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Unit fractions

CONCEPTUAL
Mathematics›Fractions|Ages 7—8|ID: mt_k2WE0-22-4

Recognise, find, and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Mastery Evidence

  • Find 1/4 of 12 objects by dividing into 4 equal groups
  • Find 3/4 of 12 objects
  • Write the fraction of a set that is shaded or selected

Assessment Prompt

“If there are 15 books on a shelf, can [child] work out how many two-thirds of them is — and check by grouping the books into three equal piles?”

Curriculum Standards1 alignment

Ma/KS2/Y3/F/2The national curriculum in England
Recognise fractions of objects

recognise, find and write fractions of a discrete set of objects: unit fractions and non-unit fractions with small denominators

Mathematics · Key Stage 2

Prerequisites2

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  • Fractions of amounts hard

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

    • Finding halves and quarters (age 5+) hard

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

      • What Is a Half? hard

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

        • Division as equal sharing hard

          Finding a half requires equal sharing into 2 groups — a division concept

          • Subtraction as taking away or separating hard

            Division as equal sharing/grouping requires understanding subtraction as taking away/separating

            • How Many in Total? hard

              Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

              • One-to-one counting hard

                Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

    • What Is a Half? hard

      Working with fractions extends from Y1 understanding of halves

      • Division as equal sharing hard

        Finding a half requires equal sharing into 2 groups — a division concept

        • Subtraction as taking away or separating hard

          Division as equal sharing/grouping requires understanding subtraction as taking away/separating

          • How Many in Total? hard

            Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

            • One-to-one counting hard

              Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

    • Division as equal sharing soft

      Finding fractions of quantities uses equal sharing (division)

      • Subtraction as taking away or separating hard

        Division as equal sharing/grouping requires understanding subtraction as taking away/separating

        • How Many in Total? hard

          Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

          • One-to-one counting hard

            Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

    • Fraction Notation hard

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

  • Division as equal sharing soft

    Finding 1/4 of 12 objects connects to division as sharing equally

    • Subtraction as taking away or separating hard

      Division as equal sharing/grouping requires understanding subtraction as taking away/separating

      • How Many in Total? hard

        Understanding subtraction as taking away requires knowing numbers represent quantities (cardinality)

        • One-to-one counting hard

          Cardinality principle builds on one-to-one correspondence — you must count correctly to know the last number tells 'how many'

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