Whole Earth Curriculum WEC

Lesson 03 — Sources of Error in an Investigation

Learners measure the same thing five times and discover that careful measurements still differ a little. They learn to name the sources of that difference — tool limits, human reading, and conditions — and suggest how to reduce each, by repeating trials, averaging, and using finer, steadier methods.

D06 P3: Intellectual & Cognitive Awareness D06.S1 50 minutes Draft

Objectives

Essential question

Why do careful measurements still come out a little different — and how can we make them better?

errormeasurementprecisionrepeataverageaccuracyreaction timetrial

Materials

Standard materials

Low-tech / no-cost

Enriched / lab & device

Works in different contexts

A diagram of the same object measured five times. At the top, a pencil is shown with five rulers beneath it, each showing a slightly different reading: 12.1, 12.0, 12.2, 11.9, and 12.1 centimetres. Each reading is labeled trial 1 through trial 5. An average box reads 'average ≈ 12.1 cm.' Below, three small panels each name a source of error: 'tool limits — the ruler marks are coarse,' 'human reading — the eye sits at a slight angle,' and 'conditions — the object shifted.' A caption reads: careful measurements still differ a little; naming the source lets us reduce it. Labels and numbers, not color alone, carry the meaning so it prints clearly in grayscale.
A diagram of the same object measured five times. At the top, a pencil is shown with five rulers beneath it, each showing a slightly different reading: 12.1, 12.0, 12.2, 11.9, and 12.1 centimetres. Each reading is labeled trial 1 through trial 5. An average box reads 'average ≈ 12.1 cm.' Below, three small panels each name a source of error: 'tool limits — the ruler marks are coarse,' 'human reading — the eye sits at a slight angle,' and 'conditions — the object shifted.' A caption reads: careful measurements still differ a little; naming the source lets us reduce it. Labels and numbers, not color alone, carry the meaning so it prints clearly in grayscale.

Lesson 3 — Sources of Error in an Investigation

Summary

Learners measure the same object five times and find that their numbers are almost the same — but not exactly. They learn that error is not a mistake to hide but a feature of every real measurement, and they name its three usual sources — tool limits, human reading, and conditions — then suggest how to reduce each: repeat trials, average, and use finer, steadier methods.

Objectives

  • Identify sources of error in a simple investigation and suggest how to reduce them. (D06.S1.06.02)

Connection

A tailor cutting cloth, a pharmacist weighing medicine, a builder setting a wall, a runner timing a lap — every one of them measures, and every one of them knows their measurement is never perfect. The mark on the ruler is a little coarse, the eye sits at a slight angle, the thing being measured shifts. Good measuring is not pretending there is no error; it is knowing where the error comes from and shrinking it. Today you learn to see the difference in your own measurements and to name it.

Materials

  • A ruler or marked stick
  • A small object to measure (pencil, stick, or seed)
  • Error-hunt page

Preparation

  • Print the error-hunt page with five trial rows and an average row.
  • Prepare a ruler and a small object per pair.
  • Recall Lesson 1–2: data goes in tables and graphs; now we ask how trustworthy it is.

Facilitator note

Written to the learner (“you”). The distinction to land is error is a spread, not a mistake — careful measurements differ a little because of the tool, the reader, and the conditions, and that is normal and reducible. Model the worked example: measure one object at the front, read the value aloud, then point out why the next reading might differ (the mark falls between two lines). Three named sources: tool limits (coarse marks), human reading (angle of the eye, reaction time), and conditions (the object moved, wind, light). Three named fixes: repeat (more trials), average (the middle of the spread), and standardize (same tool, same method, steadier setup). Keep the word “error” gentle — it is not a grade or a judgment; it is information. This is a Grade 6 first pass; the statistical treatment of uncertainty comes later. See docs/facilitation.md.

Procedure

  1. Gather (5 min). How long is the object in front of you? Guess once. Now what do you think will happen if you measure it five times — all five numbers the same, or a little different?
  2. Measure five times (15 min). With a partner, measure the same object five times and write each number in its own row on your page. Use the same ruler and the same method each time. What do you notice about the five numbers?
  3. Find the spread and the average (10 min). Line the five numbers up from smallest to largest. How far apart are the biggest and smallest? Now find the average: add them and divide by five. The average is a steadier answer than any single measurement.
  4. Name the sources (10 min). Look at the diagram. Why were your numbers not all identical? Sort your reasons into the three sources: tool limits (the ruler’s marks are coarse), human reading (your eye sat at an angle; your hand was slow), and conditions (the object shifted). For each source, write one way to reduce it — repeat, average, use finer marks, hold things steady.
  5. Close (5 min). Error is not a secret to hide; it is a sign that you are measuring the real world. Naming where it comes from — and repeating, averaging, and standardizing — makes an investigation stronger.

Differentiation

  • Support: Provide a two-source sort (tool | human) and a sentence starter: “the numbers differed because…”; do the averaging with a calculator or counters.
  • Extension: Compare a rough ruler against a finer one, measure both ways, and explain which set has less spread and why precision matters for small objects.

Assessment

  • Formative (observation): Can the learner name at least one source of error and one way to reduce it, and explain why the average is steadier than a single trial?
  • Self-check: The learner asks, “If someone repeated my measurement, would they get about the same answer — and can I say what might change it?”

Home connection

Measure one thing at home five times (a door, a plant, a shelf). Show someone the five numbers and the average, and tell them which source of error you think made them differ.

Resources