Carnival sample diagrams

Overview

In this lesson, students create sample spaces and use tree diagrams to model single-stage and two-stage chance events in carnival-style games. Students connect outcome thinking to probability predictions and make sure their representations include all possibilities.

Learning intentions

• Students will represent all outcomes for single-stage events using lists and tables.
• Students will construct sample spaces and tree diagrams for two-stage events.
• Students will use tree diagrams to count outcomes and determine event probabilities.
• Students will justify whether two representations match the same chance situation.

Success criteria

• I can list or create a sample space that includes every possible outcome once.
• I can draw a correct tree diagram for a two-stage event and label branches clearly.
• I can use a tree diagram to count outcomes and find the probability of an event.
• I can explain how my sample space and tree diagram show the same set of outcomes.

Curriculum links

• Chance experiments and probability language (outcomes, events, likelihood)
• Representing possible outcomes using lists, tables, sample spaces, and tree diagrams
• Developing theoretical probability by using structured outcome models
• Using mathematical reasoning to describe and compare chance events

Lesson structure (45 minutes)

1. 0–5 Starter: “Spot the missing outcomes”

• Display a partially completed sample space for a simple single-stage spinner or coin outcome (e.g., {Red, Blue, Green} with one blank).
• Students quickly write what is missing and why each outcome must appear. Teacher checks misconceptions: “not repeating” and “not forgetting”.

2. 5–12 Mini-teach: sample spaces then tree diagrams

• Model: single-stage first (outcomes in a list/table), then move to two-stage (e.g., “first choose a colour, then choose a prize”).
• Emphasise structure: stage 1 branches on the first line; stage 2 branches from each stage 1 outcome; probabilities go on branches if known.
• Teacher makes a clear distinction between “all outcomes” and “event outcomes” (a subset).

3. 12–22 Guided practice (templates): single-stage to first branch

• In pairs, students use a provided scaffold sheet:
• Task A: create a sample space for a single-stage event (e.g., coin + one die or one carnival wheel).
• Task B: identify an event (e.g., “get a head” or “get a number greater than 4”) and list outcomes that belong to the event.
• Teacher circulates using quick checks: “Have you listed every outcome? Are any duplicated?”

4. 22–34 Guided practice: two-stage tree diagram

• Scenario: “Draw once from a colour bag, then draw once from a second bag” or “Choose a token from Stage 1, then a token from Stage 2” (use a clear, classroom-friendly setup).
• Students complete a two-stage tree diagram using the same templates:
• Step 1: write stage 1 outcomes.
• Step 2: for each stage 1 outcome, write stage 2 outcomes.
• Step 3: count terminal outcomes and determine probabilities for one given event.
• Teacher does one full example on the board, then students mirror it with their template.

5. 34–41 Check for understanding: “Tree vs sample space match”

• Students convert one completed tree diagram into a short list of ordered outcomes (e.g., Colour then Prize).
• Quick partner swap: Partner A reads the event definition; Partner B highlights which branches/terminal outcomes match it. Teacher observes accuracy and language use.

6. 41–45 Exit ticket

• Students answer: “For the carnival event shown, what is the sample space for the two-stage outcome?” and “What is the probability of the event ‘winning condition’?”
• Require one sentence justification: “I included/excluded outcomes because…”

Resources

• Scenario cards for single-stage and two-stage carnival chance events
• Pre-printed tree diagram templates (differentiated sizes with clear branch lines)
• Sample space grids and list-making worksheets
• Coloured counters or paper strips to model stage 1 and stage 2
• Dice/spinners/coin props (or digital equivalents with no internet required)
• Board/markers, projector (optional), student workbooks
• Exit ticket slips with two short questions
• Dyslexia-friendly reading options: simplified text cards with icons (coin icon, die icon, bag icon), and a “read-aloud” teacher script

Assessment

• Ongoing teacher observation of tree diagram structure and complete outcome listing.
• Guided practice product: accuracy of terminal outcomes and event subset selection.
• Exit ticket: correct probability calculation from counted outcomes and an explanation that links to the diagram.

Differentiation

• Guided practice with templates for students who need structure (pre-drawn branches, sentence starters for justifications).
• Support for working memory: students use “one stage at a time” prompts (write stage 1 first, then complete stage 2 for each branch).
• Dyslexia-friendly reading options: provide icon-supported scenario cards, allow teacher read-aloud, and offer extra time; reduce visual clutter on worksheets.
• Extension for students who finish early by asking them to create an alternative event definition and re-identify matching branches.

Extension (optional)

• Challenge: Students create their own challenging two-stage carnival probability scenario (choose/assume two stages with different outcome counts). They must:
• Draw the correct tree diagram,
• Provide a complete sample space of ordered outcomes,
• State one event (e.g., “win if you get A then B, or C then D”),
• Calculate the event probability and justify using their diagram.