Variability in Outcomes

Overview

In this lesson, students talk about variability using results from previous chance investigations. They compare outcomes from repeated trials and describe how results can differ while still following the same chance process.

Learning intentions

• Students will understand that variability means outcomes can be different each time.
• Students will compare results from repeated experiments and note patterns in how results spread out.
• Students will use simple language and representations (tables, pictures, tally marks) to explain differences in outcomes.

Success criteria

• I can explain that variability is why repeated trials can give different results.
• I can compare at least two sets of results and say what changed (more/less, more frequent/less frequent).
• I can describe how many outcomes occurred using numbers and appropriate representations.
• I can give a reason why differences happen even when the experiment is fair.

Curriculum links

• Probability and chance concepts: describe likelihoods and recognise outcomes can vary across repeated trials.
• Data skills: collect, organise, and interpret data from investigations.
• Mathematical communication: explain thinking using words, numbers, and simple displays.

Lesson structure (45 minutes)

1. 5 min – Start-up discussion Display a familiar example (e.g., “roll a die 10 times”). Ask: “If we did it again tomorrow, would we get exactly the same rolls?” Students think-pair-share and share one idea about why not.

2. 10 min – Share findings from last experiments In small groups, students use their experiment notes (e.g., tally marks, simple tables, pictures of outcomes). Each group chooses one question they answered last lesson (such as “Which outcome happened most?” or “How many times did each outcome occur?”). Teacher circulates, prompting: “What was different from your expected results?” and “Did you all get the same results?”

3. 10 min – Class comparison: variability spread Create a shared class data display (could be on chart paper or board) using one outcome type from their experiments. Students contribute their counts and the teacher sums them. Focus prompts:

• “Which result is most common in our class data?”
• “Which result is least common?”
• “Are the counts similar or quite different?” Emphasise that differences between groups show variability.

4. 8 min – Explicit teaching: variability vs. randomness Teach a clear definition in student-friendly language: “Variability means outcomes change from trial to trial.” Use a simple sentence frame:

• “Our results varied because…”
• “We noticed that sometimes…” Discuss that chance experiments are not “wrong” when results differ; the spread is expected.

5. 7 min – Guided activity: “Spot the variability” Provide two short, teacher-prepared result sets (as simple tally/table summaries) from repeated trials. Students work in pairs to decide:

• Do the two sets look different?
• How are they different (more of one outcome, less of another, totals by category)?
• What does that tell us about variability? Teacher uses targeted questioning and checks for correct use of terms like “sometimes”, “varied”, “more/less often”.

6. 5 min – Whole-class debrief and exit ticket Each student completes an exit ticket prompt verbally or in writing: “In our experiment, variability means…” plus one example from their own results. Collect quickly for formative assessment.

Resources

• Student experiment notes from lesson 4 (tally sheets, simple tables, pictures)
• Class data chart (paper or board) and markers/colour pens
• Teacher-prepared “Spot the variability” result sets (two simple tables/tallies)
• Sentence starters for discussion and writing (“We noticed…”, “Our results varied because…”)
• Small sticky notes for adding counts to the class display
• Exit ticket slips or a half-page reflection sheet
• Timer for timed steps
• Optional: counters or dice/drawing cards for quick demonstrations

Assessment

• Formative: teacher listens during group sharing for correct understanding of variability and ability to describe differences using data.
• Formative: guided activity responses—students identify differences and explain what those differences mean.
• Exit ticket: checks that students can define variability and give an example from their results.

Differentiation

• Support: provide partially completed sentence frames and a worked example of comparing two simple result sets; offer a “choose from words” bank (more often, less often, sometimes, different).
• Support: allow students to use pictorial representations (e.g., tally marks or drawn symbols) instead of writing full sentences.
• Extension: ask students to predict what might happen if they did more trials and to justify using variability (“With more trials, we might see… but it could still vary”).
• EAL/SEN: use consistent language and visuals for “variability” and “most/least common”; rehearse discussion prompts before group work; pair with a supportive peer.