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Comparing fractions

PROCEDURAL
Mathematics›Fractions|Ages 7—8|ID: mt_IfEgu0X449

Compare and order unit fractions, and fractions with the same denominator

Mastery Evidence

  • Order 1/2, 1/3, 1/4, 1/5 from largest to smallest
  • Explain that a larger denominator means smaller unit fractions
  • Compare 2/5 and 4/5 and explain that 4/5 is larger because it has more fifths

Assessment Prompt

“If [child] has eaten 3/8 of a cake and a friend has eaten 5/8 of the same cake, can they tell you who has eaten more — and put those fractions in order from smallest to biggest?”

Curriculum Standards1 alignment

Ma/KS2/Y3/F/6The national curriculum in England
Compare and order fractions

compare and order unit fractions, and fractions with the same denominators

Mathematics · Key Stage 2

Prerequisites2

Show full prerequisite tree
  • Decomposing a shape into more equal shares soft

    More shares = smaller helps understand why 1/5 < 1/3

    • Halves & Quarters of Shapes hard

      Comparing share sizes requires experience partitioning into halves and quarters

      • Finding halves and quarters (age 5+) hard

        Partitioning into fourths/quarters 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

        Partitioning shapes into halves 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'

  • Fractions on a number line hard

    Comparing fractions requires understanding them as numbers on a line

    • Fractions of amounts hard

      Placing fractions on number line requires knowing what fractions are

      • 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

    • Tenths soft

      Counting in tenths supports placing fractions on a number line

      • Fractions of amounts hard

        Tenths extend fraction understanding from halves, thirds, quarters

        • 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

      • Counting in 2s soft

        Skip counting supports counting in tenths

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