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Fractions of a whole

CONCEPTUAL
MathematicsFractions|Ages 8—9|ID: mt_ndGqFPWyen

Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b

Mastery Evidence

  • Given a shape divided into 5 equal parts, identify one shaded part as 1/5
  • Explain that 3/4 means 3 parts each of size 1/4
  • Draw a model showing 2/6 as 2 pieces of a whole cut into 6

Assessment Prompt

“If you cut a pizza into 6 equal slices, can [child] explain what 1/6 means — and then work out what 4/6 of the pizza looks like?”

Prerequisites3

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  • Fractions of amounts hard

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

    • 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

  • Fraction Notation hard

    Understanding a/b as a parts of 1/b requires numerator, denominator, and unit fraction vocabulary

  • Splitting shapes into equal parts (age 7+) hard

    Partition into equal shares is prerequisite to understanding unit fractions