Using Spinners Probability

Overview

This is lesson 7 of 10 in the "Understanding Probability Concepts" unit, designed for Year 6 students in New Zealand. Students will explore probability using spinners to calculate the likelihood of various outcomes expressed as fractions. The lesson is 45 minutes long, designed for a class of 30 students, carefully aligning with the New Zealand Curriculum (mathematics and statistics for Year 6). Activities are structured to accommodate diverse learners, with dyslexia-friendly materials and opportunities for extension.

Learning Objectives (WALT)

We Are Learning To calculate probabilities using spinners in chance-based investigations.
We will use fractions to represent the likelihood of different outcomes.
We will explore and record equally likely and not equally likely outcomes.
We will compare theoretical probabilities with outcomes from practical experiments.

Aligned with NZ Curriculum Mathematics and Statistics Achievement Objectives:

Investigate chance by posing questions, anticipating outcomes, conducting experiments, recording outcomes, and calculating probabilities as fractions.
Represent probability outcomes using lists, tables, and visualisations, connecting theoretical and experimental probabilities.
Engage in chance-based investigations with equally and not equally likely outcomes.

Success Criteria

Can calculate fractions representing the chance of various spinner outcomes.
Can record and visualise spinner results using tables or tally charts.
Can compare and discuss results of theoretical probability and experimental outcomes.
Can explain their reasoning about equal and unequal probabilities using the correct vocabulary.

Resources

Physical spinners divided into coloured sections (preferably three types):
Spinner with fewer sections (e.g. 2-3 sections) for learners who need simplification.
Spinner with equal sections (e.g. 4-6 sections) for the main activity.
Blank/spinner template for designing custom spinners (extension).
Colour-coded spinner printouts and digital spinner tools.
Fraction strips or fraction cards.
Whiteboard and markers.
Recording sheets for tallying results.
Projector or interactive whiteboard for modelling.

Lesson Structure (45 minutes)

1. Introduction & Recap (5 mins)

Recap previous lessons on understanding probability, focusing on the vocabulary (impossible, unlikely, equally likely, likely, certain).
Briefly explain what a spinner is and how it relates to probability through examples.
Show a spinner divided into equal sections and ask: "What are the chances of landing on each colour?"
Use fraction language related to total sections.

2. Demonstration (5 mins)

Display a spinner with 4 equal sections (coloured differently).
Spin it a few times and record outcomes on the whiteboard.
Write the fraction representing the theoretical probability of landing on each colour (e.g. 1/4).
Show the experimental fraction from recorded spins (e.g. 3 out of 12).
Highlight the difference and discuss why experimental results might differ from theoretical.

3. Main Activity: Spinner Investigations (20 mins)

Differentiation:
Struggling learners: Use spinners with fewer sections (2 or 3 sections), and provide colour-coded spinner diagrams.
Main group: Use 4-6 section spinners.
Advanced learners (Extension): Design their own spinner with unequal sections; calculate theoretical probabilities.
Process:
Students work in pairs or small groups.
Each group has a spinner and a recording sheet.
Spin 20 times, tally results, and calculate experimental probability as fractions.
Predict outcomes before spinning and compare predictions with results.
Record theoretical probabilities for each section.
Use colour-coded spinner printouts and ensure clarity for dyslexic learners, e.g., using consistent colours and large fonts.

4. Class Discussion & Reflection (10 mins)

Gather students and invite groups to share their results.
Discuss:
Did the results match the theoretical probabilities? Why or why not?
Which outcomes were more or less likely and how can we tell?
How does changing the number of sections affect probabilities?
Reinforce the success criteria: calculating fractions and using probability vocabulary.

5. Extension (for early finishers or homework)

Challenge students to design their own spinner with unequal-sized sections.
Calculate the probability for each section as a fraction.
Present their spinner and reasoning to the class next lesson.

Differentiation Strategies

Learner Group	Strategy
Struggling learners	Spinners with fewer sections; use visual and tactile aids; colour-coded sections for clarity.
On-track learners	Standard spinners; calculating and recording probabilities normally.
Advanced learners	Design customised spinners with unequal sections; calculate theoretical probabilities for each segment; explain reasoning in groups.
Dyslexic learners	Provide colour-coded spinner diagrams, use large clear fonts, and oral explanations; pair with supportive peer.

Literacy and Numeracy Integration

Use mathematical language explicitly: "probability," "fraction," "equally likely," "outcome," "theoretical," "experimental."
Visual supports with colour coding help students decode information easily.
Encourage students to express findings in complete sentences orally and in writing, e.g., “The probability of landing on red is 1/4.”

Assessment Opportunities

Observe students calculating fractions for outcomes during activity.
Check students’ recording sheets for correct fraction calculations.
Question students during discussions about why experimental and theoretical probabilities might differ.
Extension presentations provide evidence of higher-order thinking and application.

Alignment to New Zealand Curriculum

Achievement Objective Level 2 – Number and Algebra:

Use proportional reasoning to find probabilities of simple events described using fractions and decimals.

Achievement Objective Level 2 – Statistics and Probability:

Investigate chance by identifying and describing possible outcomes, conducting chance-based investigations, representing outcomes with appropriate recording methods, and describing probabilities using fraction language.

Key Competencies:

Thinking: Students engage critically with probability experiments and conjectures.
Using Language, Symbols, and Text: Mathematical vocabulary and fraction notation are used effectively.
Participating and Contributing: Collaborative exploration in pairs and groups encourages social interaction and shared learning.

These alignments reflect the teaching considerations and goals for Year 6 probability investigations in the Mathematics and Statistics section of the NZ Curriculum / Te Mātaiaho.

This lesson thoughtfully integrates theory and practice, includes hands-on materials and visual supports consistent with dyslexia-friendly approaches, offers layered differentiation to meet diverse student needs, and emphasises the critical thinking inherent in comparing theoretical and experimental probabilities—all firmly anchored in the New Zealand Curriculum, thus enabling teachers to confidently teach probability concepts using spinners.

Teaching Instructions