← Home

Experimental vs Theoretical

PROCEDURAL
Mathematics›Probability|Ages 10—11|ID: mt_-bMnJcPJy8

Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results

Mastery Evidence

  • Roll a die 60 times and compare experimental frequencies with the expected 10 per number
  • Explain why experimental results don't exactly match theoretical predictions but get closer with more trials
  • Predict what would happen if the experiment were repeated 600 times instead of 60

Assessment Prompt

“If [child] flips a coin 10 times and gets 7 heads, do they understand why this doesn't mean heads is "more likely" — and that the more times you flip, the closer the results get to 50:50?”

Prerequisites2

Show full prerequisite tree
  • Simple Chance Experiments hard

    Comparing experimental and theoretical probability requires prior experience conducting simple experiments and recording results

    • 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

  • Calculating Simple Probability hard

    Comparing experimental results with theoretical predictions requires being able to calculate the theoretical probability first

    • The 0-to-1 Probability Scale hard

      Calculating probability using favourable/total outcomes requires understanding probability as a number on a 0-1 scale

      • 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

    • Equally Likely Outcomes hard

      The probability formula only applies to situations with equally likely outcomes — this concept must be secure 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)

Unlocks1