Introduction to Probability

Overview

In this lesson you will introduce probability language, identify the sample space for single-stage events, and start assigning probabilities to outcomes using simple games. This builds from earlier work on data and chance to support later predictions and simulations in the unit.

Learning intentions

• Students will understand the meaning of probability terminology such as “sample space”, “trial”, “event”, “outcome”, and “favourable outcome”.
• Students will identify the sample space for single-stage chance events (coin, dice, spinner).
• Students will assign probabilities to outcomes (as fractions and/or simple percentages) and link probability to expected relative frequency.
• Students will explain probability ideas using complete sentences and correct vocabulary.

Success criteria

• I can define probability in my own words.
• I can list all outcomes in the sample space for a single-stage event.
• I can assign a probability to at least one outcome and justify it using fair-event reasoning.
• I can use correct terms (trial, outcome, event, sample space, favourable outcome).

Curriculum links

• Probability: identify the sample space for single-stage events; assign probabilities to outcomes; predict relative frequencies for related events.
• Probability: discuss probability terminology and meaning of key terms (AC9M7P01_E1).
• Data displays are not the focus today; this lesson sets up later simulations and comparisons.

Lesson structure (60 minutes)

1. 0–5 min · Hook (conversation). Teacher shows three quick scenarios: “flip a coin”, “roll a dice”, “spin a spinner”, and asks: “What outcomes are possible in each? Which ones feel more likely and why?” Students share quick thoughts in pairs.
2. 5–15 min · Direct teach (terminology + model). Teacher introduces WALT language and key terms using an anchor chart:

• trial/experiment (what we do once)
• outcome (what happens)
• sample space (set of all outcomes)
• event (a group of outcomes)
• favourable outcome (outcomes that match the event) Teacher models one example: rolling a fair dice, sample space {1,2,3,4,5,6}. Students copy a clean example into books.
• Success check: students give a one-sentence “probability means…” definition to the class.

3. 15–28 min · Guided game: Coin or Dice. Teacher runs a class “fairness check” with volunteers:

• Students choose one: coin or dice.
• Teacher says: “We are doing single-stage events only—one trial.”
• Students list the sample space, then identify an event (e.g., “getting Heads”, “rolling an even number”, “rolling a 6”). Teacher prompts: “What is the favourable outcome(s)? What is the probability of the event?” Students work in groups, then one group shares their probability reasoning.
• Teacher emphasises: for fair events, probability = favourable outcomes / total outcomes.

4. 28–40 min · Partner task: Spinner sample spaces. Students complete a worksheet with a spinner divided into 4 equal sectors labelled A, B, C, D.

• Q1: List the sample space.
• Q2: Event examples: “landing on a vowel-like label” (teacher chooses labels so one sector counts, e.g., A and C), or “landing on B”.
• Q3: Assign probability as a fraction (e.g., 1/4) and then as a percentage (optional, if ready). Teacher circulates and uses questioning: “How do you know you listed every outcome?” “Which outcomes are favourable?”

5. 40–52 min · Checkpoint discussion: Probability vs predictions. Teacher connects probability to expected relative frequency without running full experiments yet:

• Prompt: “If P(rolling a 6) = 1/6, in 6 rolls what would you expect? In 60 rolls?” Students write brief predictions in words (“roughly”, “often”, “not guaranteed”) and share with a partner. Teacher clarifies the difference between expectation and actual results.
• Mini success criteria check: “Can you explain probability using at least one key term?”

6. 52–60 min · Exit ticket (individual). Students complete 3 short items:

• Item 1: For one dice roll, write the sample space.
• Item 2: Event “rolling an odd number”. Write favourable outcomes and probability.
• Item 3: Define probability in your own words (1–2 sentences).

Resources

• Dice (real or digital), coin, and a simple 4-sector spinner (physical or paper spinner)
• Worksheet: “Sample Spaces and Events” (coin/dice/spinner)
• Anchor chart template: Terminology + Example
• Student notebooks or printed writing space
• Sentence starters (printed): “The sample space is…”, “The event is…”, “Favourable outcomes are…”
• Timer for game rotations
• Dyslexia-friendly handout: one-page summary of terms + worked example (large font)
• Optional: small whiteboards and markers for quick sharing

Assessment

• Formative checks during guided game: teacher listens for correct terminology and complete sample spaces.
• Worksheet monitoring: students correctly identify favourable outcomes and compute probability as favourable/total.
• Exit ticket: assesses core outcomes—definition of probability, correct sample space listing, and correct probability for an event.

Differentiation

• Support (scaffolded steps): provide a dyslexia-friendly handout with key terms and one worked example; offer sentence starters and a word bank for outcomes/event/sample space.
• Support for decoding/writing: allow students to circle outcomes on a printed sample space grid rather than writing long lists; provide extra time for exit ticket.
• Extension (for fast finishers): include a challenge question such as “Spinner has sectors of different sizes—how would you change the probabilities?” (use qualitative reasoning only if no unequal-sector diagram is provided).
• Language supports: pre-teach vocabulary with gestures (sample space = “all possible boxes”), and allow oral responses before writing.
• EAL learners: encourage using partially completed frames on the worksheet (e.g., “P(event) = /”) and allow bilingual support for definitions if permitted by school routines.