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Comparing fractions (age 8+)

PROCEDURAL
Mathematics›Fractions|Ages 8—9|ID: mt_HnKbuCliNS

Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols

Mastery Evidence

  • Compare 3/8 and 3/4: same numerator, larger denominator means smaller pieces so 3/8 < 3/4
  • Compare 5/6 and 2/6: same denominator so 5/6 > 2/6
  • Justify a comparison using a visual model and explain why both fractions must refer to the same whole

Assessment Prompt

“If [child] sees 3/5 and 3/8, can they tell you which is bigger just by thinking about the size of each piece — without needing to draw it out?”

Prerequisites2

Show full prerequisite tree
  • Comparing fractions hard

    Same-denominator comparison experience is prerequisite to same-numerator comparison

    • 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

  • Fractions of a whole hard

    Must understand unit fraction size reasoning for same-numerator comparison

    • 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

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