Measurement is a topic that many students often struggle with largely in part because measurement is experiential. Students must have opportunities to build landmarks about measurements. Reading a ruler, measuring with a ruler, and understanding fractions are all connected and work together very well in helping give fractions a context while offering students an opportunity to build a deeper understanding of the connected topics.
By the way, this activity can be done from primary grade all the way to high school. I have used in from first grade through contextual algebra and geometry in HS.
Tell students we are going to investigate an inch on a ruler. Give each student a piece of plain 8.5″ by 11″ paper. I like to use color and often let students choose the color they prefer. We begin by folding the paper over in half but we only “pinch” halfway down the fold. I model this first for the students. We then write over the fold line and mark it with 1/2. We then take the left side and fold it over to the center line and pinch a fourth of the way down. When unfolded, again write over the 1/4 line and label with 1/4. Discuss the 1/2 line and what quantity that will now also model. Looking at fractions as being the interval or space is one way I have used to help students understand what 2/4 really means and represents.
Repeat the left-sided fold on the right side. I let students discuss how far to pinch and how to name this representation – this interval length.
This activity can be extended to 1/8’s , 1/16’s, etc as appropriate for students readiness. This “inch” also serves as a visual aid as students are working with rulers. An extension can be to use legal paper and model two inches – and with this extension I usually start at a number other than 1 or 0.
