C1 — Connecting Fractions to Division Using the Double Number Line

A big idea for students is the understanding that fractions represent division. A double number line can be used to support students in flexibly thinking about representing both fractions and whole numbers, for example how one foot divided into 2 equal sections equals 1/2, which is also equal to 6/12—6" out of 12". The first few strings in this section are designed to introduce fractions as division and to emerge the double number line model within a measurement context.

Use a ruler and draw a line on your white board that is exactly 1 foot in length. Mark the beginning point 0, and the endpoint with 1 foot. As you work with this double number line keep in mind that the fractions should go above the line and the whole numbers should go underneath the line. There should be no other markings on the number line. Once you begin the string, show one number at a time, and ask "Where should we place this number on the number line and how do you know? After sufficient discussion time and agreement on the placement of the number, use the ruler to check and mark the exact spot so students can see how close they came. Leave it up and move onto the next number in the string. Again ask, "Where should we place this number on the number line and how do you know?"