Probability on a Scale from 0 to 1

Learning goal

Students place impossible, unlikely, even-chance, likely and certain events on a numerical scale and convert among equivalent probability forms.

Success criteria

• I can represent or identify the concept.
• I can explain the underlying relationship.
• I can select an appropriate strategy or feature.
• I can apply it in a new context.
• I can justify and verify the response.

Teaching routine

1. Represent
2. Reason
3. Calculate
4. Interpret
5. Verify

Locate probability values on one scale

Use the visual model first. Ask students to identify the quantities, structure or conditions before calculating or explaining.

Connect fractions, decimals and percentages

Connect the central relationship to a new context, then verify the conclusion with a second representation, estimate, inverse operation or reasonableness check.

AC9M6P01: recognise that probabilities lie on numerical scales of 0 - 1 or 0% - 100% and use estimation to assign probabilities that events occur in a given context, using common fractions, percentages and decimals

• E1: recognising that the probability of an event occurring can be represented numerically as either a number ranging from zero to one or a percentage from 0% to 100% where zero or 0% means it won’t happen and one or 100% means it is certain to happen
• E2: using a scale of zero to one or 0% to 100% to estimate chances of events
• E3: listing the different possible outcomes for rolling a dice and using a scale to locate the relative probability by considering the chance of more or less than for each possible event; for example, the probability of getting a number greater than 4
• E4: recognising the language used to describe situations involving uncertainty, such as what it means to be lucky, a 75% chance of rain or a 1-in-100 years flood
• E5: exploring how probabilities are used in artificial intelligence for machine learning and decision-making; for example, when choosing a video on a streaming service or travelling in a self-driving autonomous car, where artificial intelligence algorithms estimate the probability of a pedestrian crossing the road, which helps the autonomous car make decisions about when to stop or slow down
• E6: exploring First Nations Australian children’s instructive games, such as Weme from the Warlpiri Peoples of Central Australia, to investigate and assign probabilities that events will occur, indicating their estimated likelihood

Use the central and application models above to connect each elaboration to the same underlying concept.

Check understanding

• Place 0.35 on scale.
• Convert 3/5.
• Compare 45% and 0.5.
• Name impossible/certain.
• Explain likelihood not guarantee.

Evidence of mastery

• Represent or identify the concept
• Explain the underlying relationship
• Select an appropriate strategy or feature
• Apply it in a new context
• Justify and verify the response

Decision: continue when students can explain the model, apply it to a new example and justify their check. Otherwise return to the central model and reduce the numerical or representational load.

Australian Curriculum v9.0

AC9M6P01: recognise that probabilities lie on numerical scales from 0 to 1 and use fractions, decimals and percentages to compare the likelihood of events

The Australian Curriculum code and wording are exact. International teachers can use the underlying mathematical concept while matching the lesson to their local grade or year outcomes.

• Australian Curriculum Version 9.0
• NSW Curriculum
• Victorian Curriculum F–10