Unit 4, Lesson 13
Measurement Error
Grade 7
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Learn how to use instructional routines to facilitate problem-based learning!
To Copy (from Blackline Masters)
Measurement to the Nearest Cutouts
In this Warm-up, students use two rulers that have different levels of precision to measure the same lines. Students notice how differences in recorded measurements can result from the level of precision of the measuring device. This prepares students for expressing measurement error as a percentage of the correct amount.
Students will need to use the rulers again later in this lesson, so make sure they keep track of them.
Arrange students in groups of 2. Distribute one set of 2 pre-cut rulers to each group.
Give students 3–5 minutes of partner work time, then follow with a whole-class discussion.
Your teacher will give you two rulers and three line segments labeled A, B, and C.
Use the centimeter ruler to measure each line segment to the nearest centimeter. Record these lengths in the first column of the table.
Use the millimeter ruler to measure each line segment to the nearest tenth of a centimeter. Record these lengths in the second column of the table.
| line segment | length (cm) as measured with the first ruler |
length (cm) as measured with the second ruler |
|---|---|---|
| A | ||
| B | ||
| C |
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Students might not line up the edge of the ruler with the end of the line. Remind students that we need to line up the 0 mark on the ruler (in this case, the edge of the ruler) with the beginning edge of the line being measured.
Ask students to describe what they notice about the lengths they got when they used the two different measuring devices. Explain to students that one source of measurement error can be the precision level of their measuring device. Ask students, “Assuming the measurements to the nearest tenth of a centimeter are exact, how much error was in each measurement when you used the centimeter ruler?” (7 cm was 0.3 cm too long, 0.1 cm too long, and 0.3 cm too short, respectively.)
MLR7: Compare and Connect
Learn how to use instructional routines to facilitate problem-based learning!
None
In this activity, students determine the amount of error in a measurement and express the error as a percentage of the correct value. They brainstorm possible sources of error and discuss how real-world limitations on humans using measuring devices can introduce measurement errors. As students interpret these results, they consider sources for error and improvement in a mathematical model (MP4).
The actual length is given in yards, while the measured length is given in feet and inches. Students must choose which unit to use and convert the other measurement before they can calculate the measurement error. Regardless of which unit they use, the percentage that the error is of the correct amount should be the same. Monitor for students who choose to use different units for their calculations: yards, feet, or inches.
Also monitor for mistakes students may make in their solution process, such as:
The key focus is distinguishing between different solution processes that give the same answer versus solution processes that give an incorrect answer.
Keep students in the same groups. Tell students that a soccer field is 120 yards long, and ask them how they can use a 30-foot-long tape measure to measure that length. (Note the use of two different units of measure, yards and feet.) If not mentioned by students, suggest measuring off 30 feet, making a mark, measuring off another 30 feet, and so on. Ask the class if they would all get exactly the same answer by this method.
Give the students 3–4 minutes of quiet work time to calculate the amount of the error and the percent error, followed by time for partner discussion. Then hold a whole-class discussion.
Select work from students with different strategies, such as those described in the Activity Narrative, to share later. Look for a mixture of correct and incorrect solutions.
A soccer field is 120 yards long. Han uses a 30-foot-long tape measure to measure the length of the field and gets a measurement of 376 feet 6 inches.
The goal of this discussion is to contrast different methods that get the correct answer with methods that get an incorrect answer for the percentage that the error is of the correct amount. Display 2–3 approaches from previously selected students for all to see. If time allows, invite students to briefly describe their approach. Use Compare and Connect to help students compare, contrast, and connect the different approaches. Here are some questions for discussion:
The key takeaway is that it doesn't matter which unit students chose. The percentage of the error should be the same as long as their units match on both the measured length and the actual length (and as long as students divided by the actual length, not the measured length).
Explain to students that measurement error is the positive difference between the measurement and the actual value. It is often expressed as a percentage of the actual value. We can use words to describe whether the measurement is greater than or less than the actual value. In this case, we might say that the measured length is more than the actual length with an error of about 4.6%.
When we use a ruler or measuring tape to measure a length, we can get a measurement that is different from the actual length. This could be because we positioned the ruler incorrectly, or it could be because the ruler is not very precise. There is always at least a small difference between the actual length and a measured length, even if it is a microscopic difference!
Here are two rulers with different markings.
Two rulers, of equal length, each measuring 19 centimeters long. The top ruler has centimeter markings only. The bottom ruler has centimeter markings with 10 milimeter markings in between each centimeter marking.
The second ruler is marked in millimeters, so it is easier to get a measurement to the nearest tenth of a centimeter with this ruler than with the first. For example, a line that is actually 6.2 cm long might be measured to be 6 cm long by the first ruler because we measure to the nearest centimeter.
The measurement error is the positive difference between the measurement and the actual value. Measurement error is often expressed as a percentage of the actual value. We always use a positive number to express measurement error and, when appropriate, use words to describe whether the measurement is greater than or less than the actual value.
For example, if we get 6 cm when we measure a line that is actually 6.2 cm long, then the measurement error is 0.2 cm, or about 3.2%, because
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If students fail to see the need for converting units of measure, ask, “How many feet are in 120 yards? How many inches?”
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