Overview

While measurement is often taught as a set of “skills” to be learned, there are set of foundational concepts that underlie ability to measure. This part of the session introduces these key concepts in the context of length measurement and a task (The Broken Ruler Task) that can be used to see students’ use and understanding of them. Videos of students working on this task are used to launch discussions about students’ thinking and about notetaking as a tool that can support interpreting students’ engagement in, and reasoning about, geometric measurement.

Key Points

• Foundational concepts of measurement include: understanding of the attribute, conservation, transitivity, equal partitioning, iteration of a standard unit, accumulation, origin, and relation between measurement and number. For example:

All measurement depends upon identifying what attribute needs to be measured.

The ability to measure an attribute of an object depends on the conservation of the attribute—even if the object being measured is moved or rearranged in some way.

Length is a characteristic of an object and can be measured by quantifying the distance between the endpoints of an object.

• Measuring length consists of two aspects:
  • Identifying a unit of measure and subdividing (mentally and physically) the object by that unit, and
  • Placing that unit end to end (iterating) alongside the object being measured.