This is the first of three lessons where students encounter the idea of percent error. Unlike situations involving percent increase and percent decrease, where there is an initial amount and a final amount, situations expressed with percent error involve a measured amount and a correct amount. The measurement error is the positive difference between the measured amount and the correct amount, and the percent error is the measurement error expressed as a percentage of the correct amount. In this first lesson students see how measurement error can arise in two different ways: from the level of precision in the measurement device, and from human error. In this lesson students encounter one of the important aspects of mathematical modeling, namely that mathematical representations are usually an approximation of the real situation (MP4).
- Compare and contrast (orally) multiple measurements of the same length that result from using rulers with different levels of precision.
- Describe (orally) possible sources of “measurement error” when measuring lengths.
- Generalize a process for calculating measurement error and expressing it as a percentage of the actual length.
Let’s use percentages to describe how accurately we can measure.
Print the Measuring to the Nearest blackline master. Prepare 1 copy for every 2 students. The blackline master contains two versions of a centimeter ruler that students will cut out (or you may cut out ahead of time) and use to measure things, so card stock would be preferable if available. In the instructions, students are told to cut out the rulers they will use from the blackline master, but to save class time you may want to do this for them ahead of time. These same rulers are also used in the Measuring Your Classroom activity in this lesson, so they should be used carefully during the warm-up.
Measure the height or length of several objects in your classroom to the nearest tenth of a centimeter. If possible, have at least one object per student in the class so that students don’t have to wait too long to measure things. Most of the items should be greater than 20 cm in length, but some can be less than or equal to 20 cm in length. Examples of such objects might be the width of the door, the length of the stick that holds a flag, the length of an eraser, or a side of a table or desk top.
- I can represent measurement error as a percentage of the correct measurement.
- I understand that all measurements include some error.
Measurement error is the positive difference between a measured amount and the actual amount.
For example, Diego measures a line segment and gets 5.3 cm. The actual length of the segment is really 5.32 cm. The measurement error is 0.02 cm, because \(5.32-5.3=0.02\).