Probability as a Fraction
REPRESENTATIONALDescribe 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
- Simple Chance ExperimentssoftAges 9—10
- Unit fractionshardAges 7—8
- Equally Likely OutcomeshardAges 9—10
Show full prerequisite tree
- 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
- 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'
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- Sorting Data into Categories soft
Data representation formats (pictograms, tally charts) support organising data
- 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
- 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'
- Counting objects to 20 hard
Counting objects in each category requires being able to count sets of objects
- 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'
- 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'
- 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'
- 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
- 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)
Unlocks1
- The 0-to-1 Probability ScalehardAges 10—11