters make one whole', 'two quarters make a half'
  • Use continuous and discrete models so 'a quarter' is not tied to one shape

Activities to try

  1. 1

    Halve, then halve again: making four equal quarters

    Why it works: A quarter is one of four EQUAL parts; repeated halving is a reliable way to produce them, four quarters rebuild the whole, and two quarters together make a half.

    1. Fold (or partition) a symmetrical shape such as a square, rectangle or circle in half, then fold each half in half again so the shape opens into four matching parts.
    2. Check the four parts are equal by matching or overlaying them; only equal parts count as quarters.
    3. Count aloud: 'four quarters make one whole'.
    4. Join two of the quarters to make a half, then place that pair over the other two quarters (or over an identical shape folded once into halves) to see that 'two quarters make a half'.
    5. Compare with a shape cut into four UNEQUAL pieces and explain why those are not quarters.
  2. 2

    A quarter of a set: sharing 12 into four equal groups

    Why it works: A quarter of a set is found by sharing the whole set into four equal groups and taking one group — not by making groups of four.

    1. Take 12 counters and share them, one at a time, into four equal groups (four hoops or circles).
    2. Keep going until all 12 are placed and every group has the same number.
    3. Report how many are in one group — 'a quarter of 12 is 3'.
    4. Contrast with making groups OF four and notice that gives three groups, which is a different question.
  3. 3

    Naming by counting equal parts: halves vs quarters

    Why it works: The fraction name follows the number of equal parts: two equal parts are halves, four equal parts are quarters; of the SAME whole, a quarter is smaller than a half.

    1. Partition one shape into two equal parts and name each a 'half'; partition another into four equal parts and name each a 'quarter'.
    2. Count the equal parts aloud and attach the name to the count: two equal parts = halves, four equal parts = quarters.
    3. Use halve-then-halve-again on the same shape to see how a half becomes two quarters.
    4. Decide, for a correctly-made part, whether it is a half or a quarter and justify by counting the equal parts.

Topic // Standards

Curriculum standards

Codes for the curriculum statements this topic maps to. Each publisher owns its standard text.
The national curriculum in England: Key stages 1 and 2 framework document
Maths/Y1/F/2

Math // Fractions

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