Overview

Understanding the precision and accuracy of measurements is a crucial skill scientists must develop to do their work. All measurements involve some degree of error. Knowing how to assess and work with error is an essential part of making sense of scientific observations. What is accuracy? What is precision? How do we make our measurements more accurate or precise? Why would two measurements of the same object yield different values? How can error in measurement be reduced? Students investigate these questions through a series of measurement tasks involving heights, mass, and different scales of measurement.

Objectives

• To develop skills in measuring;
• To become familiar with properties of materials that can be measured;
• To develop an understanding of accuracy, precision, and measurement error; and
• To develop an understanding of how measurement error changes with the instrument used to make measurements.

Process Skills

• Observing,
• Measuring, and
• Communicating.

Activity Duration

60 minutes

Background

If you ask 30 people to measure the width of a room, it is likely you’ll get many different answers. Variation in measurement is always present and is a part of doing science. Why does this variation in measurement occur? How much measurement variation is tolerable? These questions are considered as students make measurements and compare their measurements with those of other students. It is important for students to recognize how errors in measurement occur and to be able to describe how to minimize both random and systematic errors. Ultimately there will always be some error or level of uncertainty. Students must also learn this is a fundamental part of science. Nothing is known with quantitative exactness. A level of uncertainty in measurement is usually referred to as the “error.” A sophisticated understanding of the occurrence of random errors develops after students have many opportunities to make repeated measurements and see the patterns of data that emerge. Encouraging students to check their own measurements, as well as to compare them with those made by others, is a fundamental part of this developmental process.

Materials

Each group will need

• 1 thermometer (inexpensive alcohol thermometers work best),
• metric measuring tape, and
• scale for measuring mass.

Class materials needed

• shoe box,
• egg (hard-boiled),
• metric ruler,
• 2 meter sticks,
• centimeter ruler,
• yarn, and
• meter tape.

Engage

Pass out one thermometer to every two students. Ask the students to record the temperature of the room. Then record the temperatures from the different groups on the board in a table. Look across the data and ask the students to explain why there is variation in the temperature measurements. Make note of the different reasons they provide. Possible explanations include readings to the nearest half-degree versus the nearest whole degree, thermometers with various calibrations, inaccurate thermometers, variations in temperature throughout the room, thermometers being under a vent or in the sunlight, and readings of thermometers from different angles. Explore how the different thermometers give different readings by placing the thermometers side by side on a table and having the students view them as a group. Ask, “Why do different thermometers show different temperatures?” Explain in this lesson they will investigate the different sources of errors in measurement and the different types of errors that occur. In the case of the thermometers, the differences are due in part to their manufacturing, which results in variable readings. However, other human sources of error are inherent in the act of measurement.

Explore

Divide the class into groups of two students each. Explain the focus is to make accurate measurements for the following: (a) a student’s height in meters; (b) a shoe box length measured in centimeters; (c) a shoe box length measured in millimeters; (d) a shoe box length measured in meters; and (e) the mass of an egg in grams. Each measurement should be recorded on a Student Data Sheet.

A. How Tall Am I? Select a student volunteer who is willing to have his or her height measured. The first task is to measure the student’s height in centimeters. Provide Group 1 with a meter stick, Group 2 with meter tape, Group 3 with a ruler marked in inches and centimeters, Group 4 with yarn and a meter stick taped down to a table, and Group 5 with a small centimeter ruler (approximately 25 cm). Remind them to convert units to centimeters if they use a different unit for their initial measurement.

After the students make measurements, have the groups report their measurements to the class. Record the different measurements on the board on a chart (see Figure 1). Note the variation in students’ measurements. Discuss possible sources of error. Students should note some of the differences in the answers are the result of different measurement tools. Ask, “Which tool is the most accurate? Why?” Discuss the ways students made the measurements and how they could be more consistent in their measurement strategy.

Extend the discussion by taking the mean of the different values and asking the students if the mean is more likely to be accurate than an individual measurement.

B, C, and D. Shoe Box Measurements. Each group should measure the same shoe box length (long side) in centimeters, millimeters, and meters, using either a ruler or metric tape. Record the measurements on the Student Data Sheet. Ask, “Which unit gave the most consistent measurements across the different groups—the centimeter, millimeter, or meter units? Which unit of measurement gave the most precise measurement? Why would the smaller unit of measurement be more precise?”

E. Egg Mass. Each group should measure the egg in grams using a scale. (Note: Use hard-boiled eggs to avoid possible breakage and mess.) Why did different groups get different measurements? What are the possible sources of errors students could make when measuring with a scale? How could they increase both the precision and the accuracy of the measurement?