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The 0-to-1 Probability Scale

CONCEPTUAL
Mathematics›Probability|Ages 10—11|ID: mt_t0g2SlP404

Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages

Mastery Evidence

  • Place events on a number line from 0 (impossible) to 1 (certain), expressing positions as fractions or decimals
  • Explain that a probability of 0.5 means 'even chance' and connect this to the informal word 'likely'
  • Convert between informal language ('very unlikely') and a numerical position on the 0-to-1 scale

Assessment Prompt

“Can [child] write the same probability as a fraction, a decimal, and a percentage — for example, knowing that an even chance is ½, 0.5, and 50%?”

Prerequisites2

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  • Probability as a Fraction hard

    The formal 0-1 probability scale formalises the fractional representation of equally-likely outcomes introduced at age 9-10

    • 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)

  • Comparing fractions soft

    Expressing probability as fractions, decimals, and percentages requires comparing and ordering fractions — a skill built in the Fractions domain

    • 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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