Lesson Q2 L1 – Measuring Plant Height: Protocol, Calibration, and Measurement Error

Lesson Overview

Quarter 2 · Unit D: Measuring Growth and Probability · Week 10 · AP Statistics (Grades 10–12) · Lesson length: 50 minutes

Essential Question: How do we make measurements that are precise, accurate, and comparable from week to week?

Lesson Focus: Weekly height is our second dependent variable; a consistent protocol matters more than any single measurement.

Why It Matters: A statistic is only as good as the measurement behind it. Consistent protocols keep weekly heights comparable, and recognizing systematic versus random measurement error is part of judging a study (Topics 1.2 and 1.7).

Source: Adapted from Seeds of Science, Lesson 10 “Quantitative Measurement” and the Chapter 3 sections on measuring height to the tip of the tallest leaf, the unfurl method, and partner calibration.

Standards & Learning Targets

Standards Alignment

AP Statistics CED (Fall 2026) — Topics & Learning Objectives: Topic 1.2 Variables (Unit 1: Exploring One-Variable Data and Collecting Data) — 1.2.A: Identify observational units, variables, parameters, and statistics from a statistical study or data set.; 1.2.B: Identify types of variables.; 1.2.C: Identify types of quantitative variables. • Topic 1.7 Summary Statistics for One Quantitative Variable (Unit 1: Exploring One-Variable Data and Collecting Data) — 1.7.A: Calculate measures of center and position for quantitative data.; 1.7.B: Calculate measures of variability for quantitative data.; 1.7.C: Calculate different units of measurement for summary statistics.; 1.7.D: Calculate outliers for quantitative data.; 1.7.E: Compare multiple quantitative one-variable summary statistics.; 1.7.F: Justify the selection of a summary statistic for describing quantitative data.

AP Statistics Practices / Skills: 2.A (Collect Data) — Identify information to answer a question or solve a problem; 3.B (Analyze Data) — Calculate summary statistics, relative positions of points within a distribution, and predicted responses

Student Learning Targets

Learning Targets — students will be able to

Measure plant height from the soil line to the tip of the tallest leaf using the unfurl method

Distinguish accuracy from precision and random from systematic error

Record weekly heights for every plant in a data table with plant IDs and units

Key Vocabulary

precision · accuracy · random error · systematic error · soil line · unfurl method · plant ID · significant figures · protocol

Materials & Teacher Prep

Lesson Flow & Timing

Phase 1 · Engage — The Hook

Teacher Talk

PCM: Curiosity. Sketch four dartboards on the board (accurate and precise; precise not accurate; accurate not precise; neither). “Which board matches a ruler that starts 3 mm from the end? Which matches measuring a different leaf each week?”

Ask Students

“What is the difference between accurate and precise?” “Where should the ruler start?” “What happens to our data if partners measure differently?”

PCM Differentiation

Thinker Students: Predict which kind of error, random or systematic, is more dangerous for comparing treatment and control, and why.

Harmonizer Students: Measuring with a partner builds trust in our data. How will you settle a disagreement about a measurement politely?

Phase 2 · Explore — Kagan Cooperative Activity

Cooperative Structure

Kagan structure: RallyCoach. One partner measures while the other coaches with the protocol card and records, then switch, so each plant is measured and checked by both (See the Teaching Reference for the structure’s steps.) Introduce soil line, plant ID, and protocol briefly now so the discussion stays precise; the formal definitions come in Explain.

Step-by-Step

• Step 1 — Protocol review (4 min): Ruler zero at the soil line, ruler vertical, eye level, unfurl drooping leaves, record to the nearest 0.1 cm.

• Step 2 — Treatment cell (8 min): Partner A measures each plant by ID; Partner B coaches and records.

• Step 3 — Control cell (8 min): Switch roles.

• Step 4 — Cross-check (2 min): Each partner remeasures three plants the other measured; differences greater than 0.3 cm trigger a remeasure.

Teacher Moves During Explore

Check that the ruler zero, not the ruler end, sits at the soil

Ask “Which leaf is tallest after unfurling?”

Insist on units and plant IDs in every row

Phase 3 · Explain — Direct Instruction

Mini-lesson — Types of Measurement Error. Teacher move: Use cross-check differences from the class as examples.

Accuracy: closeness to the true value; precision: closeness of repeated measurements to each other

Random error: unpredictable variation (leaf movement, eye angle) that averages out with more measurements

Systematic error: consistent bias in one direction (ruler offset, always pressing into soil); it does not average out and can create a false treatment difference if applied to one cell

Reducing error: same tools, same protocol, same measurer per cell or swapped evenly, repeated measurements

Reporting: record 0.1 cm precision with units; never round inconsistently between weeks

Key Message: Good data come from a consistent, written protocol. Random error is reduced by replication; systematic error must be prevented by design.

Check for Understanding — Ask Students

“Give an example of systematic error in our garden.” “How does replication help with random error?” “Why do we unfurl drooping leaves?”

Phase 4 · Elaborate — Student Product & Differentiation

Student Product

Each pair submits a complete height table for both cells with cross-check results.

Differentiation

Support (scaffolded entry): Provide a protocol card with photos for each step.

AP Extension: Calculate the mean absolute difference between partners for cross-checked plants and propose a tolerance rule for the class.

Multilingual Learners: Pair the protocol with gestures (zero, straight, eye level, unfurl) and model with think-aloud.

Phase 5 · Evaluate — Closure, Exit Ticket & Assessment

Exit Ticket

1. Explain the difference between accuracy and precision.

1. Describe one systematic error you prevented today.

1. Record the tallest plant in each cell.

Answer Key / Look-Fors: Accuracy = near true; precision = repeatable. Systematic examples: ruler offset, measuring to a different leaf. Heights recorded with units.

AP Exam Practice

(MCQ) A student measures every treatment plant with a ruler whose zero mark is 0.5 cm from its end but measures every control plant with a ruler that begins at zero. Which statement is correct? (A) The error is random and will average out (B) The error is systematic and will make treatment plants appear 0.5 cm shorter (C) The error is systematic and will make treatment plants appear 0.5 cm taller (D) There is no error because both rulers are metric

Answer & Rationale: (B). Placing the ruler end at the soil puts the zero 0.5 cm above it, so every reading is 0.5 cm too short. The bias applies to one group only, so it confounds the comparison.

Expanding Circles

How does this connect to… Self — When have you measured something carefully at home? • Classroom — How will our class keep measurements consistent? • School — Who at school measures precisely (nurse, coach)? • Community — Why do Phoenix weather stations follow strict protocols? • World — Why do global datasets require standard methods?

Formative Assessment

Formative Assessment (group students using the complete height table with cross-check results, the exit-ticket accuracy-versus-precision answer, and the AP item)

Meets (3): Complete table, cross-check within 0.3 cm, correct error explanation.

Approaching (2): Table complete but cross-check not done or error types confused.

Not Yet (1): Missing IDs or units; reteach protocol in the garden.

Extend & Looking Ahead

Extension: Photograph a ruler against one plant each week to create a visual growth record.

Looking Ahead: Lesson 2.2 graphs our weekly growth with error bars.