Diagrams for Compound Events

Overview

In this lesson (Lesson 11 of 30), students build on earlier probability work by representing events using tables and diagrams. Students will focus on compound events, identifying the outcomes in an organised way and then representing them visually.

Learning intentions

WALT: Represent compound events using tables and diagrams.

Success criteria

Students can…

• create a correct table listing all outcome pairs for a compound event
• draw a clear diagram (e.g. grid/array) that matches the table outcomes
• describe the event using correct probability language (outcome, sample space, event)
• check that their diagram and table represent the same set of outcomes

Curriculum links

• Probability — identify sample spaces for single-stage events, assign probabilities, and predict relative frequencies (used as the foundation for organising outcomes for compound events)
• Probability — conduct repeated chance experiments and simulations to compare predictions with observed results (linked to later lessons when we test predictions)
• Mathematics — create numerical data displays and interpret distributions (linked to later probability simulations where results form distributions)

Lesson structure (60 minutes)

1. 0–5 min · Conversation hook. Teacher writes: “If you flip a coin and roll a dice, what are the possible results?” Students share quick ideas in pairs about how to list them.

2. 5–15 min · Direct teach: from listing to representation. Teacher models a compound event example: “Coin = Heads/Tails and Dice = 1–6.” On the board, teacher shows how to make:

• a table of outcomes (coin down the side, dice across, or vice versa)
• a grid/array diagram linking pairs (e.g. Heads with each dice number, and Tails with each dice number) Students copy the structure, not every detail, then complete a partially filled version as the teacher checks.

3. 15–25 min · Guided practice: one event together. Teacher poses: “Event A: You get Heads and a 4.” Students identify the favourable outcomes on the table/diagram (only one cell/outcome pair). Teacher then asks: “What would Event B be if it was ‘Tails or a 4’?” Students respond with suggested cells, and teacher clarifies how “or” changes which outcomes are selected (without yet calculating probability).

4. 25–45 min · Independent/pairs work: represent three compound events. Students work in pairs for peer assistance and dyslexia-friendly templates. Each pair completes:

• Table representation for Event 1 and Event 2
• Diagram representation for Event 2 and Event 3 Teacher circulates and asks students to explain how they know their representation is complete.

5. 45–55 min · Share and check. Pairs show their diagrams/tables on the board or on paper at stations. Teacher uses a checklist: “Are all outcomes included? Does the diagram match the table? Is the event selection clearly marked?”

6. 55–60 min · Exit ticket (quick). Students answer: “For the compound event ‘roll an even number and flip Heads’, list the outcomes in table form (or state the outcome pairs).” Collect to assess accuracy and completeness.

Resources

• Dice (one per group) and coin counters (or coin cards)
• Printed table and grid templates (with pre-drawn rows/columns)
• Coloured pencils or highlighters (to mark event outcomes)
• Example worked solutions (visible on board only, not on worksheets for guidance)
• Student “Probability words” mini-poster: outcome, event, sample space
• Timer for switching between tasks
• Exit ticket slips

Assessment

• Formative checks during guided practice: students can point to the correct outcome pair for a given event
• Teacher observation during paired work: representations are complete and consistent between table and diagram
• Exit ticket: correct outcome pairs for a compound event

Differentiation

• Pairing: intentionally mix abilities so students can explain reasoning and check accuracy together.
• Dyslexia-friendly reading options:
• Provide short verbal explanations before students read the task sheet.
• Offer an audio option of the instructions (teacher reads aloud; students follow with a finger on the page).
• Use larger font worksheets and high-contrast printing.
• Scaffolds:
• Provide partially filled templates with headings already labelled (e.g. Heads/Tails rows, dice 1–6 columns).
• Sentence starters: “My sample space includes…”, “The event includes… because…”
• Extension (for early finishers):
• Add a second event using the same compound setup, e.g. “Heads and an odd number”, and mark favourable outcomes in a different colour.

Success criteria for this lesson (repeat for students)

• I can list all outcome pairs in a table for a compound event.
• I can draw a grid/array diagram that matches the table.
• I can mark the favourable outcomes for a specified event clearly.
• I can explain how I know my representation is complete.