Building Statistical Questions

Overview

In this lesson (19 of 30), students begin a statistical investigation by forming a clear question, choosing appropriate variables, and planning a simple data collection method. This supports later work on analysing distributions using summary statistics and shape.

Learning intentions

Students will:

• formulate a statistical investigation question that can be answered using data
• identify whether the variable is discrete or continuous (and justify their choice)
• plan a practical method for collecting data fairly
• anticipate what summary measures (range, median, mean, mode) might help describe the data

Success criteria

Students can:

• write an investigation question with a clear context and population
• name the variable(s) and state whether they are discrete or continuous
• describe a feasible collection plan (how, where, who, and how often)
• explain how they will summarise the results (e.g., range/median/mean/mode) and comment on distribution shape later

Curriculum links

• AC9M7ST03: plan and conduct statistical investigations; analyse and interpret distributions of data and report findings in terms of shape and summary statistics
• AC9M7ST01: acquire data sets for discrete and continuous numerical variables and calculate range, median, mean and mode; justify which measures suit the distribution
• AC9M7ST02: create numerical data displays (e.g., stem-and-leaf) and describe distribution features such as centre, spread, outliers and shape (preparing for this next lessons)
• Mathematical proficiency: use reasoning to make decisions about measures; use representation to plan data handling

Lesson structure (60 minutes)

1. 0–5 min · Starter conversation (Hook). Teacher shows two example questions on the board (one vague, one specific) and asks: “Which one would you be able to investigate with real data, and why?” Students pair-share quick thoughts.

2. 5–15 min · Mini-lesson: What makes a good investigation question? Teacher models a “good question checklist”: clear population, clear variable, measurable method, and answerable with data; then links discrete vs continuous with quick examples (e.g., number of steps vs height). Students respond to 2 teacher prompts using thumbs up/down and short verbal justification.

3. 15–25 min · Guided brainstorming (Differentiated groups). Teacher assigns students to mixed-ability groups and provides 3 context options (e.g., reaction time proxy using paper-drop trials; favourite snack ratings with a numeric scale; time spent reading at home in minutes). Students complete a “Question Builder” sheet: choose context → decide variable → draft an investigation question.

4. 25–35 min · Turn questions into collection plans. Teacher demonstrates how to choose a fair collection method (sample size, repeated measurements when relevant, consistent units, avoiding bias). Students update their draft to include: who they will collect from, how many data points, and how they’ll record the data.

5. 35–45 min · Variable sorting and justification. Teacher gives a set of candidate variables and students decide whether each is discrete or continuous, then write one sentence explaining why. Students then self-check their own investigation: underline their variable and add the discrete/continuous label.

6. 45–55 min · Gallery walk: feedback for clarity. Each group posts their question + plan. Students use sentence starters to give feedback: “Your question is clear because…” “I’m wondering about…”. Teacher circulates with prompts targeting clarity, feasibility, and variable choice.

7. 55–60 min · Exit ticket (Formative assessment). Individually, students submit: (1) final investigation question, (2) variable type (discrete/continuous), (3) one planned summary statistic they think will be useful (range/median/mean/mode) and one reason.

Resources

• “Question Builder” printable (one per student or shared per pair)
• Discrete vs continuous examples cards (teacher set)
• Gallery walk feedback slips with sentence starters
• Data collection plan template (simple table: who/how many/how often/units)
• Coloured pencils or highlighters (to mark variable and units)
• Projector/board with checklist and worked example
• Dyslexia-friendly font version of templates (or larger text print)
• Optional: digital timer for consistency discussion

Assessment

• Teacher observation during group drafting: identify students who need support to make questions answerable with data
• Variable sorting justification: checks understanding of discrete vs continuous
• Exit ticket (3 items): question clarity, variable type, and justification for a likely useful summary statistic

Differentiation

• Guided brainstorming (core support): provide a worked example of a “vague → improved” question for all groups; for students needing extra help, give a partially completed Question Builder (choose context and variable, students finish the wording).
• Sentence starters: “I will collect data about… from… to answer: …”; “My variable is continuous because I can measure it in …”
• Visuals: colour-code parts of the plan (context = green, variable = blue, units = yellow, method = pink).
• Dyslexia-friendly reading options:
• offer audio read-aloud of the prompt/checklist by teacher or student device
• provide large-print templates with short lines and ample spacing
• allow oral responses to be recorded by a partner before writing
• Extension (for early finishers): add a “fairness note” describing one source of bias and how they will reduce it (e.g., consistent measurement technique).

Exit criteria (what success looks like today)

By the end of the lesson, most students will have a data-collectable investigation question with a clearly identified numerical variable (discrete or continuous) and a feasible plan to gather enough data for later analysis of distribution shape and summary statistics.