3 - Measurement (Length and Time)

The measurement foci of this unit are length and time.

Work with length revolves around measuring indirectly with non-standard units (transitivity¹) and understanding the concept of measuring with “a unit” (iteration²). Standard units of linear measure (e.g., inch, centimeter) are not mentioned in the Common Core standards and are not part of this unit.

The first grade Common Core standard for time is limited to reading and writing time as it is displayed on digital and analog clocks, to the hour and half-hour. Because understanding the duration of time is an important concept that is more meaningful to children, but only developed over time, this concept is also addressed in this unit.

¹transitivity principle: measuring indirectly by comparing the length of two concrete objects by using a different (third) concrete object as a measuring tool. For example: To determine whether tables in two different rooms are the same length, use a piece of rope (R) to determine the length of Table A, then use the same length of rope to measure the length of Table B. If T^A = R and T^B = R, then T^A = T^B

²unit iteration: using multiple copies of one object (the unit) to measure a larger object. For example, using one linking cube to measure the width of a desk by moving it along the path (width) and counting the units each time the linking cube is moved. An example using a standard measurement tool would be using one ruler (the unit) to measure the width of a room.

NOTE:

Limiting measuring to those objects whose span is “a whole number of length units with no gaps or overlaps” (as stated in Standard 2 below) may be counter-productive. If students are freely choosing objects in the classroom to measure, these objects are not all going to have a span that is a whole number of units. Letting students think that objects will always span a whole number of units encourages them to create gaps or overlaps in their measuring in order to come out with a whole number of units. Since measurements are always approximations, a concept we want students to understand, they need to learn that sometimes a measurement is “a little more” or “a little less” than a whole number of units. They need to learn to use those terms until they learn more exact standard units. For these reasons, this unit and the corresponding Highlight Lesson will intentionally include contexts that extend beyond those spanned by a whole number of length units.

1. How do we measure the length of an object?
2. Why are measurement tools used in finding length?
3. How do we use a clock to measure time?
4. What is the relationship between minutes and hours?
5. What do we need to be thinking about to measure something accurately?
6. How does the knowledge of measuring length and time support problem solving in the real world?