Math // Probability

Likelihood Language

Use probability language to describe and compare the likelihood of everyday events using words such as certain, likely, even chance, unlikely, impossible

Ages
9 to 10
Type
Language
Builds on
0 topics
Leads to
2 topics

Quick check

Does the learner use words like "certain," "likely," "unlikely," and "impossible" correctly — for example, knowing that rolling a 7 on a normal die is impossible but rolling an even number is likely?

Ask this to see whether the topic is secure.

Topic // Mastery

What mastery looks like

What a learner can do once this topic is secure.
  • Place five everyday events (e.g. 'the sun will rise tomorrow', 'it will snow in July', 'I'll flip heads') on a scale from impossible to certain
  • Use 'likely', 'unlikely', 'certain', 'impossible', and 'even chance' correctly to describe different events
  • Explain why pulling a red ball from a bag of mostly red balls is 'likely' but not 'certain'

Topic // Map

Where this fits

What to learn first and what this topic opens up, with the reason for each link. Required links come first.
  • RequiredMust come first
  • HelpfulHelps, but not essential

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Likelihood Language

Ages 9 to 10 // Language

Leads to

2 topics
  • Simple Chance ExperimentsRequired

    Probability // Ages 9 to 10

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

  • Ordering LikelihoodsRequired

    Probability // Ages 9 to 10

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

Topic // Research-informed

Teaching notes

From the Marble Skill Taxonomy. These notes have not been validated in classrooms, so treat them as a starting point for your own judgement.

The approach

Likelihood Language (ages 9-10, Mathematics/Probability): children learn to USE and justify the words impossible, unlikely, even chance, likely, certain to describe how probable everyday events and chance-device outcomes are, before any numbers. The teaching aim is correct use in context — mapping each word onto the composition of a situation (how many of each outcome), reserving 'certain'/'impossible' for the true endpoints and using the graded middle for everything else. This is the gateway to the 0-to-1 scale and to comparing likelihoods. Core activity is open dialogue where the child generates and repairs their own wording against outcomes that push back; a live likelihood line/strip and sorting tasks are strong supports, and a tap-to-reveal reference scene can accompany them.

Common misconceptions

  • Treating 'even chance' as meaning 'any situation with two possible outcomes' (e.g. calling a 1-red / 5-blue draw 'even chance' because there are two colours)
  • Collapsing the graded words to guarantees — 'likely' taken to mean it will definitely happen, 'unlikely' that it definitely won't
  • Confusing 'impossible' (cannot happen, probability 0) with 'very unlikely' (rare but possible) — e.g. calling a rare draw 'impossible'
  • Judging likelihood by personal preference or wishful thinking rather than by how many of each outcome there are

Useful representations

  • Likelihood line / probability word-scale strip (impossible ↔ certain)
  • Bags of coloured counters with visible, countable composition
  • Spinners with equal vs unequal sections
  • Everyday-event cards to sort and order

Teaching practices

  • Anchor a physical 'likelihood line' (a washing line / strip labelled impossible → even chance → certain) and have children peg real events onto it, justifying placements aloud
  • Start from everyday, personally-meaningful events ('it will get dark tonight', 'it will snow in July') then move to structured chance devices (bags of counters, spinners) where the composition can be inspected
  • Deliberately contrast 'likely' with 'certain' and 'unlikely' with 'impossible' using a mostly-red bag: red is likely but a blue draw is still possible, so red is not certain
  • Insist children give a reason grounded in the numbers ('most of them are red') rather than personal desire ('I want red')
  • Use unequal situations early (7 red, 3 blue; a spinner with one big section) so 'even chance' is not over-generalised to any two-outcome case

Activities to try

  1. 1

    The Chance-master's bag: say it, then watch it happen

    Why it works: Each likelihood word corresponds to how many of each outcome there are; 'likely' is not a guarantee and 'impossible' (cannot happen at all) is stronger than 'very unlikely' (rare but possible). 'Even chance' requires equal numbers, not merely two possible outcomes.

    1. Look into a bag you can see holds mostly red counters (e.g. 7 red and 3 blue) with the composition visible.
    2. Before any draw, say in words how likely a red draw is and WHY, grounding the reason in the numbers ('most of them are red') rather than wanting red.
    3. When you declare red 'certain', watch the game-master take out and show a blue counter (picked on purpose, or by drawing until one appears, because a single random draw will usually be red), then repair your word: was red certain, or only likely? Explain the difference.
    4. Answer the opposite trap: the game-master suggests 'landing on 7 with this ordinary 1–6 die is only very unlikely, isn't it?' — decide whether 7 is very unlikely (rare but possible) or impossible (cannot happen at all), and say why.
    5. Describe a green draw ('there are no green counters'), and a 'red or blue' draw ('only those two colours exist'), choosing and justifying a word for each.
  2. 2

    Physical likelihood line: peg real events and justify

    Why it works: Events can be ordered along a graded scale from impossible to certain, and placement is decided by composition, not by preference — unequal situations sit away from 'even chance'.

    1. Set up a washing line or paper strip labelled impossible → unlikely → even chance → likely → certain.
    2. Peg everyday, personally-meaningful events onto it, saying your placement aloud: 'it will get dark tonight', 'it will snow in July', 'I'll flip heads', 'the sun will rise tomorrow' (for the weather and daylight events, think about where you live: snow in July is likely in some southern places, and near the poles there are times with no sunset or no sunrise).
    3. Move to structured chance devices where composition is inspectable — bags of counters, spinners with equal and unequal sections — and peg outcomes from those.
    4. Place at least one deliberately unequal situation (7 red/3 blue; a spinner with one big section) and justify why it is NOT an even chance.
    5. Say out loud the reason for each placement, referring to how many of each outcome there are.
  3. 3

    Live likelihood strip with an adjustable bag

    Why it works: The word that fits a situation depends on and moves with the composition; as favourable outcomes dominate, the likelihood slides toward 'certain', and only when none of the other outcome remains is it 'certain' (and the absent outcome 'impossible').

    1. Drop an event card onto a 0-to-1 likelihood strip and SAY the word that fits before confirming.
    2. Change the number of red vs blue counters (e.g. with a slider) and watch which word best fits shift as the composition changes.
    3. Remove the blue counters one at a time and predict, then say, which word changes and why ('likely' sliding toward 'certain' as blue is removed).
    4. Always voice the word yourself rather than only reading the suggested-word zone.

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