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Probability as a Fraction

REPRESENTATIONAL
MathematicsProbability|Ages 9—10|ID: mt_-c4Ca_nBzX

Describe the probability of simple equally-likely outcomes using unit fractions: the probability of rolling a 6 on a fair die is 1/6, flipping heads is 1/2, picking one specific colour from three equally represented colours is 1/3; place these fractional probabilities on a 0-to-1 probability scale

Mastery Evidence

  • State that the probability of rolling a 6 on a fair die is 1/6 and explain why
  • Express the probability of picking a red card from a standard deck as 26/52 or 1/2
  • Write the probability of a simple event as a fraction: favourable outcomes over total outcomes

Assessment Prompt

“If [child] flips a fair coin, do they know the probability of getting heads is 1/2 — and can they express similar simple probabilities as fractions and place them on a 0-to-1 scale?”

Prerequisites3

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  • Simple Chance Experiments soft

    Practical experiment experience provides the intuitive grounding that makes fractional probability representation meaningful

    • Pictograms and tally charts soft

      Recording probability experiment results in tally charts uses the data-recording skills taught in Data & Statistics

      • Pictograms and tally charts (age 6+) hard

        Constructing pictograms, tally charts, and bar charts requires these display vocabulary terms

      • Sorting into categories hard

        Constructing pictograms and tally charts requires classifying and counting objects first

        • Comparing groups: more or fewer soft

          Sorting categories by count benefits from ability to compare quantities

          • Counting objects to 20 soft

            Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

            • How Many in Total? hard

              Answering 'how many?' requires the cardinality principle

              • 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'

            • One-to-one counting hard

              Counting objects to answer 'how many?' requires one-to-one correspondence

        • Counting objects to 20 hard

          Counting objects in each category requires being able to count sets of objects

          • How Many in Total? hard

            Answering 'how many?' requires the cardinality principle

            • 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'

          • One-to-one counting hard

            Counting objects to answer 'how many?' requires one-to-one correspondence

      • Sorting Data into Categories soft

        Data representation formats (pictograms, tally charts) support organising data

        • How Many in Total? soft

          Counting data in categories requires understanding 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'

        • Pictograms and tally charts (age 6+) hard

          Organising and representing data requires data, tally, frequency, and category vocabulary

        • Sorting into categories hard

          Organising data in categories builds on classifying and counting objects in categories

          • Comparing groups: more or fewer soft

            Sorting categories by count benefits from ability to compare quantities

            • Counting objects to 20 soft

              Counting a set helps when comparing groups, but younger children (GB age 4) can compare using matching without formal counting to 20

              • How Many in Total? hard

                Answering 'how many?' requires the cardinality principle

                • 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'

              • One-to-one counting hard

                Counting objects to answer 'how many?' requires one-to-one correspondence

          • Counting objects to 20 hard

            Counting objects in each category requires being able to count sets of objects

            • How Many in Total? hard

              Answering 'how many?' requires the cardinality principle

              • 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'

            • One-to-one counting hard

              Counting objects to answer 'how many?' requires one-to-one correspondence

    • Likelihood Language hard

      Conducting probability experiments and describing results requires knowing the language used to describe likelihood

  • Unit fractions hard

    Expressing probabilities as unit fractions (1/6, 1/2, 1/3) requires prior knowledge of unit fractions from the Fractions domain

    • 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'

  • Equally Likely Outcomes hard

    Using fractions to represent probability only makes sense for equally-likely outcomes, so the equally-likely concept must come first

    • Ordering Likelihoods hard

      Understanding what 'equally likely' means is a specific case of comparing likelihoods that requires the general comparison skill first

      • Likelihood Language hard

        Comparing and ordering likelihoods requires first knowing the vocabulary of likelihood (certain, likely, unlikely, impossible)

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