Overview

These two detailed 35-minute lessons introduce Year 5 students in New Zealand to the exciting world of probability, aligned with the New Zealand Curriculum Refresh for Mathematics and Statistics (Phase 2). The lessons engage students of varying abilities through hands-on activities, group and individual tasks, visual aids, and opportunities to explore both theoretical and experimental probability. The teaching approach incorporates clear learning intentions, use of fractions to express probabilities, critical thinking, and formative assessment to support student understanding.

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Curriculum Links

• Mathematics and Statistics – Number and Algebra / Statistics and Probability (Phase 2, Years 4–6)
• Achievement Objectives:
• Engage in chance-based investigations with equally and unequally likely outcomes (Year 5 focus)
• Pose investigative questions, identify and generate possible outcomes (theoretical and experimental)
• Collect, record, and create data visualisations for outcomes
• Express probabilities using fractions
• Reflect on findings and evaluate statements about chance-based situations
• Develop critical thinking by agreeing or disagreeing with statements about investigations

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Lesson 1: Investigating Chance

Learning Objectives

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

• Pose a simple investigative question involving chance (e.g., What is the probability of rolling an even number on a dice?).
• Identify and list all possible equally likely outcomes for the question.
• Conduct a probability experiment by using physical objects to collect data.
• Record outcomes using tally charts.
• Express the probability of selected outcomes as fractions.
• Begin to use vocabulary describing chance (impossible, unlikely, possible, likely, certain).
• Work collaboratively to discuss findings.

Resources

• Large dice, coins, and spinners
• Tally charts and recording sheets
• Fraction strips or visual fraction cards
• Probability vocabulary flashcards
• Whiteboard and markers

Lesson Outline

1. Warm-Up and Introduction (5 minutes)

• Begin with a whole-class discussion asking: "Have you ever played a game where chance mattered? What might happen if you roll a dice?"
• Introduce the investigative question: "What is the chance of rolling an even number on a dice?"
• Briefly discuss what “chance” means, introducing vocabulary words.

2. Exploring Possible Outcomes (7 minutes)

• Students work in pairs to list all possible outcomes when rolling a dice (1,2,3,4,5,6).
• Discuss how all outcomes are equally likely.
• Visual aid: Use a large drawn number line or poster showing the sample space.

3. Conducting an Experiment (10 minutes)

• In groups of 4-5, students roll dice 30 times, recording each result on tally charts.
• Teacher circulates to scaffold recording and encourage accuracy.
• For students needing more support, facilitate smaller numbers of trials, or provide pre-prepared tally charts with some data filled.

4. Expressing Probability with Fractions (8 minutes)

• After collecting data, students count how many times an even number came up.
• Introduce fraction notation: "Number of even rolls / total rolls" (e.g., 12/30). Use fraction strips to visualise this.
• Discuss what the fraction tells us about the chance, connecting to terms like “likely” or “unlikely.”
• Challenge more able students to predict what might happen if rolls increase to 100.

5. Reflection and Sharing (5 minutes)

• Groups share their findings. Teacher writes several example probabilities on the whiteboard.
• Wrap up with questions: “Was the chance of rolling an even number close to what you expected? Why or why not?”
• Set a reflective task: Write one sentence explaining what you learned about chance today.

Differentiation

• Provide sentence starters for reflections for students who need support.
• Extend higher-ability students by asking them to think about removing one number and how that changes probabilities.
• Use manipulatives for all students to support conceptual understanding.

Formative Assessment

• Check students' tally charts and ability to express outcomes as fractions.
• Listen to group discussions for use of probability vocabulary.
• Collect reflective sentences to assess understanding.

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Lesson 2: Theoretical vs Experimental Probability

Learning Objectives

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

• Understand and explain theoretical probability from equally likely outcomes.
• Compare theoretical probabilities with experimental results.
• Create simple visual representations (tables/graphs) of results.
• Use critical thinking to evaluate statements about chance-based situations.
• Express probabilities as fractions and discuss differences between expected and actual outcomes.

Resources

• Dice, coins, spinners (if needed from Lesson 1)
• Pre-prepared probability tables and blank tables for recording
• Graph paper or digital tools (if available) for simple bar graphs
• Example statements about probability for critical thinking task

Lesson Outline

1. Recap and Introduction (5 minutes)

• Review key ideas and findings from previous lesson.
• Introduce the idea of theoretical probability: For a dice, 6 possible outcomes; 3 are even numbers, so probability of even number = 3/6 = 1/2.

2. Generating Outcomes Theoretically (7 minutes)

• Together as a class, fill a table on the board listing all outcomes for rolling a dice or spinning a spinner.
• Students complete a similar table individually or in pairs for a coin toss (Heads or Tails).

3. Experiment and Record (10 minutes)

• Conduct a new set of trials in groups (e.g., coin toss 40 times).
• Record results in tables and create simple bar graphs to show frequency of Heads and Tails.
• Encourage students to note differences from the expected theoretical outcome (1/2 Heads, 1/2 Tails).

4. Comparing and Critical Thinking (8 minutes)

• As a class, compare theoretical probability fractions with experimental results.
• Present simple statements about chance (e.g., “It is impossible to get Heads twice in a row,” “You are likely to get Tails.”).
• Students work in pairs to agree or disagree with these statements, justifying with their data.
• Discuss why experimental results may differ from theoretical probabilities (chance, variation, number of trials).

5. Reflection and Closure (5 minutes)

• Facilitate a discussion: What did you learn about chance today? How can experiments and theory be different?
• Students write or share one new thing they learned about probability.

Differentiation

• Provide scaffolded sentence frames for evaluation tasks.
• Offer more challenging questions to advanced learners (e.g., What if the coin is weighted?).
• Use manipulatives and visual aids extensively to support different learning styles.

Formative Assessment

• Observe students' ability to relate theoretical probability to experimental data.
• Assess reasoning in agree/disagree task with probability statements.
• Review reflections for depth of understanding.

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Notes for Teachers

• Embed mathematical language throughout: probability, outcomes, sample space, experimental, theoretical, fraction, unlikely, likely.
• Encourage collaboration and discussion to develop critical thinking.
• Use manipulatives and visual aids to make abstract probability concrete.
• Adjust the number of trials to accommodate class time and student stamina.
• Digital tools can be employed if available for conducting many trials or graphing results.
• Reflective tasks support metacognition and help identify misconceptions early.

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This detailed two-lesson plan for Year 5 students ensures engagement with key probability concepts through active learning, formative assessment, and alignment with the New Zealand Curriculum Refresh recommendations for chance-based investigations using fractions and critical thinking about outcomes. It supports diverse learners and empowers teachers to create a dynamic, inquiry-based learning environment.