# Filling the space in length measurement

Session presented at the Michigan Council of Teachers of Mathematics annual conference in Traverse City, MI. In this session we provided a variety of tasks to enhance student learning of length measure. We examined the meaning of length as an attribute and ways of quantifying length. We explored length measurement with a variety of tasks that can push us (and our students) to think about aspects of measurement, such as filling a space without leaving gaps or overlaps.

In this session, we provided stations, each with a different measurement task and set of physical tools. Tasks were created based on tasks designed by Strengthening Tomorrow’s Education in Measurement project, based on articles from Teaching Children Mathematics, or based on observed tasks from methods courses. Participants engaged in two or more stations, tracking the tools and ideas they used, and we finished with a discussion. The hand-outs and a brief description are provided below:

• Station01-Comparing Units – An illustration of three “wrong” strategies for measuring and comparing the lengths of paths is given. Students are asked to explain why or why not they agree with the measurement. Students could also be asked to explain the possible thinking behind each of the three strategies, and why it would or would not “work.”
• Station02-Measuring Paths – Fourth paths are given. Each path is partitioned in different ways. Students are asked to compare lengths of paths, to explain their reasoning, and how they chose measurement units.
• Station03-Measuring Height – Students in pairs compare their heights and indicate who is taller. They use non-standard units of measure to prove they are correct by measuring each other and comparing responses. They should each measure each other with two tools.
• Station04-Measuring Tools – Students choose an object to measure, and use a non-standard unit of measurement to measure the object. They write or draw their strategy and then write or draw their understanding of the meaning of length.
• Station05-Popsicle Comparison – Students measure two objects, each with a longer popsicle stick and shorter popsicle stick. The students then discuss any ideas they have or anything they notice about the measurements.
• Station06-Strange Rulers – In order to make sense of the important features of standard rulers, students use several “strange rulers” to measure a paperclip and a piece of string and make sense of which rulers “work” and which don’t.

Stehr, E.M., Gönülateş, F., & Nimtz, J.L. (2013, August) Filling the space in length measurement. Paper presented at the Michigan Council of Teachers of Mathematics Conference, Traverse City, MI.