Calculating Probabilities

Lesson Overview

WALT: Calculate probability of outcomes.

Success Criteria:

• Solve probability problems accurately.
• Calculate probabilities as fractions of total possible outcomes.
• Represent probability problems visually and numerically.

Class: Year 6 Duration: 45 minutes Class size: 30 students Unit: Understanding Probability Concepts (Lesson 6 of 10)

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Curriculum Links

This lesson aligns with the New Zealand Curriculum (Te Mātaiaho Mathematics and Statistics Years 0–8, Phase 2) expectations for Year 6 students, particularly in the Probability strand:

• Engage in chance-based investigations with equally likely outcomes by:
• Posing investigative questions
• Identifying possible outcomes
• Generating all possible outcomes theoretically or through experiments
• Creating data visualisations
• Using fractions to find probabilities
• Answering investigative questions and reflecting on outcomes
• Supporting representation of probability outcomes using lists, tables, tally charts, visualisations, words, and numbers
• Connecting anticipated outcomes with theoretical and experimental distributions
• Using critical thinking to agree or disagree with others' statements about chance-based investigations, referring to evidence (Te Mātaiaho Years 0–8, October 2024).

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Learning Objectives

By the end of this lesson, students will:

• Calculate the probability of rolling specific numbers on a six-sided die.
• Understand probability as a fraction of the number of favourable outcomes over total outcomes.
• Solve basic to advanced probability problems involving dice.
• Create their own probability questions and solve them.

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Key Vocabulary

• Probability
• Outcome
• Event
• Sample space
• Fraction
• Certain, likely, unlikely, impossible

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Materials Needed

• Six-sided dice (at least one per student or pair)
• Whiteboard and markers
• Probability recording sheets (with tables and tally charts)
• Visual aids showing dice faces
• Digital calculator or app for experimental trials (optional)
• Dyslexia-friendly printed handouts with step-by-step calculation instructions in bullet points

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Lesson Structure

1. Introduction (5 minutes)

• Engage: Pose a simple question - "What is the chance of rolling a 3 on a six-sided die?"
• Discuss: Recall prior knowledge of chance words (impossible, unlikely, likely, certain).
• Explain: Introduce 'We Are Learning To' (WALT): Calculate probability of outcomes.
• Show the sample space on a dice: {1, 2, 3, 4, 5, 6}

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2. Modelling & Guided Practice (10 minutes)

• Visual demonstration: Roll a die several times, record outcomes on board.
• List possible outcomes: 6 numbers on the die.
• Calculate theoretical probability:
• Probability of rolling a 3 = Number of favourable outcomes (1) / Total outcomes (6) = 1/6
• Dyslexia-friendly bullet points for calculation steps:
• Step 1: Count all possible outcomes on the die (6).
• Step 2: Identify the outcome you are interested in (e.g., 3 is 1 outcome).
• Step 3: Write the probability as a fraction: favourable outcomes / total outcomes.
• Repeat for other numbers or events like rolling an even number.

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3. Student Activity – Calculating Probability (15 minutes)

• Task: In pairs, students roll dice 30 times each, record outcomes in a tally chart.
• Calculate experimental probabilities: For example, how often did a 4 appear? Calculate relative frequency and compare with theoretical 1/6.
• Basic problems: Calculate probability of rolling a specific number.
• Advanced problems: Calculate probability of rolling an even number or a number greater than 4.
• Provide differentiated worksheets:
• Basic: Single outcome probabilities (e.g., rolling a 2).
• Advanced: Combined outcomes (e.g., rolling a 2 or 5).

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4. Extension Activity (10 minutes)

• Students create their own probability questions based on dice rolls or other chance-based situations they invent.
• Challenge peers to solve these questions.
• Encourage use of fractions and clear explanation of steps.

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5. Reflection and Wrap-Up (5 minutes)

• Discuss and compare experimental and theoretical probabilities.
• Ask students: Were the experimental results close to what you expected? Why or why not?
• Recap success criteria and have a few students share their problem solutions.
• Reinforce the connection between listing outcomes, calculating fractions, and understanding chance.

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Differentiation

• Support for diverse learners:

• Dyslexia-friendly handouts with bullet-point steps for calculations and clear fonts.

• Visual supports with dice faces and number lines.

• Peer support and group discussion.

• Extension for advanced learners:

• Problems involving two dice and finding combined probabilities.

• Creating more complex probability scenarios.

• Use simple probability models for events that are not equally likely.

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Assessment Opportunities

• Observation during paired activities (collaboration and problem-solving approach).
• Review of completed probability recording sheets for accuracy.
• Student-created probability questions and explanations demonstrate understanding.
• Informal questioning during wrap-up discussion to gauge conceptual clarity.

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Teaching Tips

• Encourage the use of familiar language before introducing formal probability terminology.
• Emphasise hands-on experience with dice to make abstract concepts tangible.
• Use digital tools if available to run larger simulations for more accurate experimental probability estimation.
• Highlight real-life applications of probability to maintain engagement.

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This plan closely adheres to the New Zealand Curriculum's teaching for Probability at Year 6, focusing on key competencies such as thinking critically, reasoning with data, and using mathematical language appropriately.

Should you wish for additional lesson plans or further unit support, feel free to ask!