Math // Fractions

Fractions of amounts

Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity

Ages
6 to 7
Type
Concept
Builds on
4 topics
Leads to
5 topics
Standards
1 code

Quick check

If you put 12 grapes on the table, can the learner count out a quarter of them — and then show you what three-quarters of the grapes looks like?

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.
  • Find 1/3 of 12 objects by sharing into 3 equal groups
  • Shade 3/4 of a rectangle that has been divided into 4 equal parts
  • Identify 1/4 of a length on a number line or ruler

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

4 topics
  • What Is a Half?Required

    Fractions // Ages 5 to 6

    Working with fractions extends from Y1 understanding of halves

  • Finding halves and quarters (age 5+)Required

    Fractions // Ages 5 to 6

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

  • Fraction NotationRequired

    Fractions // Ages 6 to 9

    Writing fractions like 1/3 and 3/4 requires knowing numerator and denominator

  • Division as equal sharingHelpful

    Multiplication & Division // Ages 4 to 6

    Finding fractions of quantities uses equal sharing (division)

You are here

Fractions of amounts

Ages 6 to 7 // Concept

Leads to

5 topics
  • Understanding fractionsRequired

    Fractions // Ages 6 to 7

    Writing fractions and recognising equivalence requires knowing what the fractions mean

  • TenthsRequired

    Fractions // Ages 7 to 8

    Tenths extend fraction understanding from halves, thirds, quarters

  • Fractions on a number lineRequired

    Fractions // Ages 7 to 8

    Placing fractions on number line requires knowing what fractions are

  • Unit fractionsRequired

    Fractions // Ages 7 to 8

    Finding fractions of discrete sets extends finding fractions of shapes/quantities

  • Fractions of a wholeRequired

    Fractions // Ages 8 to 9

    Recognising fractions of shapes/quantities is prerequisite to formal unit fraction understanding

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

Year 2 pupils (ages 6-7) recognise, find, name, and write the fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity. Two linked ideas mature: the DENOMINATOR says how many EQUAL parts (or equal groups) to share the whole into, and the NUMERATOR says how many of those parts to take, so a non-unit fraction like 3/4 is three of the quarter-parts, not a single piece. Work moves between continuous wholes (shading part of a rectangle or marking a length) and discrete sets (a third of 12 counters), always keeping the whole explicit and fixed.

Common misconceptions

  • Reading the denominator as the group SIZE, not the number of groups (1/3 of 12 -> makes groups of 3)
  • Treating a non-unit fraction like a unit fraction - taking only ONE part for 3/4
  • Number-vs-quantity: sharing an equal COUNT of unequal-sized items rather than equal amount
  • Losing track of the whole, or ignoring leftover items when a set doesn't divide evenly

Useful representations

  • A set of counters shared into equal groups (denominator groups; take numerator)
  • A rectangle/strip partitioned and shaded (e.g. 3 of 4 parts for 3/4)
  • A length/number line marked into equal parts
  • Unit-fraction tiles combined to build a non-unit fraction

Teaching practices

  • Find a unit fraction by sharing the whole into denominator-many EQUAL parts and taking one; build the non-unit fraction as repeated unit fractions (3/4 = three quarters)
  • Move between continuous (shade 3/4 of a rectangle) and discrete (1/3 of 12 counters) models
  • For a set, share into denominator-many equal GROUPS (not groups of that size), then take numerator-many groups
  • Name and write alongside the action so notation is tied to meaning
  • Keep the whole explicit and fixed while working

Activities to try

  1. 1

    Fraction-of-a-set bench: share into equal groups, then take some

    Why it works: The denominator sets how many EQUAL groups/parts to make; the numerator says how many of those to take - so 3/4 is three quarters, not one piece, and the same fraction describes both a set and a shape.

    1. Put out 12 counters as the whole. To find 1/3, share ALL 12 into 3 equal groups (one group per hoop) and take one group - record '1/3 of 12 = 4'.
    2. To find 3/4, share all 12 into 4 equal groups (3 in each) and take THREE of the four groups - record '3/4 of 12 = 9'.
    3. Say aloud 'the bottom number is how many equal groups; the top number is how many groups I take' as you act it out.
    4. Re-show the same fraction as a shaded strip or rectangle divided into the denominator and shaded to the numerator, to see the continuous and discrete versions side by side.
    5. Check a non-dividing case: with a different set of items that does not share evenly (for example 10 counters into 3 groups), notice the leftover. It means the groups cannot all be equal with whole items, so that fraction of the set cannot be found exactly with whole counters (1/3 of 10 is not 3).
  2. 2

    Build a non-unit fraction from unit-fraction parts

    Why it works: A non-unit fraction is repeated unit fractions: 3/4 is three quarters, built by taking one quarter three times.

    1. Find a unit fraction first: share the whole into denominator-many equal parts and take one (e.g. 1/4 of a strip, or 1/4 of 12 counters = 3).
    2. Build 3/4 by repeating that quarter three times (1/4 + 1/4 + 1/4), counting the quarters taken.
    3. State the link: 3/4 means three of the four equal parts, so it is three unit-fractions put together.
    4. Write the fraction next to the action each time so the notation stays tied to the meaning.
  3. 3

    Same number or same amount? Guarding against the count-vs-quantity trap

    Why it works: When the whole is an amount of stuff, fair sharing means giving each share an equal AMOUNT. With identical counters, counting gives equal amounts, but with unequal-sized pieces an equal count is NOT the same as an equal amount, so children must check the amount, not just the number of things. When the question is about the number of objects in a set, the count is what matters.

    1. Compare a third of 12 LARGE counters with a third of 12 TINY counters: is the NUMBER of things the same? Is the total AMOUNT the same?
    2. With a mixed set of big and small pieces of the same stuff (e.g. pieces of food to share fairly), check whether equal-COUNT groups also hold an equal AMOUNT. When the whole is an amount of stuff, amount, not count, is what fair sharing must make equal. Exact equal amounts may not be possible without cutting pieces.
    3. Discuss aloud: 'same number of things, or same amount?' to separate the two ideas.

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/Y2/F/1

Math // Fractions

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