Probability in Action

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Lesson Title

Project: Probability in Action

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Curriculum Context

• Australian Curriculum: Mathematics – Year 9
• Strand: Statistics and Probability
• Sub-strand: Chance
• Content Descriptions:
  • ACMSP225: List all outcomes for two-step chance experiments and assign probabilities for those outcomes.
  • ACMSP226: Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'.
  • ACMSP227: Use the language of ‘if’, ‘then’, ‘else’, ‘and’, ‘or’ to investigate conditional statements and identify common misconceptions in interpreting chance.

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Duration

45 minutes

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Learning Intentions

By the end of this lesson, students will be able to:

• Apply their understanding of probability to a real-world scenario.
• Collaborate in groups to plan and present a statistical investigation.
• Analyse and communicate results using appropriate probability terms and mathematical representations.
• Demonstrate their synthesis of knowledge gained across the unit “Probability in Action”.

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Success Criteria

Students will:
✔ Select a real-world scenario involving chance and justify its relevance.
✔ Design an investigation plan involving simulations, data collection or historical data analysis.
✔ Use probability notation and language appropriately in their analysis.
✔ Present their findings clearly using visual representations (e.g. diagrams, trees, tables) and spoken explanation.

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Resources Required

• Whiteboard and markers
• Student laptops or tablets
• A3 poster paper, coloured markers
• Dice, coins, decks of cards (for physical simulations)
• Printed student instruction sheet (Project Brief)
• Real-world data sources (e.g. AFL statistics, weather forecasts, Lotto results – pre-downloaded)

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Prior Learning Review

Students have:

• Explored theoretical, experimental and relative frequencies
• Performed simulations using coins, dice, and spreadsheets
• Analysed outcomes using probability trees and Venn diagrams
• Interpreted compound events and conditional probability

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Lesson Outline

🕒 0 – 5 min: Welcome and Hook

• Teacher welcomes students and explains that this final lesson is designed to bring together everything we've learnt in a practical way.
• Hook Question: “Have you ever wondered if your favourite sports team really wins 50% of the time – or if that’s just how it feels?”
• Introduce today’s aim: Use probability to investigate a real-world question and present your findings.

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🕒 5 – 10 min: Project Brief and Grouping

• Distribute the “Probability in Action: Project Brief” (printed sheet with assessment criteria, possible ideas and structure outline).
• Students form groups of 2-3.
• Teacher guides group formation to ensure balanced skill levels.

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🕒 10 – 25 min: Group Project Preparation

Students begin working on their chosen investigation from suggested prompts or personal ideas:

Suggested Prompts:

• What’s the probability of winning a certain Lotto game?
• Do AFL teams perform better at home than away?
• What is the likelihood of getting four heads in a row when flipping a coin? How often does it happen in practice?
• Is it really “luckier” to choose odd numbers on scratchies? Analyse winning data (fictional or pre-provided).
• Use conditional probability to determine: "If it’s cloudy, what’s the chance it will rain in Perth?"

Students must:

1. Write down their key question.
2. Decide whether to use theoretical, experimental or historical data (or a combination).
3. Sketch a plan using probability tools (Venn diagrams, trees, tables or simulations).

Teacher Role: Rotate between groups, prompting deep thinking:

• “How will you collect reliable data?”
• “Is this a single event or compound event?”
• “What assumptions are you making?”
• “How does your model reflect real-world behaviour?”

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🕒 25 – 40 min: Presentation and Sharing

Each group shares their problem and investigation in a 2-minute mini-presentation:

• Describe your key question
• Explain how you investigated it
• Share a key finding using a visual model or probability statement (e.g. “The probability of drawing two red cards is 1/4.”)

Optional Presentation Formats:

• A3 poster display
• Slide on shared screen (if access to device)
• Physical model (e.g. coin toss simulation live)

Teacher to encourage peer feedback – Asking questions like:

• “Is their method valid?”
• “Did they consider all outcomes?”
• “Could they improve their assumptions?”

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🕒 40 – 45 min: Reflection and Wrap-Up

• Whole class debrief: What did these investigations show us about how probability can explain or challenge our assumptions?

• Students fill out an Exit Ticket (written or verbal) with:

  • One thing they discovered
  • One question they still have about probability
  • One way they could apply this outside the classroom

• Teacher affirms learning journey over the term and hands out optional “Citizen of Probabilities” certificates to celebrate unit completion.

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Differentiation Strategies

• Support:

  • Provide structured templates for investigation design and visual organisation
  • Pair EAL/D or low-literacy learners with peers strong in verbal explanation
  • Provide simplified data sets or simulation tools

• Extension:

  • Invite students to compare theoretical vs. experimental outcomes
  • Incorporate more advanced scenarios like conditional probability or multiple-step experiments
  • Challenge students to critique each other’s assumptions using probability language

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Assessment Opportunities

• Formative Assessment:

  • Observation of group conversations
  • Analysis of students’ plan and strategy
  • Participation in peer questions and feedback

• Summative Assessment:

  • Project rubric included in the Project Brief (criteria: mathematical communication, strategy, interpretation, real-world connection)

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Student Voice Opportunities

• Student-chosen topics and investigations
• Opportunities to lead peer questioning in presentations
• Personal reflections on how probability applies to their interests and future choices

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Teacher Reflection

Following the lesson, consider:

• Which groups demonstrated strongest transfer of learning into real-world contexts?
• Were misconceptions about randomness or probability language still evident?
• How might these projects be expanded into cross-curricular links (e.g. with HASS or Science)?

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Notes for WOW Factor

• Print mini “Probability Champion” stickers for students who had particularly insightful analysis
• Use a rotating “Roaming Reporter” role next unit: the student who investigates how probability (or other Maths concepts) show up in the news
• Frame the lesson as the final step in becoming a “Probability Detective” — can they use chance and logic to solve real-world mysteries?

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Conclusion

This capstone lesson empowers Year 9 students to apply their probability knowledge within meaningful contexts, choosing problems that matter to them while developing critical thinking and collaboration. It adheres precisely to Australian Curriculum: Mathematics Year 9 achievement standards and provides an engaging, well-scaffolded end to the unit.