Perimeter, Area, Volume, and All That: A Study of Measurement

Measuring Distance as Counting

Young students often struggle to see the connection between math and measurement. A common misconception that my students have is that math is confined to just addition and subtraction.  While my students are measuring, they do not realize that the strategies they are using are mathematical. In first grade measuring can be easily connected to counting. “The connection of arithmetic to geometry through measurement both enlarges the conception of arithmetic, and provides concrete and conceptual tools to help students think about arithmetic.”⁸ In the primary grades' measurement can be explained as counting: how many units of the relevant measure will fit in this object or quantity? This will help my young learners realize that measurement is indeed related to mathematics. The first grade Common Core Math Standards state that “the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.” Students determine the number of same-size length units by counting them. They are counting the distance between the start point and the end point. They can then state the number of units when explaining how long the object is.

Roger Howe states that first grade students should make the connection between counting numbers and measurement numbers. “The most basic and probably the simplest type of measurement is linear measurement: measurement of length or distance.”⁹ Distance can be measured by counting the number of inches from one end to the other end of an object. Kindergarten students spend a majority of the year working on their counting abilities and should be able to count from 1 to 100 by the end of kindergarten.¹⁰ Unfortunately, many students come to my first grade classroom being unable to count to 100. Some students are not even able to count to 20 without experiencing difficulty. When using nonstandard units of measure, the numbers can be contained. Some students need practice with numbers less than ten, other students can count much bigger numbers. I will be able to differentiate tasks based on the needs of my students. Eventually, when we use rulers all students will get repeated practice with counting up to twelve since there are twelve inches in a foot (the length of a ruler). Overall, measurement can greatly help my students become better at counting by implementing new strategies for them to use. 

Using a ruler is not the expectation in first grade but will add relevance for my first grade students. “This kind of work with lengths can strengthen the learning of arithmetic by reinforcing symbolic work and work with unstructured collections of objects. Equally important, it should get children used to the idea that measurement is a natural domain for application of number ideas”¹¹ By using a manipulative such as a ruler, students will begin to see the connection between counting and measurement. They will need repeated practice with using a ruler. However, over time they will begin to see that the length of the object is the number of inches that they count. Hopefully, they will begin to realize that they will not need to count all the inches as they get fluent in using the ruler. Beyond this connection, they will see that measurement is relevant in their lives, as we use inches to measure in real life. Most importantly for my first graders, they will see that the counting sequence of whole numbers is critically important for the real life application of measuring in standard units.