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Simple Fraction Sums

PROCEDURAL
Mathematics›Fractions|Ages 7—8|ID: mt_a1FdAsRKOF

Add and subtract fractions with the same denominator within one whole (e.g. 5/7 + 1/7 = 6/7)

Mastery Evidence

  • Calculate 2/5 + 2/5 = 4/5
  • Calculate 6/8 − 3/8 = 3/8
  • Explain that when denominators are the same, you add/subtract the numerators

Assessment Prompt

“If a recipe calls for 2/8 of a cup of milk and then another 3/8 of a cup, can [child] work out the total without a calculator?”

Curriculum Standards1 alignment

Ma/KS2/Y3/F/5The national curriculum in England
Add and subtract fractions

add and subtract fractions with the same denominator within one whole [for example, 5/7 + 1/7 = 6/7]

Mathematics · Key Stage 2

Prerequisites2

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  • Fractions on a number line hard

    Adding fractions requires understanding fractions as numbers

    • 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

  • Addition as combining or putting together two soft

    Adding fractions extends the concept of addition as combining

    • How Many in Total? hard

      Understanding addition as combining groups 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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