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Decimals and fractions

PROCEDURAL
Mathematics›Fractions|Ages 8—9|ID: mt_wB-GBDkoNr

Solve simple measure and money problems involving fractions and decimals to two decimal places

Mastery Evidence

  • Calculate 1/4 of £3.20
  • A rope is 2.5 m long; how much is left after cutting 0.75 m?
  • Find 3/10 of 1 kg and express the answer in grams and as a decimal of a kg

Assessment Prompt

“If a bottle holds 1.5 litres and [child] drinks 0.75 litres, can they work out how much is left — and write it as both a decimal and a fraction?”

Prerequisites3

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  • Fractions of amounts (harder) soft

    Fraction-of-quantity skills support measure/money problems

    • Adding Fractions (Same Denominator) soft

      Fraction addition supports solving fraction problems

      • Simple Fraction Sums hard

        Add/sub within one whole is prerequisite to extending beyond one whole

        • 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

        • 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'

    • Unit fractions hard

      Finding fractions of discrete sets is prerequisite to harder fraction-of-quantity problems

      • 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'

  • Adding Fractions (Same Denominator) soft

    Fraction addition/subtraction supports measure/money problem-solving

    • Simple Fraction Sums hard

      Add/sub within one whole is prerequisite to extending beyond one whole

      • 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'

  • Decimal equivalents of tenths and hundredths hard

    Must understand decimal notation for measure/money problems

    • Tenths (age 8+) hard

      Must understand hundredths before writing decimal equivalents

      • Tenths hard

        Count in tenths is prerequisite to extending to hundredths

        • 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

    • Decimal & Percent Notation hard

      Writing decimal equivalents of tenths and hundredths requires decimal point and place-value vocabulary

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