Height Data Investigation

Overview

Students begin a practical multivariate statistical investigation using the first three stages of the PPDAC cycle: Problem, Plan and Data. They develop a fair measurement protocol, collect paired categorical and numerical data, and consider how data quality and ethical decisions affect later conclusions.

Learning intentions

• WALT formulate a statistical question involving a categorical variable and a numerical variable.
• WALT plan and carry out a consistent, fair data-collection process.
• WALT record multivariate data accurately and identify possible sources of bias.
• WALT explain why a carefully designed plan is essential before collecting data.

Success criteria

• I can state the investigation question and identify both variables.
• I can agree on clear, consistent rules for measuring height.
• I can record data using an appropriate unit and sensible precision.
• I can identify at least one possible source of bias, error or ethical concern.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking and challenge for advanced learners.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting statistical thinking with relevant mathematical content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: extending learners through an authentic investigation requiring reasoning, planning and evaluation.
• New Zealand Curriculum Refresh: statistical investigations, mathematical communication, critical thinking and responsible participation in data-informed decisions.

Lesson structure (60 minutes)

1. 0–7 min · Hook and context. Teacher displays the question, “Is there a difference between the typical heights of two groups in our class?” using the investigation hook slide, and explains that the class will collect evidence rather than make assumptions. Students complete a think-pair-share: what data would be needed, and what could make the comparison unfair?

2. 7–15 min · Problem stage. Teacher introduces the PPDAC cycle and uses the PPDAC overview and variables slides to model that height is numerical and the grouping variable is categorical. Discuss respectful data collection: students may record a self-described gender category, use an agreed alternative grouping variable, or choose not to disclose; no student is required to share personal information. Students write or select a clear investigation question on the multivariate PPDAC investigation worksheet and identify the population, observational units and variables.

3. 15–25 min · Plan stage. Teacher distributes the Statistical Investigation Planning Frame and facilitates agreement on a shared measurement protocol. Record the class decisions on the board: measure in centimetres, to the nearest 0.5 cm; remove shoes; stand upright with heels together and eyes facing forward; use the same measuring tool and measurer where possible. Students complete the planning frame, considering population, sample, variables, sample size, materials, privacy and possible confounding variables.

4. 25–32 min · Check the plan. Teacher presents two scenarios from the fair-test scenario slides: one student measures in shoes and another without, and one student records inches while others record centimetres. Students identify the problem, predict its effect on the data and suggest a control. Teacher checks that groups have a workable protocol before measurement begins.

5. 32–47 min · Data stage: measurement. Teacher organises students in pairs, provides measuring tools and monitors the agreed protocol. Students measure themselves or a partner, record the agreed category and height on the measurement recording table, and then transfer their result to the teacher’s anonymous master data table. Students who do not wish to be measured or disclose a category may use a prepared anonymous value or assist as a recorder; do not publish names alongside data.

6. 47–55 min · Data quality review. Teacher displays the class data using the data-check and discussion slides and asks students to look for missing values, inconsistent units, unusual precision or possible recording errors without guessing who supplied any value. Students independently check their own entry, then discuss: Is this a census of our class or a sample? What limitations will affect any conclusion? The class agrees on corrections, documenting changes transparently.

7. 55–60 min · Plenary and exit response. Teacher returns to the original question and uses the plenary prompt slide to connect the completed Problem, Plan and Data stages to the next lesson’s displays and analysis. Students complete the final questions on the reflection and exit questions: “Why must the plan come before data collection?” and “Name one limitation or source of bias in this investigation.”

Resources

• the PPDAC investigation slide deck
• the multivariate PPDAC investigation worksheet
• the Statistical Investigation Planning Frame
• Tape measures or height measures
• Rulers or a flat object for marking height
• Class master data table or spreadsheet
• Board and markers
• Calculators or spreadsheet software for the next lesson
• Privacy-safe recording system using codes rather than names

Assessment

• Listen during the hook and planning discussion for accurate identification of categorical and numerical variables.
• Check planning frames for a consistent protocol, suitable units, recognition of bias and consideration of privacy.
• Review measurement records and exit responses for accurate data entry and an explanation of why planning improves validity. Retain the anonymised master dataset for the next lesson’s dot plots, box plots, medians and IQR comparisons.

Differentiation

• Support learners with a completed example, a word bank on the worksheet, oral rehearsal and sentence starters such as “The numerical variable is…” and “This could cause bias because…”.
• Offer dyslexia-friendly copies: clear sans-serif font, large spacing, uncluttered tables, short numbered instructions and the option to hear instructions read aloud. Pair students strategically and allow speech-to-text or scribing.
• Reduce cognitive load by assigning roles—measurer, recorder, protocol checker and data-entry checker—and provide a partially completed planning frame where needed.
• Extend advanced learners by asking them to compare a census with a sample, propose a more representative sampling method, identify confounding variables, or redesign the investigation question to avoid an inappropriate binary grouping.