The Concept of Length Begins with Direct Comparison, a Concept That Kindergartners Explore

3/9/15 Length

The concept of length begins with direct comparison, a concept that kindergartners explore. Which of these is longer?

Kindergarten students will line up the objects next to each other to determine which is longer. They will directly compare their heights by standing next to each other and describe one student as “taller” or “shorter”.

In first grade, students will use a third object (paper clip, their hands or feet, or cubes) to compare the lengths of two objects. They no longer need to line the two objects together, but can use the number of cubes or clips that they measure in order to compare. This is called indirect comparison.

They express the length of an object as the number of length units, by laying down a unit over and over again. The units must line up end to end (with no spaces) and must not overlap. Early on in the children’s learning about length, they will use non-standard units, such as paper clips or cubes. After exploration with these tools, they will use rulers and measuring tapes with standard units.

A Kindergartener might initially look at these four towers and think that the third one is the tallest, because it peeks out above the last one. As students get older, they will begin to see that the length is determined by the number of units.

For this activity, the students will measure an object with two different units. They will discover that the lengths are different according to the unit. They will also discover that the longer paper clip will result in a smaller number of units, and the shorter paper clip will result in a larger number of units? Why is this true?

After spending time working with non-standard units (paper clips), the students realize that if we use our feet to measure things, different people will wind up with very different lengths. This is a problem! We need standard units!

One challenge that learners face when measuring with standard units (inches, centimeters) is where to start on the ruler. Some students will start at one instead of zero, as zero is not always indicated on the ruler. Lining the ruler up correctly to the object being measured takes quite a bit of practice. Older students will start to measure lengths with fractions of units. Measurement is an excellent context for dealing with fractional parts.

What would be the length of this eraser?

In order for students to explore topics such as area (2D) and volume (3D), they must have a strong understanding of length (1-D).